%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP299-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3J8u6MingH true
% Computer : n024.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 04:36:11 PM UTC 2025
% Result : Unsatisfiable 0.54s 0.88s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP299-1 : TPTP v9.2.0. Released v2.5.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3J8u6MingH true
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 14:20:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.52/0.61 % Total configuration time : 435
% 0.52/0.61 % Estimated wc time : 1092
% 0.52/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.54/0.88 % Solved by fo/fo7.sh.
% 0.54/0.88 % done 171 iterations in 0.106s
% 0.54/0.88 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.54/0.88 % SZS output start Refutation
% 0.54/0.88 thf(sk_c1_type, type, sk_c1: $i).
% 0.54/0.88 thf(sk_c5_type, type, sk_c5: $i).
% 0.54/0.88 thf(sk_c4_type, type, sk_c4: $i).
% 0.54/0.88 thf(sk_c3_type, type, sk_c3: $i).
% 0.54/0.88 thf(identity_type, type, identity: $i).
% 0.54/0.88 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.54/0.88 thf(sk_c6_type, type, sk_c6: $i).
% 0.54/0.88 thf(inverse_type, type, inverse: $i > $i).
% 0.54/0.88 thf(sk_c2_type, type, sk_c2: $i).
% 0.54/0.88 thf(sk_c7_type, type, sk_c7: $i).
% 0.54/0.88 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(prove_this_21, conjecture,
% 0.54/0.88 (~( ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c5 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 0.54/0.88 thf(zf_stmt_0, negated_conjecture,
% 0.54/0.88 (( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c5 @ sk_c7 ) = ( sk_c6 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 0.54/0.88 thf(zip_derived_cl23, plain,
% 0.54/0.88 ((((multiply @ sk_c2 @ sk_c6) = (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c5 @ sk_c7) = (sk_c6)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.54/0.88 thf(prove_this_16, conjecture,
% 0.54/0.88 (~( ( ( multiply @ sk_c3 @ sk_c4 ) = ( sk_c6 ) ) |
% 0.54/0.88 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.88 thf(zf_stmt_1, negated_conjecture,
% 0.54/0.88 (( ( multiply @ sk_c3 @ sk_c4 ) = ( sk_c6 ) ) |
% 0.54/0.88 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 0.54/0.88 thf(zip_derived_cl18, plain,
% 0.54/0.88 ((((multiply @ sk_c3 @ sk_c4) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(zip_derived_cl38, plain,
% 0.54/0.88 ((((multiply @ sk_c7 @ sk_c1) = (identity))
% 0.54/0.88 | ((multiply @ sk_c3 @ sk_c4) = (sk_c6)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(associativity, axiom,
% 0.54/0.88 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 0.54/0.88 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 0.54/0.88 thf(zip_derived_cl2, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.88 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.88 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.88 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.88 thf(zip_derived_cl52, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((multiply @ identity @ X0)
% 0.54/0.88 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 0.54/0.88 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 0.54/0.88 thf(zip_derived_cl0, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl85, plain,
% 0.54/0.88 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.54/0.88 | ((multiply @ sk_c3 @ sk_c4) = (sk_c6)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl68])).
% 0.54/0.88 thf(prove_this_10, conjecture,
% 0.54/0.88 (~( ( ( multiply @ sk_c3 @ sk_c4 ) = ( sk_c6 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 0.54/0.88 thf(zf_stmt_2, negated_conjecture,
% 0.54/0.88 (( ( multiply @ sk_c3 @ sk_c4 ) = ( sk_c6 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 0.54/0.88 thf(zip_derived_cl12, plain,
% 0.54/0.88 ((((multiply @ sk_c3 @ sk_c4) = (sk_c6))
% 0.54/0.88 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.54/0.88 thf(zip_derived_cl211, plain,
% 0.54/0.88 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 0.54/0.88 = (sk_c6))
% 0.54/0.88 | ((multiply @ sk_c3 @ sk_c4) = (sk_c6))
% 0.54/0.88 | ((multiply @ sk_c3 @ sk_c4) = (sk_c6)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl85, zip_derived_cl12])).
