TSTP Solution File: GRP203-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP203-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.eFV34Y8kpF true
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:42 EDT 2023
% Result : Unsatisfiable 104.97s 15.78s
% Output : Refutation 104.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP203-1 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.eFV34Y8kpF true
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 02:24:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 104.97/15.78 % Solved by fo/fo4.sh.
% 104.97/15.78 % done 1055 iterations in 14.996s
% 104.97/15.78 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 104.97/15.78 % SZS output start Refutation
% 104.97/15.78 thf(c_type, type, c: $i).
% 104.97/15.78 thf(identity_type, type, identity: $i).
% 104.97/15.78 thf(multiply_type, type, multiply: $i > $i > $i).
% 104.97/15.78 thf(b_type, type, b: $i).
% 104.97/15.78 thf(left_inverse_type, type, left_inverse: $i > $i).
% 104.97/15.78 thf(a_type, type, a: $i).
% 104.97/15.78 thf(prove_moufang2, conjecture,
% 104.97/15.78 (( multiply @ ( multiply @ ( multiply @ a @ b ) @ c ) @ b ) =
% 104.97/15.78 ( multiply @ a @ ( multiply @ b @ ( multiply @ c @ b ) ) ))).
% 104.97/15.78 thf(zf_stmt_0, negated_conjecture,
% 104.97/15.78 (( multiply @ ( multiply @ ( multiply @ a @ b ) @ c ) @ b ) !=
% 104.97/15.78 ( multiply @ a @ ( multiply @ b @ ( multiply @ c @ b ) ) )),
% 104.97/15.78 inference('cnf.neg', [status(esa)], [prove_moufang2])).
% 104.97/15.78 thf(zip_derived_cl3, plain,
% 104.97/15.78 (((multiply @ (multiply @ (multiply @ a @ b) @ c) @ b)
% 104.97/15.78 != (multiply @ a @ (multiply @ b @ (multiply @ c @ b))))),
% 104.97/15.78 inference('cnf', [status(esa)], [zf_stmt_0])).
% 104.97/15.78 thf(left_inverse, axiom,
% 104.97/15.78 (( multiply @ ( left_inverse @ X ) @ X ) = ( identity ))).
% 104.97/15.78 thf(zip_derived_cl1, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ (left_inverse @ X0) @ X0) = (identity))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_inverse])).
% 104.97/15.78 thf(zip_derived_cl1, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ (left_inverse @ X0) @ X0) = (identity))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_inverse])).
% 104.97/15.78 thf(moufang3, axiom,
% 104.97/15.78 (( multiply @ ( multiply @ ( multiply @ X @ Y ) @ X ) @ Z ) =
% 104.97/15.78 ( multiply @ X @ ( multiply @ Y @ ( multiply @ X @ Z ) ) ))).
% 104.97/15.78 thf(zip_derived_cl2, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ (multiply @ X0 @ X1) @ X0) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('cnf', [status(esa)], [moufang3])).
% 104.97/15.78 thf(zip_derived_cl9, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ identity @ (left_inverse @ X1)) @ X0)
% 104.97/15.78 = (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 104.97/15.78 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl12, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X1) @ X0)
% 104.97/15.78 = (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl1, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ (left_inverse @ X0) @ X0) = (identity))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_inverse])).
% 104.97/15.78 thf(zip_derived_cl12, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X1) @ X0)
% 104.97/15.78 = (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl258, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X0) @ X0)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @ (multiply @ X0 @ identity)))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl12])).
% 104.97/15.78 thf(zip_derived_cl1, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ (left_inverse @ X0) @ X0) = (identity))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_inverse])).
% 104.97/15.78 thf(zip_derived_cl263, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((identity)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @ (multiply @ X0 @ identity)))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl258, zip_derived_cl1])).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl2, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ (multiply @ X0 @ X1) @ X0) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('cnf', [status(esa)], [moufang3])).
% 104.97/15.78 thf(zip_derived_cl8, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ identity) @ X1)
% 104.97/15.78 = (multiply @ identity @
% 104.97/15.78 (multiply @ X0 @ (multiply @ identity @ X1))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl11, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ identity) @ X1) = (multiply @ X0 @ X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl8, zip_derived_cl0, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl2, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ (multiply @ X0 @ X1) @ X0) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('cnf', [status(esa)], [moufang3])).
% 104.97/15.78 thf(zip_derived_cl16, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ X0) @ X1)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ identity @ (multiply @ X0 @ X1))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl2])).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl28, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ X0) @ X1)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X0 @ X1)))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl2, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ (multiply @ X0 @ X1) @ X0) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('cnf', [status(esa)], [moufang3])).
