%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP099-1 : TPTP v9.2.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bmjc2SzsAj 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 04:35:37 PM UTC 2025
% Result : Unsatisfiable 4.63s 1.25s
% Output : Refutation 4.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP099-1 : TPTP v9.2.0. Bugfixed v2.7.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bmjc2SzsAj true
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 14:15:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in FO mode
% 0.54/0.64 % Total configuration time : 435
% 0.54/0.64 % Estimated wc time : 1092
% 0.54/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 4.63/1.25 % Solved by fo/fo5.sh.
% 4.63/1.25 % done 666 iterations in 0.451s
% 4.63/1.25 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 4.63/1.25 % SZS output start Refutation
% 4.63/1.25 thf(a3_type, type, a3: $i).
% 4.63/1.25 thf(identity_type, type, identity: $i).
% 4.63/1.25 thf(multiply_type, type, multiply: $i > $i > $i).
% 4.63/1.25 thf(c3_type, type, c3: $i).
% 4.63/1.25 thf(a2_type, type, a2: $i).
% 4.63/1.25 thf(a1_type, type, a1: $i).
% 4.63/1.25 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 4.63/1.25 thf(inverse_type, type, inverse: $i > $i).
% 4.63/1.25 thf(b4_type, type, b4: $i).
% 4.63/1.25 thf(a4_type, type, a4: $i).
% 4.63/1.25 thf(b3_type, type, b3: $i).
% 4.63/1.25 thf(prove_these_axioms, conjecture,
% 4.63/1.25 (~( ( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 4.63/1.25 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 4.63/1.25 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 4.63/1.25 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 4.63/1.25 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) ) ))).
% 4.63/1.25 thf(zf_stmt_0, negated_conjecture,
% 4.63/1.25 (( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 4.63/1.25 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 4.63/1.25 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 4.63/1.25 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 4.63/1.25 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) )),
% 4.63/1.25 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 4.63/1.25 thf(zip_derived_cl4, plain,
% 4.63/1.25 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 4.63/1.25 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 4.63/1.25 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 4.63/1.25 | ((multiply @ identity @ a2) != (a2))
% 4.63/1.25 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 4.63/1.25 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.63/1.25 thf(inverse, axiom, (( inverse @ X ) = ( double_divide @ X @ identity ))).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(multiply, axiom,
% 4.63/1.25 (( multiply @ X @ Y ) =
% 4.63/1.25 ( double_divide @ ( double_divide @ Y @ X ) @ identity ))).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl7, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((multiply @ identity @ X0)
% 4.63/1.25 = (double_divide @ (inverse @ X0) @ identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl10, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl30, plain,
% 4.63/1.25 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 4.63/1.25 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 4.63/1.25 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 4.63/1.25 | ((inverse @ (inverse @ a2)) != (a2))
% 4.63/1.25 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 4.63/1.25 thf(identity, axiom,
% 4.63/1.25 (( identity ) = ( double_divide @ X @ ( inverse @ X ) ))).
% 4.63/1.25 thf(zip_derived_cl3, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 4.63/1.25 inference('cnf', [status(esa)], [identity])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl6, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl33, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 4.63/1.25 thf(zip_derived_cl74, plain,
% 4.63/1.25 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 4.63/1.25 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 4.63/1.25 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 4.63/1.25 | ((inverse @ (inverse @ a2)) != (a2))
% 4.63/1.25 | ((inverse @ identity) != (identity)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl33])).
% 4.63/1.25 thf(zip_derived_cl33, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 4.63/1.25 thf(zip_derived_cl33, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 4.63/1.25 thf(zip_derived_cl3, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 4.63/1.25 inference('cnf', [status(esa)], [identity])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(single_axiom, axiom,
% 4.63/1.25 (( double_divide @
% 4.63/1.25 ( double_divide @
% 4.63/1.25 X @
% 4.63/1.25 ( double_divide @
% 4.63/1.25 ( double_divide @ Y @ ( double_divide @ X @ Z ) ) @
% 4.63/1.25 ( double_divide @ identity @ Z ) ) ) @
% 4.63/1.25 ( double_divide @ identity @ identity ) ) =
% 4.63/1.25 ( Y ))).
% 4.63/1.25 thf(zip_derived_cl0, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 4.63/1.25 (double_divide @ identity @ X2))) @
% 4.63/1.25 (double_divide @ identity @ identity)) = (X0))),
% 4.63/1.25 inference('cnf', [status(esa)], [single_axiom])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl13, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 4.63/1.25 (double_divide @ identity @ X2))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl16, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X1 @ identity)) @
% 4.63/1.25 (inverse @ identity))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl22, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @ (double_divide @ X0 @ (inverse @ X1)) @
% 4.63/1.25 (inverse @ identity))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl152, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X0 @
% 4.63/1.25 (double_divide @ identity @ (inverse @ identity))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 4.63/1.25 thf(zip_derived_cl3, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 4.63/1.25 inference('cnf', [status(esa)], [identity])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl158, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((double_divide @ (inverse @ X0) @ (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl152, zip_derived_cl3, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl171, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 4.63/1.25 (inverse @ identity)) = (identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl158])).