% 0.54/0.88 thf(zip_derived_cl2, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.88 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.88 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.88 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.88 thf(zip_derived_cl0, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(zip_derived_cl226, plain,
% 0.54/0.88 ((((identity) = (sk_c6))
% 0.54/0.88 | ((multiply @ sk_c3 @ sk_c4) = (sk_c6))
% 0.54/0.88 | ((multiply @ sk_c3 @ sk_c4) = (sk_c6)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl211, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.88 zip_derived_cl1])).
% 0.54/0.88 thf(zip_derived_cl227, plain,
% 0.54/0.88 ((((multiply @ sk_c3 @ sk_c4) = (sk_c6)) | ((identity) = (sk_c6)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl226])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl249, plain,
% 0.54/0.88 ((((sk_c4) = (multiply @ (inverse @ sk_c3) @ sk_c6))
% 0.54/0.88 | ((identity) = (sk_c6)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl227, zip_derived_cl68])).
% 0.54/0.88 thf(prove_this_17, conjecture,
% 0.54/0.88 (~( ( ( inverse @ sk_c3 ) = ( sk_c4 ) ) |
% 0.54/0.88 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.88 thf(zf_stmt_3, negated_conjecture,
% 0.54/0.88 (( ( inverse @ sk_c3 ) = ( sk_c4 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 0.54/0.88 thf(zip_derived_cl19, plain,
% 0.54/0.88 ((((inverse @ sk_c3) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(zip_derived_cl33, plain,
% 0.54/0.88 ((((multiply @ sk_c7 @ sk_c1) = (identity))
% 0.54/0.88 | ((inverse @ sk_c3) = (sk_c4)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl1])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl82, plain,
% 0.54/0.88 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.54/0.88 | ((inverse @ sk_c3) = (sk_c4)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl68])).
% 0.54/0.88 thf(prove_this_11, conjecture,
% 0.54/0.88 (~( ( ( inverse @ sk_c3 ) = ( sk_c4 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 0.54/0.88 thf(zf_stmt_4, negated_conjecture,
% 0.54/0.88 (( ( inverse @ sk_c3 ) = ( sk_c4 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 0.54/0.88 thf(zip_derived_cl13, plain,
% 0.54/0.88 ((((inverse @ sk_c3) = (sk_c4)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.54/0.88 thf(zip_derived_cl111, plain,
% 0.54/0.88 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 0.54/0.88 = (sk_c6))
% 0.54/0.88 | ((inverse @ sk_c3) = (sk_c4))
% 0.54/0.88 | ((inverse @ sk_c3) = (sk_c4)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl82, zip_derived_cl13])).
% 0.54/0.88 thf(zip_derived_cl2, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.88 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.88 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.88 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.88 thf(zip_derived_cl0, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(zip_derived_cl126, plain,
% 0.54/0.88 ((((identity) = (sk_c6))
% 0.54/0.88 | ((inverse @ sk_c3) = (sk_c4))
% 0.54/0.88 | ((inverse @ sk_c3) = (sk_c4)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl111, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.88 zip_derived_cl1])).
% 0.54/0.88 thf(zip_derived_cl127, plain,
% 0.54/0.88 ((((inverse @ sk_c3) = (sk_c4)) | ((identity) = (sk_c6)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl126])).
% 0.54/0.88 thf(zip_derived_cl259, plain,
% 0.54/0.88 ((((inverse @ sk_c3) = (multiply @ (inverse @ sk_c3) @ sk_c6))
% 0.54/0.88 | ((identity) = (sk_c6))
% 0.54/0.88 | ((identity) = (sk_c6)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl249, zip_derived_cl127])).