% 104.97/15.78 thf(zip_derived_cl11, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ identity) @ X1) = (multiply @ X0 @ X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl8, zip_derived_cl0, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl19, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ identity))) @ X2)
% 104.97/15.78 = (multiply @ (multiply @ (multiply @ X0 @ X1) @ X0) @ X2))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl11])).
% 104.97/15.78 thf(zip_derived_cl2, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ (multiply @ X0 @ X1) @ X0) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('cnf', [status(esa)], [moufang3])).
% 104.97/15.78 thf(zip_derived_cl23, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ identity))) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 104.97/15.78 thf(zip_derived_cl368, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X0 @
% 104.97/15.78 (multiply @ X1 @ (multiply @ X1 @ (multiply @ X0 @ identity)))) @
% 104.97/15.78 X2)
% 104.97/15.78 = (multiply @ X0 @
% 104.97/15.78 (multiply @ (multiply @ X1 @ X1) @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl23])).
% 104.97/15.78 thf(zip_derived_cl28, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ X0) @ X1)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X0 @ X1)))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl396, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X0 @
% 104.97/15.78 (multiply @ X1 @ (multiply @ X1 @ (multiply @ X0 @ identity)))) @
% 104.97/15.78 X2)
% 104.97/15.78 = (multiply @ X0 @
% 104.97/15.78 (multiply @ X1 @ (multiply @ X1 @ (multiply @ X0 @ X2)))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl368, zip_derived_cl28])).
% 104.97/15.78 thf(zip_derived_cl4956, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ identity)) @ X0)
% 104.97/15.78 = (multiply @ X1 @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0)))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl263, zip_derived_cl396])).
% 104.97/15.78 thf(zip_derived_cl9194, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X1)) @ identity)) @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0)))
% 104.97/15.78 = (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X1)) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X1)) @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ X0)))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4956])).
% 104.97/15.78 thf(zip_derived_cl1, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ (left_inverse @ X0) @ X0) = (identity))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_inverse])).
% 104.97/15.78 thf(zip_derived_cl263, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((identity)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @ (multiply @ X0 @ identity)))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl258, zip_derived_cl1])).
% 104.97/15.78 thf(zip_derived_cl23, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ identity))) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 104.97/15.78 thf(zip_derived_cl377, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X1 @ identity) @ X0)
% 104.97/15.78 = (multiply @ X1 @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl263, zip_derived_cl23])).
% 104.97/15.78 thf(zip_derived_cl11, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ identity) @ X1) = (multiply @ X0 @ X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl8, zip_derived_cl0, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl405, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X1 @ X0)
% 104.97/15.78 = (multiply @ X1 @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl377, zip_derived_cl11])).
% 104.97/15.78 thf(zip_derived_cl457, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X0) @ X0)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X0)) @ identity)))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl405])).
% 104.97/15.78 thf(zip_derived_cl1, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ (left_inverse @ X0) @ X0) = (identity))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_inverse])).
% 104.97/15.78 thf(zip_derived_cl471, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((identity)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X0)) @ identity)))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl457, zip_derived_cl1])).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl4956, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ identity)) @ X0)
% 104.97/15.78 = (multiply @ X1 @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0)))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl263, zip_derived_cl396])).
% 104.97/15.78 thf(zip_derived_cl471, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((identity)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X0)) @ identity)))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl457, zip_derived_cl1])).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl9253, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0)) = (X0))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9194, zip_derived_cl471, zip_derived_cl0,
% 104.97/15.78 zip_derived_cl4956, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl9381, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl9253, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0)) = (X0))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9194, zip_derived_cl471, zip_derived_cl0,
% 104.97/15.78 zip_derived_cl4956, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl9498, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ X0 @ (left_inverse @ X0)) = (identity))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl9381, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl9253, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0)) = (X0))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9194, zip_derived_cl471, zip_derived_cl0,
% 104.97/15.78 zip_derived_cl4956, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl10038, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((multiply @ X0 @ identity) = (left_inverse @ (left_inverse @ X0)))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl9498, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl9381, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl10052, plain,
% 104.97/15.78 (![X0 : $i]: ((X0) = (left_inverse @ (left_inverse @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl10038, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl23, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ identity))) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 104.97/15.78 thf(zip_derived_cl9381, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl9435, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ (multiply @ X1 @ X0)) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl9253, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0)) = (X0))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9194, zip_derived_cl471, zip_derived_cl0,
% 104.97/15.78 zip_derived_cl4956, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl9381, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl2, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ (multiply @ X0 @ X1) @ X0) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('cnf', [status(esa)], [moufang3])).