% 4.63/1.25 thf(zip_derived_cl22, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @ (double_divide @ X0 @ (inverse @ X1)) @
% 4.63/1.25 (inverse @ identity))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl191, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ identity @
% 4.63/1.25 (double_divide @ identity @ (inverse @ identity))) @
% 4.63/1.25 (inverse @ identity)) = (multiply @ (inverse @ X0) @ X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl22])).
% 4.63/1.25 thf(zip_derived_cl3, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 4.63/1.25 inference('cnf', [status(esa)], [identity])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl158, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((double_divide @ (inverse @ X0) @ (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl152, zip_derived_cl3, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl204, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl191, zip_derived_cl3, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl158])).
% 4.63/1.25 thf(zip_derived_cl206, plain, (((identity) = (inverse @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl216, plain,
% 4.63/1.25 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 4.63/1.25 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 4.63/1.25 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 4.63/1.25 | ((inverse @ (inverse @ a2)) != (a2))
% 4.63/1.25 | ((identity) != (identity)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl206])).
% 4.63/1.25 thf(zip_derived_cl217, plain,
% 4.63/1.25 ((((inverse @ (inverse @ a2)) != (a2))
% 4.63/1.25 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 4.63/1.25 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 4.63/1.25 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 4.63/1.25 inference('simplify', [status(thm)], [zip_derived_cl216])).
% 4.63/1.25 thf(zip_derived_cl158, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((double_divide @ (inverse @ X0) @ (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl152, zip_derived_cl3, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl206, plain, (((identity) = (inverse @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl251, plain,
% 4.63/1.25 ((((a2) != (a2))
% 4.63/1.25 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 4.63/1.25 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 4.63/1.25 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl217, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl252, plain,
% 4.63/1.25 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 4.63/1.25 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 4.63/1.25 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 4.63/1.25 inference('simplify', [status(thm)], [zip_derived_cl251])).
% 4.63/1.25 thf(zip_derived_cl3, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 4.63/1.25 inference('cnf', [status(esa)], [identity])).
% 4.63/1.25 thf(zip_derived_cl13, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 4.63/1.25 (double_divide @ identity @ X2))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl19, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @ (double_divide @ X0 @ identity) @
% 4.63/1.25 (double_divide @ identity @ (inverse @ X1)))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl25, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @ (inverse @ X0) @
% 4.63/1.25 (double_divide @ identity @ (inverse @ X1)))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl206, plain, (((identity) = (inverse @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl3, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 4.63/1.25 inference('cnf', [status(esa)], [identity])).
% 4.63/1.25 thf(zip_derived_cl13, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 4.63/1.25 (double_divide @ identity @ X2))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl17, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X1 @ (inverse @ identity))) @
% 4.63/1.25 identity)) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl23, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (multiply @ (double_divide @ X1 @ (inverse @ identity)) @ X0)) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl206, plain, (((identity) = (inverse @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl206, plain, (((identity) = (inverse @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl231, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ (inverse @ X1) @ X0) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl23, zip_derived_cl206, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl206, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl235, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ (multiply @ identity @ X0) @ identity) = (X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl206, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl10, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl236, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ (inverse @ (inverse @ X0)) @ identity) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl235, zip_derived_cl10])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl278, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl236, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl6, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl3, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 4.63/1.25 inference('cnf', [status(esa)], [identity])).
% 4.63/1.25 thf(zip_derived_cl31, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((identity)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 4.63/1.25 thf(zip_derived_cl279, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((identity) = (double_divide @ (double_divide @ identity @ X0) @ X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl278, zip_derived_cl31])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl286, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((multiply @ X0 @ (double_divide @ identity @ X0))
% 4.63/1.25 = (double_divide @ identity @ identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl279, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl3, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 4.63/1.25 inference('cnf', [status(esa)], [identity])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl8, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X0) @ X0)
% 4.63/1.25 = (double_divide @ identity @ identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl204, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl191, zip_derived_cl3, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl158])).
% 4.63/1.25 thf(zip_derived_cl205, plain,
% 4.63/1.25 (((identity) = (double_divide @ identity @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl297, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((multiply @ X0 @ (double_divide @ identity @ X0)) = (identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl286, zip_derived_cl205])).