% 0.54/0.88 thf(zip_derived_cl261, plain,
% 0.54/0.88 ((((identity) = (sk_c6))
% 0.54/0.88 | ((inverse @ sk_c3) = (multiply @ (inverse @ sk_c3) @ sk_c6)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl259])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl292, plain,
% 0.54/0.88 ((((sk_c6)
% 0.54/0.88 = (multiply @ (inverse @ (inverse @ sk_c3)) @ (inverse @ sk_c3)))
% 0.54/0.88 | ((identity) = (sk_c6)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl261, zip_derived_cl68])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(zip_derived_cl294, plain,
% 0.54/0.88 ((((sk_c6) = (identity)) | ((identity) = (sk_c6)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl292, zip_derived_cl1])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl79, plain,
% 0.54/0.88 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl68])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl76, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl68, zip_derived_cl68])).
% 0.54/0.88 thf(zip_derived_cl469, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl76])).
% 0.54/0.88 thf(prove_this_13, conjecture,
% 0.54/0.88 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 0.54/0.88 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.88 thf(zf_stmt_5, negated_conjecture,
% 0.54/0.88 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 0.54/0.88 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 0.54/0.88 thf(zip_derived_cl15, plain,
% 0.54/0.88 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl0, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.88 thf(zip_derived_cl307, plain,
% 0.54/0.88 ((((sk_c7) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl15, zip_derived_cl295, zip_derived_cl0])).
% 0.54/0.88 thf(prove_this_7, conjecture,
% 0.54/0.88 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 0.54/0.88 thf(zf_stmt_6, negated_conjecture,
% 0.54/0.88 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 0.54/0.88 thf(zip_derived_cl9, plain,
% 0.54/0.88 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 0.54/0.88 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl0, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl302, plain,
% 0.54/0.88 ((((sk_c7) = (sk_c5)) | ((multiply @ sk_c1 @ sk_c7) = (identity)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl9, zip_derived_cl295, zip_derived_cl0,
% 0.54/0.88 zip_derived_cl295])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl353, plain,
% 0.54/0.88 ((((sk_c7) = (multiply @ (inverse @ sk_c1) @ identity))
% 0.54/0.88 | ((sk_c7) = (sk_c5)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl302, zip_derived_cl68])).
% 0.54/0.88 thf(zip_derived_cl416, plain,
% 0.54/0.88 ((((sk_c7) = (multiply @ sk_c7 @ identity))
% 0.54/0.88 | ((sk_c7) = (sk_c5))
% 0.54/0.88 | ((sk_c7) = (sk_c5)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl307, zip_derived_cl353])).
% 0.54/0.88 thf(zip_derived_cl423, plain,
% 0.54/0.88 ((((sk_c7) = (sk_c5)) | ((sk_c7) = (multiply @ sk_c7 @ identity)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl416])).
% 0.54/0.88 thf(prove_this_1, conjecture,
% 0.54/0.88 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c5 ) ) ))).
% 0.54/0.88 thf(zf_stmt_7, negated_conjecture,
% 0.54/0.88 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c7 @ sk_c6 ) = ( sk_c5 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 0.54/0.88 thf(zip_derived_cl3, plain,
% 0.54/0.88 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c6) = (sk_c5)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_7])).
% 0.54/0.88 thf(zip_derived_cl30, plain,
% 0.54/0.88 ((((multiply @ sk_c6 @ sk_c7) != (multiply @ sk_c7 @ sk_c6))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c6) = (sk_c5)))),
% 0.54/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl3])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl0, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl314, plain,
% 0.54/0.88 ((((sk_c7) != (multiply @ sk_c7 @ identity))
% 0.54/0.88 | ((multiply @ sk_c7 @ identity) = (sk_c5)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl30, zip_derived_cl295, zip_derived_cl0,
% 0.54/0.88 zip_derived_cl295, zip_derived_cl295])).
% 0.54/0.88 thf(zip_derived_cl315, plain,
% 0.54/0.88 ((((sk_c7) != (multiply @ sk_c7 @ identity)) | ((sk_c7) = (sk_c5)))),
% 0.54/0.88 inference('local_rewriting', [status(thm)], [zip_derived_cl314])).