% 104.97/15.78 thf(zip_derived_cl9493, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ X1) @ X0)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ identity))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl9381, zip_derived_cl2])).
% 104.97/15.78 thf(zip_derived_cl9381, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl9529, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ X1) @ X0)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9493, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl10543, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @ X1)
% 104.97/15.78 = (multiply @ X1 @
% 104.97/15.78 (multiply @ (multiply @ (left_inverse @ X1) @ X0) @ X1)))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl9253, zip_derived_cl9529])).
% 104.97/15.78 thf(zip_derived_cl4956, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ identity)) @ X0)
% 104.97/15.78 = (multiply @ X1 @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0)))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl263, zip_derived_cl396])).
% 104.97/15.78 thf(zip_derived_cl12, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X1) @ X0)
% 104.97/15.78 = (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl9152, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X1)) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X1)) @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ X0))))
% 104.97/15.78 = (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ X1 @
% 104.97/15.78 (multiply @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X1)) @ identity)) @
% 104.97/15.78 X0))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl4956, zip_derived_cl12])).
% 104.97/15.78 thf(zip_derived_cl4956, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X1) @ identity)) @ X0)
% 104.97/15.78 = (multiply @ X1 @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0)))))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl263, zip_derived_cl396])).
% 104.97/15.78 thf(zip_derived_cl471, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((identity)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X0)) @ identity)))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl457, zip_derived_cl1])).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl471, plain,
% 104.97/15.78 (![X0 : $i]:
% 104.97/15.78 ((identity)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X0)) @ identity)))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl457, zip_derived_cl1])).
% 104.97/15.78 thf(zip_derived_cl0, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 104.97/15.78 inference('cnf', [status(esa)], [left_identity])).
% 104.97/15.78 thf(zip_derived_cl9307, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((X0) = (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9152, zip_derived_cl4956, zip_derived_cl471,
% 104.97/15.78 zip_derived_cl0, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl11279, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ (left_inverse @ X0) @ X1) @ X0)
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl10543, zip_derived_cl9307])).
% 104.97/15.78 thf(zip_derived_cl10543, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @ X1)
% 104.97/15.78 = (multiply @ X1 @
% 104.97/15.78 (multiply @ (multiply @ (left_inverse @ X1) @ X0) @ X1)))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl9253, zip_derived_cl9529])).
% 104.97/15.78 thf(zip_derived_cl9253, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0)) = (X0))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9194, zip_derived_cl471, zip_derived_cl0,
% 104.97/15.78 zip_derived_cl4956, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl11289, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @ (multiply @ X1 @ (left_inverse @ X0)))
% 104.97/15.78 = (multiply @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X0)) @ X1) @
% 104.97/15.78 (left_inverse @ X0)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl10543, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl10052, plain,
% 104.97/15.78 (![X0 : $i]: ((X0) = (left_inverse @ (left_inverse @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl10038, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl11339, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @ (multiply @ X1 @ (left_inverse @ X0)))
% 104.97/15.78 = (multiply @ (multiply @ X0 @ X1) @ (left_inverse @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl11289, zip_derived_cl10052])).
% 104.97/15.78 thf(zip_derived_cl9435, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ (multiply @ X1 @ X0)) @ X2)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ (multiply @ X0 @ X2))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl11528, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @
% 104.97/15.78 (multiply @ (multiply @ X1 @ X0) @ (left_inverse @ X0)))
% 104.97/15.78 = (multiply @ X0 @
% 104.97/15.78 (multiply @ X1 @ (multiply @ X0 @ (left_inverse @ X0)))))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl11339, zip_derived_cl9435])).
% 104.97/15.78 thf(zip_derived_cl9498, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ X0 @ (left_inverse @ X0)) = (identity))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl9381, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl9381, plain,
% 104.97/15.78 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 104.97/15.78 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl11566, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @
% 104.97/15.78 (multiply @ (multiply @ X1 @ X0) @ (left_inverse @ X0)))
% 104.97/15.78 = (multiply @ X0 @ X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl11528, zip_derived_cl9498, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl11947, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @
% 104.97/15.78 (multiply @
% 104.97/15.78 (multiply @ (left_inverse @ X0) @ (multiply @ X1 @ X0)) @
% 104.97/15.78 (left_inverse @ X0)))
% 104.97/15.78 = (multiply @ X0 @ (multiply @ (left_inverse @ X0) @ X1)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl11279, zip_derived_cl11566])).
