TSTP Solution File: GRP688-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP688-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.4UFzWdEQBR true
% Computer : n016.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 01:52:57 EDT 2023
% Result : Unsatisfiable 10.24s 3.07s
% Output : Refutation 10.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP688-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.4UFzWdEQBR true
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 23:38:45 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.18/0.33 % Python version: Python 3.6.8
% 0.18/0.34 % Running in FO mode
% 0.49/0.59 % Total configuration time : 435
% 0.49/0.59 % Estimated wc time : 1092
% 0.49/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.70/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.70/0.69 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.70/0.69 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.92/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.92/0.79 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.92/0.80 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.92/0.83 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 10.24/3.07 % Solved by fo/fo3_bce.sh.
% 10.24/3.07 % BCE start: 12
% 10.24/3.07 % BCE eliminated: 0
% 10.24/3.07 % PE start: 12
% 10.24/3.07 logic: eq
% 10.24/3.07 % PE eliminated: 0
% 10.24/3.07 % done 534 iterations in 2.283s
% 10.24/3.07 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 10.24/3.07 % SZS output start Refutation
% 10.24/3.07 thf(op_d_type, type, op_d: $i).
% 10.24/3.07 thf(ld_type, type, ld: $i > $i > $i).
% 10.24/3.07 thf(rd_type, type, rd: $i > $i > $i).
% 10.24/3.07 thf(mult_type, type, mult: $i > $i > $i).
% 10.24/3.07 thf(op_c_type, type, op_c: $i).
% 10.24/3.07 thf(i_type, type, i: $i > $i).
% 10.24/3.07 thf(unit_type, type, unit: $i).
% 10.24/3.07 thf(c10, axiom,
% 10.24/3.07 (( mult @ op_c @ ( mult @ op_c @ ( mult @ op_c @ op_c ) ) ) = ( unit ))).
% 10.24/3.07 thf(zip_derived_cl9, plain,
% 10.24/3.07 (((mult @ op_c @ (mult @ op_c @ (mult @ op_c @ op_c))) = (unit))),
% 10.24/3.07 inference('cnf', [status(esa)], [c10])).
% 10.24/3.07 thf(c08, axiom, (( mult @ ( i @ A ) @ ( mult @ A @ B ) ) = ( B ))).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl38, plain,
% 10.24/3.07 (((mult @ (i @ op_c) @ unit) = (mult @ op_c @ (mult @ op_c @ op_c)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl7])).
% 10.24/3.07 thf(c05, axiom, (( mult @ A @ unit ) = ( A ))).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl40, plain,
% 10.24/3.07 (((i @ op_c) = (mult @ op_c @ (mult @ op_c @ op_c)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl4])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl51, plain,
% 10.24/3.07 (((mult @ (i @ op_c) @ (i @ op_c)) = (mult @ op_c @ op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl7])).
% 10.24/3.07 thf(c09, axiom,
% 10.24/3.07 (( i @ ( mult @ A @ B ) ) = ( mult @ ( i @ A ) @ ( i @ B ) ))).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl221, plain,
% 10.24/3.07 (((i @ (mult @ op_c @ op_c)) = (mult @ op_c @ op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl8])).
% 10.24/3.07 thf(c11, axiom, (( mult @ op_d @ ( mult @ op_d @ op_d ) ) = ( unit ))).
% 10.24/3.07 thf(zip_derived_cl10, plain,
% 10.24/3.07 (((mult @ op_d @ (mult @ op_d @ op_d)) = (unit))),
% 10.24/3.07 inference('cnf', [status(esa)], [c11])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl39, plain,
% 10.24/3.07 (((mult @ (i @ op_d) @ unit) = (mult @ op_d @ op_d))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl7])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl41, plain, (((i @ op_d) = (mult @ op_d @ op_d))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl4])).
% 10.24/3.07 thf(c07, axiom,
% 10.24/3.07 (( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) ) =
% 10.24/3.07 ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C ))).
% 10.24/3.07 thf(zip_derived_cl6, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (mult @ X0 @ X2)))
% 10.24/3.07 = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ X2))),
% 10.24/3.07 inference('cnf', [status(esa)], [c07])).