% 0.54/0.88 thf(zip_derived_cl444, plain, (((sk_c7) = (sk_c5))),
% 0.54/0.88 inference('clc', [status(thm)], [zip_derived_cl423, zip_derived_cl315])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl750, plain,
% 0.54/0.88 ((((sk_c2) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c7) = (identity)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl23, zip_derived_cl295, zip_derived_cl469,
% 0.54/0.88 zip_derived_cl444, zip_derived_cl295])).
% 0.54/0.88 thf(prove_this_20, conjecture,
% 0.54/0.88 (~( ( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c5 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 0.54/0.88 thf(zf_stmt_8, negated_conjecture,
% 0.54/0.88 (( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c5 @ sk_c7 ) = ( sk_c6 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 0.54/0.88 thf(zip_derived_cl22, plain,
% 0.54/0.88 ((((inverse @ sk_c2) = (sk_c7)) | ((multiply @ sk_c5 @ sk_c7) = (sk_c6)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_8])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl312, plain,
% 0.54/0.88 ((((inverse @ sk_c2) = (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c5 @ sk_c7) = (identity)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl295])).
% 0.54/0.88 thf(zip_derived_cl444, plain, (((sk_c7) = (sk_c5))),
% 0.54/0.88 inference('clc', [status(thm)], [zip_derived_cl423, zip_derived_cl315])).
% 0.54/0.88 thf(zip_derived_cl447, plain,
% 0.54/0.88 ((((inverse @ sk_c2) = (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) = (identity)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl312, zip_derived_cl444])).
% 0.54/0.88 thf(zip_derived_cl751, plain,
% 0.54/0.88 ((((inverse @ sk_c7) = (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) = (identity))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) = (identity)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl750, zip_derived_cl447])).
% 0.54/0.88 thf(zip_derived_cl753, plain,
% 0.54/0.88 ((((multiply @ sk_c7 @ sk_c7) = (identity))
% 0.54/0.88 | ((inverse @ sk_c7) = (sk_c7)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl751])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(zip_derived_cl755, plain,
% 0.54/0.88 ((((multiply @ sk_c7 @ sk_c7) = (identity))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) = (identity)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl753, zip_derived_cl1])).
% 0.54/0.88 thf(zip_derived_cl760, plain, (((multiply @ sk_c7 @ sk_c7) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl755])).
% 0.54/0.88 thf(zip_derived_cl68, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 0.54/0.88 thf(zip_derived_cl765, plain,
% 0.54/0.88 (((sk_c7) = (multiply @ (inverse @ sk_c7) @ identity))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl760, zip_derived_cl68])).
% 0.54/0.88 thf(zip_derived_cl469, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl76])).
% 0.54/0.88 thf(zip_derived_cl769, plain, (((sk_c7) = (inverse @ sk_c7))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl765, zip_derived_cl469])).
% 0.54/0.88 thf(prove_this_25, conjecture,
% 0.54/0.88 (~( ( ( multiply @ X4 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.88 ( ( inverse @ X3 ) != ( X4 ) ) |
% 0.54/0.88 ( ( multiply @ X3 @ X4 ) != ( sk_c6 ) ) |
% 0.54/0.88 ( ( multiply @ X1 @ sk_c6 ) != ( sk_c7 ) ) |
% 0.54/0.88 ( ( inverse @ X1 ) != ( sk_c7 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c5 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.88 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 0.54/0.88 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c5 ) ) ))).