% 4.63/1.25 thf(zip_derived_cl231, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ (inverse @ X1) @ X0) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl23, zip_derived_cl206, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl206, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl304, plain,
% 4.63/1.25 (![X0 : $i]:
% 4.63/1.25 ((multiply @ identity @ X0)
% 4.63/1.25 = (double_divide @ identity @ (inverse @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl297, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl204, plain,
% 4.63/1.25 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl191, zip_derived_cl3, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl158])).
% 4.63/1.25 thf(zip_derived_cl231, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ (inverse @ X1) @ X0) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl23, zip_derived_cl206, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl206, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl233, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl204, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl312, plain,
% 4.63/1.25 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl304, zip_derived_cl233])).
% 4.63/1.25 thf(zip_derived_cl206, plain, (((identity) = (inverse @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl339, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (double_divide @ (inverse @ X0) @ X1) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl25, zip_derived_cl312, zip_derived_cl206,
% 4.63/1.25 zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl6, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl370, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ (multiply @ X1 @ (inverse @ X0))) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl339, zip_derived_cl248])).
% 4.63/1.25 thf(zip_derived_cl231, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ (inverse @ X1) @ X0) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl23, zip_derived_cl206, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl206, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl474, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))) = (X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl370, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl13, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 4.63/1.25 (double_divide @ identity @ X2))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl15, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ identity) @
% 4.63/1.25 (double_divide @ X2 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 4.63/1.25 (double_divide @ identity @ X1))))
% 4.63/1.25 = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl29, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ identity) @
% 4.63/1.25 (double_divide @ X2 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 4.63/1.25 (double_divide @ identity @ X1))))
% 4.63/1.25 = (inverse @ X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl206, plain, (((identity) = (inverse @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl312, plain,
% 4.63/1.25 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl304, zip_derived_cl233])).
% 4.63/1.25 thf(zip_derived_cl321, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl312])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl370, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ (multiply @ X1 @ (inverse @ X0))) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl339, zip_derived_cl248])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl231, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ (inverse @ X1) @ X0) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl23, zip_derived_cl206, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl206, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl247, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl370, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ (multiply @ X1 @ (inverse @ X0))) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl339, zip_derived_cl248])).
% 4.63/1.25 thf(zip_derived_cl480, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)) = (X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl370])).
% 4.63/1.25 thf(zip_derived_cl530, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X1) @ X0)
% 4.63/1.25 = (inverse @ (multiply @ X1 @ (inverse @ X0))))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl370, zip_derived_cl480])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl233, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl204, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl693, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((inverse @
% 4.63/1.25 (multiply @
% 4.63/1.25 (multiply @ X1 @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 4.63/1.25 X2))
% 4.63/1.25 = (inverse @ X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl29, zip_derived_cl206, zip_derived_cl248,
% 4.63/1.25 zip_derived_cl248, zip_derived_cl321, zip_derived_cl248,
% 4.63/1.25 zip_derived_cl530, zip_derived_cl218, zip_derived_cl248,
% 4.63/1.25 zip_derived_cl233])).
% 4.63/1.25 thf(zip_derived_cl714, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ (inverse @ (multiply @ X1 @ X0)) @ X0))
% 4.63/1.25 = (inverse @ (inverse @ X1)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl474, zip_derived_cl693])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl741, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ (inverse @ (multiply @ X1 @ X0)) @ X0)) = (X1))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl714, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl231, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ (inverse @ X1) @ X0) @ X1) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl23, zip_derived_cl206, zip_derived_cl2,
% 4.63/1.25 zip_derived_cl206, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl247, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl425, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X0))) = (X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl231, zip_derived_cl247])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl808, plain,
% 4.63/1.25 ((((multiply @ a4 @ b4) != (multiply @ a4 @ b4))
% 4.63/1.25 | ((multiply @ c3 @ (multiply @ a3 @ b3))
% 4.63/1.25 != (multiply @ a3 @ (multiply @ c3 @ b3))))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl252, zip_derived_cl780, zip_derived_cl780,
% 4.63/1.25 zip_derived_cl780])).
% 4.63/1.25 thf(zip_derived_cl809, plain,
% 4.63/1.25 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 4.63/1.25 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 4.63/1.25 inference('simplify', [status(thm)], [zip_derived_cl808])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl247, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl247, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl419, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl247])).
% 4.63/1.25 thf(zip_derived_cl741, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ (inverse @ (multiply @ X1 @ X0)) @ X0)) = (X1))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl714, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl790, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @
% 4.63/1.25 (multiply @ (inverse @ (inverse @ X0)) @
% 4.63/1.25 (inverse @ (multiply @ X0 @ X1))))
% 4.63/1.25 = (X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl419, zip_derived_cl741])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl530, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X1) @ X0)
% 4.63/1.25 = (inverse @ (multiply @ X1 @ (inverse @ X0))))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl370, zip_derived_cl480])).
% 4.63/1.25 thf(zip_derived_cl800, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl790, zip_derived_cl218, zip_derived_cl530])).