% 10.24/3.07 thf(zip_derived_cl80, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((mult @ op_d @ (mult @ op_d @ (mult @ op_d @ X0)))
% 10.24/3.07 = (mult @ (mult @ op_d @ (i @ op_d)) @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl6])).
% 10.24/3.07 thf(zip_derived_cl10, plain,
% 10.24/3.07 (((mult @ op_d @ (mult @ op_d @ op_d)) = (unit))),
% 10.24/3.07 inference('cnf', [status(esa)], [c11])).
% 10.24/3.07 thf(zip_derived_cl41, plain, (((i @ op_d) = (mult @ op_d @ op_d))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl4])).
% 10.24/3.07 thf(zip_derived_cl45, plain, (((mult @ op_d @ (i @ op_d)) = (unit))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl41])).
% 10.24/3.07 thf(c06, axiom, (( mult @ unit @ A ) = ( A ))).
% 10.24/3.07 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c06])).
% 10.24/3.07 thf(zip_derived_cl89, plain,
% 10.24/3.07 (![X0 : $i]: ((mult @ op_d @ (mult @ op_d @ (mult @ op_d @ X0))) = (X0))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl80, zip_derived_cl45, zip_derived_cl5])).
% 10.24/3.07 thf(c02, axiom, (( ld @ A @ ( mult @ A @ B ) ) = ( B ))).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl104, plain,
% 10.24/3.07 (![X0 : $i]: ((ld @ op_d @ X0) = (mult @ op_d @ (mult @ op_d @ X0)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl31, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ (i @ X1)) @ X0) = (mult @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl7])).
% 10.24/3.07 thf(c04, axiom, (( rd @ ( mult @ A @ B ) @ B ) = ( A ))).
% 10.24/3.07 thf(zip_derived_cl3, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c04])).
% 10.24/3.07 thf(zip_derived_cl183, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X1 @ X0) @ X0) = (i @ (i @ X1)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl3, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c04])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl43, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ (i @ (i @ X1)) @ (i @ (mult @ X1 @ X0))) = (i @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl7])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl410, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (i @ (mult @ X1 @ X0))) = (i @ X0))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl411, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (i @ X0)) = (i @ (mult @ X1 @ X0)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl410, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl660, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ X0) = (i @ (mult @ X1 @ (i @ X0))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl411])).
% 10.24/3.07 thf(zip_derived_cl667, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((i @ (mult @ op_d @ (i @ X0))) = (mult @ op_d @ (mult @ op_d @ X0)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl104, zip_derived_cl660])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl2417, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((mult @ (i @ op_d) @ (i @ (mult @ op_d @ (i @ X0))))
% 10.24/3.07 = (mult @ op_d @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl667, zip_derived_cl7])).
% 10.24/3.07 thf(zip_derived_cl6001, plain,
% 10.24/3.07 (((mult @ (i @ op_d) @ (i @ (mult @ op_d @ (mult @ op_c @ op_c))))
% 10.24/3.07 = (mult @ op_d @ (mult @ op_c @ op_c)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl2417])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl3, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c04])).
% 10.24/3.07 thf(zip_derived_cl32, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (mult @ X1 @ X0)) = (i @ X1))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl249, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ (i @ X0) @ (i @ (mult @ X1 @ X0))) = (i @ (i @ X1)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl32])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl260, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (i @ X0) @ (i @ (mult @ X1 @ X0))) = (X1))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl249, zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl6056, plain,
% 10.24/3.07 (((rd @ (i @ (i @ (mult @ op_d @ (mult @ op_c @ op_c)))) @
% 10.24/3.07 (i @ (mult @ op_d @ (mult @ op_c @ op_c)))) = (i @ op_d))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6001, zip_derived_cl260])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl201, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X1 @ (i @ X0))) = (mult @ (i @ X1) @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl8])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl1818, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((ld @ (i @ X1) @ (i @ (mult @ X1 @ (i @ X0)))) = (X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl201, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl30, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ (i @ X1) @ X0) = (mult @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl3405, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((X0) = (mult @ X1 @ (i @ (mult @ X1 @ (i @ X0)))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl1818, zip_derived_cl30])).
% 10.24/3.07 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c06])).
