%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP582-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.HLvZ6HotEy true
% Computer : n022.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 04:36:43 PM UTC 2025
% Result : Unsatisfiable 1.21s 0.77s
% Output : Refutation 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GRP582-1 : TPTP v9.2.0. Released v2.6.0.
% 0.09/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.HLvZ6HotEy true
% 0.11/0.31 % Computer : n022.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Oct 1 14:06:23 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.11/0.31 % Running portfolio for 300 s
% 0.11/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.32 % Python version: Python 3.6.8
% 0.16/0.32 % Running in FO mode
% 0.17/0.53 % Total configuration time : 435
% 0.17/0.53 % Estimated wc time : 1092
% 0.17/0.53 % Estimated cpu time (7 cpus) : 156.0
% 0.90/0.62 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 1.06/0.65 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.06/0.65 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.06/0.65 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.06/0.66 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.06/0.66 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.06/0.66 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.21/0.77 % Solved by fo/fo3_bce.sh.
% 1.21/0.77 % BCE start: 5
% 1.21/0.77 % BCE eliminated: 0
% 1.21/0.77 % PE start: 5
% 1.21/0.77 logic: eq
% 1.21/0.77 % PE eliminated: 0
% 1.21/0.77 % done 44 iterations in 0.092s
% 1.21/0.77 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.21/0.77 % SZS output start Refutation
% 1.21/0.77 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.21/0.77 thf(identity_type, type, identity: $i).
% 1.21/0.77 thf(a2_type, type, a2: $i).
% 1.21/0.77 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 1.21/0.77 thf(inverse_type, type, inverse: $i > $i).
% 1.21/0.77 thf(prove_these_axioms_2, conjecture,
% 1.21/0.77 (( multiply @ identity @ a2 ) = ( a2 ))).
% 1.21/0.77 thf(zf_stmt_0, negated_conjecture, (( multiply @ identity @ a2 ) != ( a2 )),
% 1.21/0.77 inference('cnf.neg', [status(esa)], [prove_these_axioms_2])).
% 1.21/0.77 thf(zip_derived_cl4, plain, (((multiply @ identity @ a2) != (a2))),
% 1.21/0.77 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.21/0.77 thf(multiply, axiom,
% 1.21/0.77 (( multiply @ A @ B ) =
% 1.21/0.77 ( double_divide @ ( double_divide @ B @ A ) @ identity ))).
% 1.21/0.77 thf(zip_derived_cl1, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((multiply @ X1 @ X0)
% 1.21/0.77 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [multiply])).
% 1.21/0.77 thf(inverse, axiom, (( inverse @ A ) = ( double_divide @ A @ identity ))).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl5, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl6, plain, (((inverse @ (inverse @ a2)) != (a2))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl4, zip_derived_cl5, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(identity, axiom,
% 1.21/0.77 (( identity ) = ( double_divide @ A @ ( inverse @ A ) ))).
% 1.21/0.77 thf(zip_derived_cl3, plain,
% 1.21/0.77 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 1.21/0.77 inference('cnf', [status(esa)], [identity])).
% 1.21/0.77 thf(single_axiom, axiom,
% 1.21/0.77 (( double_divide @
% 1.21/0.77 ( double_divide @
% 1.21/0.77 A @
% 1.21/0.77 ( double_divide @
% 1.21/0.77 ( double_divide @ identity @ B ) @
% 1.21/0.77 ( double_divide @ C @ ( double_divide @ B @ A ) ) ) ) @
% 1.21/0.77 ( double_divide @ identity @ identity ) ) =
% 1.21/0.77 ( C ))).
% 1.21/0.77 thf(zip_derived_cl0, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ X1 @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X2) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 1.21/0.77 (double_divide @ identity @ identity)) = (X0))),
% 1.21/0.77 inference('cnf', [status(esa)], [single_axiom])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl7, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ X1 @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X2) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl10, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ (inverse @ X1) @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X1) @
% 1.21/0.77 (double_divide @ X0 @ identity))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl7])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl14, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ (inverse @ X1) @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl18, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ (inverse @ identity) @
% 1.21/0.77 (double_divide @ (inverse @ identity) @ (inverse @ X0))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl14])).
% 1.21/0.77 thf(zip_derived_cl3, plain,
% 1.21/0.77 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 1.21/0.77 inference('cnf', [status(esa)], [identity])).
% 1.21/0.77 thf(zip_derived_cl3, plain,
% 1.21/0.77 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 1.21/0.77 inference('cnf', [status(esa)], [identity])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl7, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ X1 @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X2) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl9, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ identity @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X0) @
% 1.21/0.77 (double_divide @ X1 @ (inverse @ X0)))) @
% 1.21/0.77 (inverse @ identity)) = (X1))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl7])).