% 0.54/0.88 thf(zf_stmt_9, negated_conjecture,
% 0.54/0.88 (( ( multiply @ X4 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.88 ( ( inverse @ X3 ) != ( X4 ) ) |
% 0.54/0.88 ( ( multiply @ X3 @ X4 ) != ( sk_c6 ) ) |
% 0.54/0.88 ( ( multiply @ X1 @ sk_c6 ) != ( sk_c7 ) ) |
% 0.54/0.88 ( ( inverse @ X1 ) != ( sk_c7 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c5 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.88 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 0.54/0.88 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.88 ( ( multiply @ sk_c7 @ sk_c6 ) != ( sk_c5 ) )),
% 0.54/0.88 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 0.54/0.88 thf(zip_derived_cl27, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (sk_c6))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (sk_c6))
% 0.54/0.88 | ((multiply @ X2 @ sk_c6) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c6 @ sk_c7) != (sk_c5))
% 0.54/0.88 | ((multiply @ sk_c5 @ sk_c7) != (sk_c6))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (sk_c6))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c6) != (sk_c5)))),
% 0.54/0.88 inference('cnf', [status(esa)], [zf_stmt_9])).
% 0.54/0.88 thf(zip_derived_cl28, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (sk_c6))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (sk_c6))
% 0.54/0.88 | ((multiply @ X2 @ sk_c6) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c6 @ sk_c7) != (sk_c5))
% 0.54/0.88 | ((multiply @ (multiply @ sk_c7 @ sk_c6) @ sk_c7) != (sk_c6))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (sk_c6))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c6) != (sk_c5)))),
% 0.54/0.88 inference('local_rewriting', [status(thm)], [zip_derived_cl27])).
% 0.54/0.88 thf(zip_derived_cl2, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.88 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.88 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.88 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.88 thf(zip_derived_cl48, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (sk_c6))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (sk_c6))
% 0.54/0.88 | ((multiply @ X2 @ sk_c6) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c6 @ sk_c7) != (sk_c5))
% 0.54/0.88 | ((multiply @ sk_c7 @ (multiply @ sk_c6 @ sk_c7)) != (sk_c6))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (sk_c6))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c6) != (sk_c5)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl2])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl0, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl0, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl295, plain, (((sk_c6) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.54/0.88 thf(zip_derived_cl319, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((multiply @ X2 @ identity) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((sk_c7) != (sk_c5))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (identity))
% 0.54/0.88 | ((multiply @ sk_c7 @ identity) != (sk_c5)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl48, zip_derived_cl295, zip_derived_cl295,
% 0.54/0.88 zip_derived_cl295, zip_derived_cl295, zip_derived_cl0,
% 0.54/0.88 zip_derived_cl295, zip_derived_cl0, zip_derived_cl295,
% 0.54/0.88 zip_derived_cl295, zip_derived_cl295])).
% 0.54/0.88 thf(zip_derived_cl444, plain, (((sk_c7) = (sk_c5))),
% 0.54/0.88 inference('clc', [status(thm)], [zip_derived_cl423, zip_derived_cl315])).
% 0.54/0.88 thf(zip_derived_cl444, plain, (((sk_c7) = (sk_c5))),
% 0.54/0.88 inference('clc', [status(thm)], [zip_derived_cl423, zip_derived_cl315])).
% 0.54/0.88 thf(zip_derived_cl449, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((multiply @ X2 @ identity) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((sk_c7) != (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (identity))
% 0.54/0.88 | ((multiply @ sk_c7 @ identity) != (sk_c7)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl319, zip_derived_cl444, zip_derived_cl444])).
% 0.54/0.88 thf(zip_derived_cl450, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ sk_c7 @ identity) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ X2 @ identity) != (sk_c7))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X0 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl449])).
% 0.54/0.88 thf(zip_derived_cl469, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl76])).
% 0.54/0.88 thf(zip_derived_cl469, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl76])).
% 0.54/0.88 thf(zip_derived_cl483, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((sk_c7) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X0 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('demod', [status(thm)],
% 0.54/0.88 [zip_derived_cl450, zip_derived_cl469, zip_derived_cl469])).
% 0.54/0.88 thf(zip_derived_cl484, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((X2) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl483])).
% 0.54/0.88 thf(zip_derived_cl760, plain, (((multiply @ sk_c7 @ sk_c7) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl755])).
% 0.54/0.88 thf(zip_derived_cl762, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((X2) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((identity) != (identity))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((multiply @ X3 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl484, zip_derived_cl760])).