% 10.24/3.07 thf(zip_derived_cl6, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (mult @ X0 @ X2)))
% 10.24/3.07 = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ X2))),
% 10.24/3.07 inference('cnf', [status(esa)], [c07])).
% 10.24/3.07 thf(zip_derived_cl74, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ unit @ (mult @ X0 @ X1)))
% 10.24/3.07 = (mult @ (mult @ X0 @ X0) @ X1))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 10.24/3.07 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c06])).
% 10.24/3.07 thf(zip_derived_cl85, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl5])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl2089, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((ld @ (mult @ X1 @ X1) @ (mult @ X1 @ (mult @ X1 @ X0))) = (X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl85, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl4706, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((ld @ (mult @ X1 @ X1) @ (mult @ X1 @ X0))
% 10.24/3.07 = (i @ (mult @ X1 @ (i @ X0))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl3405, zip_derived_cl2089])).
% 10.24/3.07 thf(zip_derived_cl5088, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((ld @ (mult @ X0 @ X0) @ X0) = (i @ (mult @ X0 @ (i @ unit))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl4706])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl34, plain, (![X0 : $i]: ((mult @ (i @ X0) @ X0) = (unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl7])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl139, plain, (((unit) = (i @ unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl4])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl5137, plain,
% 10.24/3.07 (![X0 : $i]: ((ld @ (mult @ X0 @ X0) @ X0) = (i @ X0))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl5088, zip_derived_cl139, zip_derived_cl4])).
% 10.24/3.07 thf(zip_derived_cl5205, plain,
% 10.24/3.07 (![X0 : $i]: ((ld @ (i @ (mult @ X0 @ X0)) @ (i @ X0)) = (i @ (i @ X0)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl5137])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl5215, plain,
% 10.24/3.07 (![X0 : $i]: ((ld @ (i @ (mult @ X0 @ X0)) @ (i @ X0)) = (X0))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl5205, zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl30, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ (i @ X1) @ X0) = (mult @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl5274, plain,
% 10.24/3.07 (![X0 : $i]: ((X0) = (mult @ (mult @ X0 @ X0) @ (i @ X0)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl5215, zip_derived_cl30])).
% 10.24/3.07 thf(zip_derived_cl3, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c04])).
% 10.24/3.07 thf(zip_derived_cl5333, plain,
% 10.24/3.07 (![X0 : $i]: ((rd @ X0 @ (i @ X0)) = (mult @ X0 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl5274, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl6089, plain,
% 10.24/3.07 (((mult @ (mult @ op_d @ (mult @ op_c @ op_c)) @
% 10.24/3.07 (mult @ op_d @ (mult @ op_c @ op_c))) = (i @ op_d))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl6056, zip_derived_cl196, zip_derived_cl5333])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl42, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((ld @ (i @ X1) @ (i @ (mult @ X1 @ X0))) = (i @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl6112, plain,
% 10.24/3.07 (((ld @ (i @ (mult @ op_d @ (mult @ op_c @ op_c))) @ (i @ (i @ op_d)))
% 10.24/3.07 = (i @ (mult @ op_d @ (mult @ op_c @ op_c))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6089, zip_derived_cl42])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl30, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ (i @ X1) @ X0) = (mult @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl6152, plain,
% 10.24/3.07 (((mult @ (mult @ op_d @ (mult @ op_c @ op_c)) @ op_d)
% 10.24/3.07 = (i @ (mult @ op_d @ (mult @ op_c @ op_c))))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl6112, zip_derived_cl196, zip_derived_cl30])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl3, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c04])).
% 10.24/3.07 thf(zip_derived_cl44, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ (i @ (mult @ X1 @ X0)) @ (i @ X0)) = (i @ X1))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl7365, plain,
% 10.24/3.07 (((rd @ (i @ (i @ (mult @ op_d @ (mult @ op_c @ op_c)))) @ (i @ op_d))
% 10.24/3.07 = (i @ (mult @ op_d @ (mult @ op_c @ op_c))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6152, zip_derived_cl44])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl34, plain, (![X0 : $i]: ((mult @ (i @ X0) @ X0) = (unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl7])).