% 104.97/15.78 thf(zip_derived_cl9529, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ X1) @ X0)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9493, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl9253, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0)) = (X0))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9194, zip_derived_cl471, zip_derived_cl0,
% 104.97/15.78 zip_derived_cl4956, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl9253, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X1 @ (multiply @ (left_inverse @ X1) @ X0)) = (X0))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9194, zip_derived_cl471, zip_derived_cl0,
% 104.97/15.78 zip_derived_cl4956, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl11972, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X1 @ X0) @ (left_inverse @ X0)) = (X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl11947, zip_derived_cl9529, zip_derived_cl9253,
% 104.97/15.78 zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl9307, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((X0) = (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9152, zip_derived_cl4956, zip_derived_cl471,
% 104.97/15.78 zip_derived_cl0, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl12014, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((left_inverse @ X1)
% 104.97/15.78 = (multiply @ (left_inverse @ (multiply @ X0 @ X1)) @ X0))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl11972, zip_derived_cl9307])).
% 104.97/15.78 thf(zip_derived_cl11339, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @ (multiply @ X1 @ (left_inverse @ X0)))
% 104.97/15.78 = (multiply @ (multiply @ X0 @ X1) @ (left_inverse @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl11289, zip_derived_cl10052])).
% 104.97/15.78 thf(zip_derived_cl11566, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @
% 104.97/15.78 (multiply @ (multiply @ X1 @ X0) @ (left_inverse @ X0)))
% 104.97/15.78 = (multiply @ X0 @ X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl11528, zip_derived_cl9498, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl11948, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X0) @
% 104.97/15.78 (multiply @
% 104.97/15.78 (multiply @ X0 @ (multiply @ X1 @ (left_inverse @ X0))) @
% 104.97/15.78 (left_inverse @ (left_inverse @ X0))))
% 104.97/15.78 = (multiply @ (left_inverse @ X0) @ (multiply @ X0 @ X1)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl11339, zip_derived_cl11566])).
% 104.97/15.78 thf(zip_derived_cl10052, plain,
% 104.97/15.78 (![X0 : $i]: ((X0) = (left_inverse @ (left_inverse @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl10038, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl9529, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ X1) @ X0)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9493, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl9307, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((X0) = (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9152, zip_derived_cl4956, zip_derived_cl471,
% 104.97/15.78 zip_derived_cl0, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl9307, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((X0) = (multiply @ (left_inverse @ X1) @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9152, zip_derived_cl4956, zip_derived_cl471,
% 104.97/15.78 zip_derived_cl0, zip_derived_cl471, zip_derived_cl0])).
% 104.97/15.78 thf(zip_derived_cl11973, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X1 @ (left_inverse @ X0)) @ X0) = (X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl11948, zip_derived_cl10052, zip_derived_cl9529,
% 104.97/15.78 zip_derived_cl9307, zip_derived_cl9307])).
% 104.97/15.78 thf(zip_derived_cl12157, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X0) @ X1)
% 104.97/15.78 = (left_inverse @ (multiply @ (left_inverse @ X1) @ X0)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl12014, zip_derived_cl11973])).
% 104.97/15.78 thf(zip_derived_cl12014, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((left_inverse @ X1)
% 104.97/15.78 = (multiply @ (left_inverse @ (multiply @ X0 @ X1)) @ X0))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl11972, zip_derived_cl9307])).
% 104.97/15.78 thf(zip_derived_cl11972, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X1 @ X0) @ (left_inverse @ X0)) = (X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl11947, zip_derived_cl9529, zip_derived_cl9253,
% 104.97/15.78 zip_derived_cl9253])).
% 104.97/15.78 thf(zip_derived_cl12153, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X0) @ (left_inverse @ X1))
% 104.97/15.78 = (left_inverse @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl12014, zip_derived_cl11972])).
% 104.97/15.78 thf(zip_derived_cl12833, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ (left_inverse @ X1) @ X0) @
% 104.97/15.78 (left_inverse @ X2))
% 104.97/15.78 = (left_inverse @
% 104.97/15.78 (multiply @ X2 @ (multiply @ (left_inverse @ X0) @ X1))))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl12157, zip_derived_cl12153])).
% 104.97/15.78 thf(zip_derived_cl10052, plain,
% 104.97/15.78 (![X0 : $i]: ((X0) = (left_inverse @ (left_inverse @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl10038, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl17454, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ X0 @ (multiply @ (left_inverse @ X1) @ X2))
% 104.97/15.78 = (left_inverse @
% 104.97/15.78 (multiply @ (multiply @ (left_inverse @ X2) @ X1) @
% 104.97/15.78 (left_inverse @ X0))))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl12833, zip_derived_cl10052])).