% 1.21/0.77 thf(zip_derived_cl32, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ identity @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X0) @ identity)) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl9])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl41, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ identity @
% 1.21/0.77 (inverse @ (double_divide @ identity @ X0))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl53, plain,
% 1.21/0.77 (((double_divide @ (double_divide @ identity @ (inverse @ identity)) @
% 1.21/0.77 (inverse @ identity)) = (inverse @ identity))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl41])).
% 1.21/0.77 thf(zip_derived_cl3, plain,
% 1.21/0.77 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 1.21/0.77 inference('cnf', [status(esa)], [identity])).
% 1.21/0.77 thf(zip_derived_cl3, plain,
% 1.21/0.77 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 1.21/0.77 inference('cnf', [status(esa)], [identity])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl59, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (double_divide @ identity @
% 1.21/0.77 (double_divide @ identity @ (inverse @ X0))))
% 1.21/0.77 = (X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl18, zip_derived_cl54, zip_derived_cl54,
% 1.21/0.77 zip_derived_cl54, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl3, plain,
% 1.21/0.77 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 1.21/0.77 inference('cnf', [status(esa)], [identity])).
% 1.21/0.77 thf(zip_derived_cl14, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ (inverse @ X1) @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl16, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((double_divide @ (double_divide @ (inverse @ X0) @ identity) @
% 1.21/0.77 (inverse @ identity)) = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl14])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl20, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((double_divide @ (inverse @ (inverse @ X0)) @ (inverse @ identity))
% 1.21/0.77 = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl61, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @ (inverse @ (inverse @ X0)))
% 1.21/0.77 = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl20, zip_derived_cl54, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl61, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @ (inverse @ (inverse @ X0)))
% 1.21/0.77 = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl20, zip_derived_cl54, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl91, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0))))))))
% 1.21/0.77 = (X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl59, zip_derived_cl61, zip_derived_cl61])).
% 1.21/0.77 thf(zip_derived_cl61, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @ (inverse @ (inverse @ X0)))
% 1.21/0.77 = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl20, zip_derived_cl54, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl3, plain,
% 1.21/0.77 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 1.21/0.77 inference('cnf', [status(esa)], [identity])).
% 1.21/0.77 thf(zip_derived_cl7, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ X1 @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X2) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl14, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ (inverse @ X1) @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X1) @ (inverse @ X0))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl17, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @
% 1.21/0.77 (inverse @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X1) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X1 @ identity)))) @
% 1.21/0.77 X0) @
% 1.21/0.77 (inverse @ identity)) = (identity))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl14])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl21, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @
% 1.21/0.77 (inverse @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X1) @
% 1.21/0.77 (double_divide @ X0 @ (inverse @ X1)))) @
% 1.21/0.77 X0) @
% 1.21/0.77 (inverse @ identity)) = (identity))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl61, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @ (inverse @ (inverse @ X0)))
% 1.21/0.77 = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl20, zip_derived_cl54, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl71, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (double_divide @
% 1.21/0.77 (inverse @
% 1.21/0.77 (double_divide @ (inverse @ (inverse @ (inverse @ X1))) @
% 1.21/0.77 (double_divide @ X0 @ (inverse @ X1)))) @
% 1.21/0.77 X0))
% 1.21/0.77 = (identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl21, zip_derived_cl61, zip_derived_cl54,
% 1.21/0.77 zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl76, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (double_divide @
% 1.21/0.77 (inverse @
% 1.21/0.77 (double_divide @ (inverse @ (inverse @ (inverse @ X0))) @ identity)) @
% 1.21/0.77 X0))
% 1.21/0.77 = (identity))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl71])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl83, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (double_divide @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0))))) @ X0))
% 1.21/0.77 = (identity))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl91, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0))))))))
% 1.21/0.77 = (X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl59, zip_derived_cl61, zip_derived_cl61])).
% 1.21/0.77 thf(zip_derived_cl121, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ identity)))))))
% 1.21/0.77 = (double_divide @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0))))) @
% 1.21/0.77 X0))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl91])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl138, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((identity)
% 1.21/0.77 = (double_divide @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0))))) @
% 1.21/0.77 X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl121, zip_derived_cl54, zip_derived_cl54,
% 1.21/0.77 zip_derived_cl54, zip_derived_cl54, zip_derived_cl54,
% 1.21/0.77 zip_derived_cl54, zip_derived_cl54])).