% 10.24/3.07 thf(zip_derived_cl6, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (mult @ X0 @ X2)))
% 10.24/3.07 = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ X2))),
% 10.24/3.07 inference('cnf', [status(esa)], [c07])).
% 10.24/3.07 thf(zip_derived_cl3, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c04])).
% 10.24/3.07 thf(zip_derived_cl62, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((rd @ (mult @ X1 @ (mult @ X2 @ (mult @ X1 @ X0))) @ X0)
% 10.24/3.07 = (mult @ X1 @ (mult @ X2 @ X1)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl989, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ (mult @ X0 @ unit) @ X1)
% 10.24/3.07 = (mult @ X0 @ (mult @ (i @ (mult @ X0 @ X1)) @ X0)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl62])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl1029, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ X0 @ X1) = (mult @ X0 @ (mult @ (i @ (mult @ X0 @ X1)) @ X0)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl989, zip_derived_cl4])).
% 10.24/3.07 thf(zip_derived_cl201, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X1 @ (i @ X0))) = (mult @ (i @ X1) @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl8])).
% 10.24/3.07 thf(zip_derived_cl2187, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ X0 @ X1)
% 10.24/3.07 = (mult @ X0 @ (i @ (mult @ (mult @ X0 @ X1) @ (i @ X0)))))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl1029, zip_derived_cl201])).
% 10.24/3.07 thf(zip_derived_cl30, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ (i @ X1) @ X0) = (mult @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl17, plain, (![X0 : $i]: ((ld @ X0 @ X0) = (unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl155, plain,
% 10.24/3.07 (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl17])).
% 10.24/3.07 thf(c03, axiom, (( mult @ ( rd @ A @ B ) @ B ) = ( A ))).
% 10.24/3.07 thf(zip_derived_cl2, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (rd @ X0 @ X1) @ X1) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c03])).
% 10.24/3.07 thf(zip_derived_cl6, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (mult @ X0 @ X2)))
% 10.24/3.07 = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ X2))),
% 10.24/3.07 inference('cnf', [status(esa)], [c07])).
% 10.24/3.07 thf(zip_derived_cl73, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X2 @ (mult @ (rd @ X0 @ X2) @ (mult @ X2 @ X1)))
% 10.24/3.07 = (mult @ (mult @ X2 @ X0) @ X1))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl6])).
% 10.24/3.07 thf(zip_derived_cl1206, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ (rd @ X1 @ X0) @ unit))
% 10.24/3.07 = (mult @ (mult @ X0 @ X1) @ (i @ X0)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl73])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl1245, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (rd @ X1 @ X0)) = (mult @ (mult @ X0 @ X1) @ (i @ X0)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl1206, zip_derived_cl4])).
% 10.24/3.07 thf(zip_derived_cl2187, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ X0 @ X1)
% 10.24/3.07 = (mult @ X0 @ (i @ (mult @ (mult @ X0 @ X1) @ (i @ X0)))))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl1029, zip_derived_cl201])).
% 10.24/3.07 thf(zip_derived_cl2632, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (i @ (mult @ (mult @ X1 @ X0) @ (i @ X1)))))
% 10.24/3.07 = (mult @ (mult @ X0 @ X1) @ (i @ X0)))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl1245, zip_derived_cl2187])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl85, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl5])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl3405, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((X0) = (mult @ X1 @ (i @ (mult @ X1 @ (i @ X0)))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl1818, zip_derived_cl30])).
% 10.24/3.07 thf(zip_derived_cl7395, plain,
% 10.24/3.07 (((mult @ op_d @ (mult @ op_c @ (mult @ op_c @ op_d)))
% 10.24/3.07 = (i @ (mult @ op_d @ (mult @ op_c @ op_c))))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl7365, zip_derived_cl196, zip_derived_cl2187,
% 10.24/3.07 zip_derived_cl2632, zip_derived_cl7, zip_derived_cl196,
% 10.24/3.07 zip_derived_cl85, zip_derived_cl8, zip_derived_cl3405])).
% 10.24/3.07 thf(zip_derived_cl6089, plain,
% 10.24/3.07 (((mult @ (mult @ op_d @ (mult @ op_c @ op_c)) @
% 10.24/3.07 (mult @ op_d @ (mult @ op_c @ op_c))) = (i @ op_d))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl6056, zip_derived_cl196, zip_derived_cl5333])).