% 0.54/0.88 thf(zip_derived_cl763, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.88 (((multiply @ X3 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X3) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X0 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl762])).
% 0.54/0.88 thf(zip_derived_cl816, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((inverse @ sk_c7) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ X2 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('eq_res', [status(thm)], [zip_derived_cl763])).
% 0.54/0.88 thf(zip_derived_cl769, plain, (((sk_c7) = (inverse @ sk_c7))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl765, zip_derived_cl469])).
% 0.54/0.88 thf(zip_derived_cl817, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.88 (((multiply @ X0 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((sk_c7) != (sk_c7))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ X2 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl816, zip_derived_cl769])).
% 0.54/0.88 thf(zip_derived_cl818, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.88 (((multiply @ X2 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X2) != (sk_c7))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X0 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl817])).
% 0.54/0.88 thf(zip_derived_cl820, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 (((sk_c7) != (sk_c7))
% 0.54/0.88 | ((multiply @ X0 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((multiply @ sk_c7 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('sup-', [status(thm)], [zip_derived_cl769, zip_derived_cl818])).
% 0.54/0.88 thf(zip_derived_cl760, plain, (((multiply @ sk_c7 @ sk_c7) = (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl755])).
% 0.54/0.88 thf(zip_derived_cl826, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 (((sk_c7) != (sk_c7))
% 0.54/0.88 | ((multiply @ X0 @ sk_c7) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((identity) != (identity)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl820, zip_derived_cl760])).
% 0.54/0.88 thf(zip_derived_cl827, plain,
% 0.54/0.88 (![X0 : $i, X1 : $i]:
% 0.54/0.88 (((multiply @ X1 @ X0) != (identity))
% 0.54/0.88 | ((inverse @ X1) != (X0))
% 0.54/0.88 | ((multiply @ X0 @ sk_c7) != (identity)))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl826])).
% 0.54/0.88 thf(zip_derived_cl841, plain,
% 0.54/0.88 (![X0 : $i]:
% 0.54/0.88 (((multiply @ (inverse @ X0) @ sk_c7) != (identity))
% 0.54/0.88 | ((multiply @ X0 @ (inverse @ X0)) != (identity)))),
% 0.54/0.88 inference('eq_res', [status(thm)], [zip_derived_cl827])).
% 0.54/0.88 thf(zip_derived_cl469, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl76])).
% 0.54/0.88 thf(zip_derived_cl79, plain,
% 0.54/0.88 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl68])).
% 0.54/0.88 thf(zip_derived_cl490, plain,
% 0.54/0.88 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl469, zip_derived_cl79])).
% 0.54/0.88 thf(zip_derived_cl1, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.88 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.88 thf(zip_derived_cl496, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.54/0.88 inference('sup+', [status(thm)], [zip_derived_cl490, zip_derived_cl1])).
% 0.54/0.88 thf(zip_derived_cl842, plain,
% 0.54/0.88 (![X0 : $i]:
% 0.54/0.88 (((multiply @ (inverse @ X0) @ sk_c7) != (identity))
% 0.54/0.88 | ((identity) != (identity)))),
% 0.54/0.88 inference('demod', [status(thm)], [zip_derived_cl841, zip_derived_cl496])).
% 0.54/0.88 thf(zip_derived_cl843, plain,
% 0.54/0.88 (![X0 : $i]: ((multiply @ (inverse @ X0) @ sk_c7) != (identity))),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl842])).
% 0.54/0.88 thf(zip_derived_cl846, plain, (((identity) != (identity))),
% 0.54/0.88 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl843])).
% 0.54/0.88 thf(zip_derived_cl855, plain, ($false),
% 0.54/0.88 inference('simplify', [status(thm)], [zip_derived_cl846])).
% 0.54/0.88
% 0.54/0.88 % SZS output end Refutation
% 0.54/0.88
% 0.54/0.88
% 0.54/0.88 % Terminating...
% 1.54/0.98 % Runner terminated.
% 1.54/1.01 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------