% 1.21/0.77 thf(zip_derived_cl7, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ X1 @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X2) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X2 @ X1)))) @
% 1.21/0.77 (inverse @ identity)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl9, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ identity @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X0) @
% 1.21/0.77 (double_divide @ X1 @ (inverse @ X0)))) @
% 1.21/0.77 (inverse @ identity)) = (X1))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl7])).
% 1.21/0.77 thf(zip_derived_cl33, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ identity @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ identity) @ X0)) @
% 1.21/0.77 (inverse @ identity))
% 1.21/0.77 = (double_divide @ X1 @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X2) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl42, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.21/0.77 ((double_divide @
% 1.21/0.77 (double_divide @ identity @
% 1.21/0.77 (double_divide @ (inverse @ identity) @ X0)) @
% 1.21/0.77 (inverse @ identity))
% 1.21/0.77 = (double_divide @ X1 @
% 1.21/0.77 (double_divide @ (double_divide @ identity @ X2) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl61, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @ (inverse @ (inverse @ X0)))
% 1.21/0.77 = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl20, zip_derived_cl54, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl61, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @ (inverse @ (inverse @ X0)))
% 1.21/0.77 = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl20, zip_derived_cl54, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl54, plain, (((identity) = (inverse @ identity))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl53, zip_derived_cl3, zip_derived_cl3])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl61, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @ (inverse @ (inverse @ X0)))
% 1.21/0.77 = (double_divide @ identity @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl20, zip_derived_cl54, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl193, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0)))))))
% 1.21/0.77 = (double_divide @ X1 @
% 1.21/0.77 (double_divide @ (inverse @ (inverse @ (inverse @ X2))) @
% 1.21/0.77 (double_divide @ X0 @ (double_divide @ X2 @ X1)))))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl42, zip_derived_cl54, zip_derived_cl61,
% 1.21/0.77 zip_derived_cl61, zip_derived_cl54, zip_derived_cl2,
% 1.21/0.77 zip_derived_cl61])).
% 1.21/0.77 thf(zip_derived_cl201, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (double_divide @ X1 @ X0)))))))))))))
% 1.21/0.77 = (double_divide @ X0 @
% 1.21/0.77 (double_divide @ (inverse @ (inverse @ (inverse @ X1))) @
% 1.21/0.77 identity)))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl138, zip_derived_cl193])).
% 1.21/0.77 thf(zip_derived_cl91, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0))))))))
% 1.21/0.77 = (X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl59, zip_derived_cl61, zip_derived_cl61])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl216, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (double_divide @ X1 @ X0)))))
% 1.21/0.77 = (double_divide @ X0 @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ X1))))))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl201, zip_derived_cl91, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl91, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0))))))))
% 1.21/0.77 = (X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl59, zip_derived_cl61, zip_derived_cl61])).
% 1.21/0.77 thf(zip_derived_cl261, plain,
% 1.21/0.77 (![X0 : $i, X1 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (double_divide @ X1 @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ X0)))))))))
% 1.21/0.77 = (double_divide @ X0 @ X1))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl216, zip_derived_cl91])).
% 1.21/0.77 thf(zip_derived_cl410, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0)))))))))))
% 1.21/0.77 = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('sup+', [status(thm)], [zip_derived_cl61, zip_derived_cl261])).
% 1.21/0.77 thf(zip_derived_cl91, plain,
% 1.21/0.77 (![X0 : $i]:
% 1.21/0.77 ((inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @
% 1.21/0.77 (inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0))))))))
% 1.21/0.77 = (X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl59, zip_derived_cl61, zip_derived_cl61])).
% 1.21/0.77 thf(zip_derived_cl2, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 1.21/0.77 inference('cnf', [status(esa)], [inverse])).
% 1.21/0.77 thf(zip_derived_cl430, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl410, zip_derived_cl91, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl430, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl410, zip_derived_cl91, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl430, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl410, zip_derived_cl91, zip_derived_cl2])).
% 1.21/0.77 thf(zip_derived_cl440, plain,
% 1.21/0.77 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 1.21/0.77 inference('demod', [status(thm)],
% 1.21/0.77 [zip_derived_cl91, zip_derived_cl430, zip_derived_cl430,
% 1.21/0.77 zip_derived_cl430])).
% 1.21/0.77 thf(zip_derived_cl456, plain, (((a2) != (a2))),
% 1.21/0.77 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl440])).
% 1.21/0.77 thf(zip_derived_cl457, plain, ($false),
% 1.21/0.77 inference('simplify', [status(thm)], [zip_derived_cl456])).
% 1.21/0.77
% 1.21/0.77 % SZS output end Refutation
% 1.21/0.77
% 1.21/0.77
% 1.21/0.77 % Terminating...
% 1.33/0.85 % Runner terminated.
% 1.88/0.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------