% 4.63/1.25 thf(zip_derived_cl13, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((double_divide @
% 4.63/1.25 (double_divide @ X1 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 4.63/1.25 (double_divide @ identity @ X2))) @
% 4.63/1.25 (inverse @ identity)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl1, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ X1 @ X0)
% 4.63/1.25 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [multiply])).
% 4.63/1.25 thf(zip_derived_cl9, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 4.63/1.25 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 4.63/1.25 thf(zip_derived_cl2, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 4.63/1.25 inference('cnf', [status(esa)], [inverse])).
% 4.63/1.25 thf(zip_derived_cl11, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 4.63/1.25 = (inverse @ (multiply @ X1 @ X0)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl104, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((multiply @ identity @ X0)
% 4.63/1.25 = (inverse @
% 4.63/1.25 (multiply @ (inverse @ identity) @
% 4.63/1.25 (double_divide @ X2 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 4.63/1.25 (double_divide @ identity @ X1))))))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl11])).
% 4.63/1.25 thf(zip_derived_cl10, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl109, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((inverse @ (inverse @ X0))
% 4.63/1.25 = (inverse @
% 4.63/1.25 (multiply @ (inverse @ identity) @
% 4.63/1.25 (double_divide @ X2 @
% 4.63/1.25 (double_divide @
% 4.63/1.25 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 4.63/1.25 (double_divide @ identity @ X1))))))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl104, zip_derived_cl10])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl206, plain, (((identity) = (inverse @ identity))),
% 4.63/1.25 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl204])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl530, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X1) @ X0)
% 4.63/1.25 = (inverse @ (multiply @ X1 @ (inverse @ X0))))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl370, zip_derived_cl480])).
% 4.63/1.25 thf(zip_derived_cl818, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X0) @ X1)
% 4.63/1.25 = (inverse @ (multiply @ (inverse @ X1) @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl780, zip_derived_cl530])).
% 4.63/1.25 thf(zip_derived_cl321, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl312])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl818, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X0) @ X1)
% 4.63/1.25 = (inverse @ (multiply @ (inverse @ X1) @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl780, zip_derived_cl530])).
% 4.63/1.25 thf(zip_derived_cl818, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((multiply @ (inverse @ X0) @ X1)
% 4.63/1.25 = (inverse @ (multiply @ (inverse @ X1) @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl780, zip_derived_cl530])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl248, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]:
% 4.63/1.25 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl233, plain,
% 4.63/1.25 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl204, zip_derived_cl231])).
% 4.63/1.25 thf(zip_derived_cl218, plain,
% 4.63/1.25 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl158, zip_derived_cl206, zip_derived_cl2])).
% 4.63/1.25 thf(zip_derived_cl1456, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((X0)
% 4.63/1.25 = (multiply @ X2 @
% 4.63/1.25 (multiply @ X1 @
% 4.63/1.25 (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0))))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl109, zip_derived_cl218, zip_derived_cl206,
% 4.63/1.25 zip_derived_cl248, zip_derived_cl248, zip_derived_cl818,
% 4.63/1.25 zip_derived_cl321, zip_derived_cl248, zip_derived_cl818,
% 4.63/1.25 zip_derived_cl818, zip_derived_cl780, zip_derived_cl248,
% 4.63/1.25 zip_derived_cl780, zip_derived_cl233, zip_derived_cl218])).
% 4.63/1.25 thf(zip_derived_cl1492, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ X2 @ X1) @ X0)
% 4.63/1.25 = (multiply @ X1 @ (multiply @ X2 @ X0)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl800, zip_derived_cl1456])).
% 4.63/1.25 thf(zip_derived_cl1579, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 4.63/1.25 = (multiply @ X1 @ (multiply @ X0 @ X2)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl780, zip_derived_cl1492])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl1826, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.63/1.25 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 4.63/1.25 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl1579, zip_derived_cl780])).
% 4.63/1.25 thf(zip_derived_cl780, plain,
% 4.63/1.25 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 4.63/1.25 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl425])).
% 4.63/1.25 thf(zip_derived_cl3936, plain,
% 4.63/1.25 (((multiply @ a3 @ (multiply @ c3 @ b3))
% 4.63/1.25 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 4.63/1.25 inference('demod', [status(thm)],
% 4.63/1.25 [zip_derived_cl809, zip_derived_cl1826, zip_derived_cl780])).
% 4.63/1.25 thf(zip_derived_cl3937, plain, ($false),
% 4.63/1.25 inference('simplify', [status(thm)], [zip_derived_cl3936])).
% 4.63/1.25
% 4.63/1.25 % SZS output end Refutation
% 4.63/1.25
% 4.63/1.25
% 4.63/1.25 % Terminating...
% 5.02/1.35 % Runner terminated.
% 5.02/1.36 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------