% 104.97/15.78 thf(zip_derived_cl32337, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ X0 @
% 104.97/15.78 (multiply @
% 104.97/15.78 (left_inverse @ (multiply @ X2 @ (left_inverse @ X1))) @ X1))
% 104.97/15.78 = (left_inverse @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @
% 104.97/15.78 (multiply @ X2 @
% 104.97/15.78 (multiply @ (left_inverse @ X1) @ (left_inverse @ X0))))))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl9435, zip_derived_cl17454])).
% 104.97/15.78 thf(zip_derived_cl10052, plain,
% 104.97/15.78 (![X0 : $i]: ((X0) = (left_inverse @ (left_inverse @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl10038, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl12153, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X0) @ (left_inverse @ X1))
% 104.97/15.78 = (left_inverse @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl12014, zip_derived_cl11972])).
% 104.97/15.78 thf(zip_derived_cl12249, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @ (left_inverse @ X1))
% 104.97/15.78 = (left_inverse @ (multiply @ X1 @ (left_inverse @ X0))))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl10052, zip_derived_cl12153])).
% 104.97/15.78 thf(zip_derived_cl9529, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (multiply @ X0 @ X1) @ X0)
% 104.97/15.78 = (multiply @ X0 @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl9493, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl12153, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X0) @ (left_inverse @ X1))
% 104.97/15.78 = (left_inverse @ (multiply @ X1 @ X0)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl12014, zip_derived_cl11972])).
% 104.97/15.78 thf(zip_derived_cl12157, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ (left_inverse @ X0) @ X1)
% 104.97/15.78 = (left_inverse @ (multiply @ (left_inverse @ X1) @ X0)))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl12014, zip_derived_cl11973])).
% 104.97/15.78 thf(zip_derived_cl12249, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i]:
% 104.97/15.78 ((multiply @ X0 @ (left_inverse @ X1))
% 104.97/15.78 = (left_inverse @ (multiply @ X1 @ (left_inverse @ X0))))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl10052, zip_derived_cl12153])).
% 104.97/15.78 thf(zip_derived_cl32430, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ X0 @
% 104.97/15.78 (multiply @ X1 @ (multiply @ (left_inverse @ X2) @ X1)))
% 104.97/15.78 = (multiply @
% 104.97/15.78 (multiply @ (multiply @ X0 @ X1) @ (left_inverse @ X2)) @ X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl32337, zip_derived_cl12249, zip_derived_cl9529,
% 104.97/15.78 zip_derived_cl12153, zip_derived_cl12157, zip_derived_cl12249])).
% 104.97/15.78 thf(zip_derived_cl60436, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ X2 @
% 104.97/15.78 (multiply @ X1 @
% 104.97/15.78 (multiply @ (left_inverse @ (left_inverse @ X0)) @ X1)))
% 104.97/15.78 = (multiply @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X1))),
% 104.97/15.78 inference('sup+', [status(thm)],
% 104.97/15.78 [zip_derived_cl10052, zip_derived_cl32430])).
% 104.97/15.78 thf(zip_derived_cl10052, plain,
% 104.97/15.78 (![X0 : $i]: ((X0) = (left_inverse @ (left_inverse @ X0)))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl10038, zip_derived_cl9381])).
% 104.97/15.78 thf(zip_derived_cl60612, plain,
% 104.97/15.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.97/15.78 ((multiply @ X2 @ (multiply @ X1 @ (multiply @ X0 @ X1)))
% 104.97/15.78 = (multiply @ (multiply @ (multiply @ X2 @ X1) @ X0) @ X1))),
% 104.97/15.78 inference('demod', [status(thm)],
% 104.97/15.78 [zip_derived_cl60436, zip_derived_cl10052])).
% 104.97/15.78 thf(zip_derived_cl61425, plain,
% 104.97/15.78 (((multiply @ a @ (multiply @ b @ (multiply @ c @ b)))
% 104.97/15.78 != (multiply @ a @ (multiply @ b @ (multiply @ c @ b))))),
% 104.97/15.78 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl60612])).
% 104.97/15.78 thf(zip_derived_cl61426, plain, ($false),
% 104.97/15.78 inference('simplify', [status(thm)], [zip_derived_cl61425])).
% 104.97/15.78
% 104.97/15.78 % SZS output end Refutation
% 104.97/15.78
% 104.97/15.78
% 104.97/15.78 % Terminating...
% 105.67/15.89 % Runner terminated.
% 105.67/15.90 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------