% 10.24/3.07 thf(zip_derived_cl44, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ (i @ (mult @ X1 @ X0)) @ (i @ X0)) = (i @ X1))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl6113, plain,
% 10.24/3.07 (((rd @ (i @ (i @ op_d)) @ (i @ (mult @ op_d @ (mult @ op_c @ op_c))))
% 10.24/3.07 = (i @ (mult @ op_d @ (mult @ op_c @ op_c))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6089, zip_derived_cl44])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl2187, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ X0 @ X1)
% 10.24/3.07 = (mult @ X0 @ (i @ (mult @ (mult @ X0 @ X1) @ (i @ X0)))))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl1029, zip_derived_cl201])).
% 10.24/3.07 thf(zip_derived_cl221, plain,
% 10.24/3.07 (((i @ (mult @ op_c @ op_c)) = (mult @ op_c @ op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl8])).
% 10.24/3.07 thf(zip_derived_cl3405, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((X0) = (mult @ X1 @ (i @ (mult @ X1 @ (i @ X0)))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl1818, zip_derived_cl30])).
% 10.24/3.07 thf(zip_derived_cl3816, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((mult @ op_c @ op_c)
% 10.24/3.07 = (mult @ X0 @ (i @ (mult @ X0 @ (mult @ op_c @ op_c)))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl3405])).
% 10.24/3.07 thf(zip_derived_cl85, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl5])).
% 10.24/3.07 thf(zip_derived_cl221, plain,
% 10.24/3.07 (((i @ (mult @ op_c @ op_c)) = (mult @ op_c @ op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl8])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl228, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((i @ (mult @ (mult @ op_c @ op_c) @ X0))
% 10.24/3.07 = (mult @ (mult @ op_c @ op_c) @ (i @ X0)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl8])).
% 10.24/3.07 thf(zip_derived_cl85, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl5])).
% 10.24/3.07 thf(zip_derived_cl85, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X0 @ X1)) = (mult @ (mult @ X0 @ X0) @ X1))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl5])).
% 10.24/3.07 thf(zip_derived_cl3124, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((i @ (mult @ op_c @ (mult @ op_c @ X0)))
% 10.24/3.07 = (mult @ op_c @ (mult @ op_c @ (i @ X0))))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl228, zip_derived_cl85, zip_derived_cl85])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl6153, plain,
% 10.24/3.07 (((mult @ op_d @ (mult @ op_c @ (mult @ op_c @ op_d)))
% 10.24/3.07 = (i @ (mult @ op_d @ (mult @ op_c @ op_c))))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl6113, zip_derived_cl196, zip_derived_cl2187,
% 10.24/3.07 zip_derived_cl3816, zip_derived_cl85, zip_derived_cl3124,
% 10.24/3.07 zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl2089, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((ld @ (mult @ X1 @ X1) @ (mult @ X1 @ (mult @ X1 @ X0))) = (X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl85, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl7432, plain,
% 10.24/3.07 (((ld @ (mult @ op_d @ op_d) @
% 10.24/3.07 (mult @ op_d @ (i @ (mult @ op_d @ (mult @ op_c @ op_c)))))
% 10.24/3.07 = (mult @ op_c @ (mult @ op_c @ op_d)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6153, zip_derived_cl2089])).
% 10.24/3.07 thf(zip_derived_cl41, plain, (((i @ op_d) = (mult @ op_d @ op_d))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl4])).
% 10.24/3.07 thf(zip_derived_cl3816, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((mult @ op_c @ op_c)
% 10.24/3.07 = (mult @ X0 @ (i @ (mult @ X0 @ (mult @ op_c @ op_c)))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl3405])).
% 10.24/3.07 thf(zip_derived_cl30, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ (i @ X1) @ X0) = (mult @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl7461, plain,
% 10.24/3.07 (((mult @ op_d @ (mult @ op_c @ op_c))
% 10.24/3.07 = (mult @ op_c @ (mult @ op_c @ op_d)))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl7432, zip_derived_cl41, zip_derived_cl3816,
% 10.24/3.07 zip_derived_cl30])).
% 10.24/3.07 thf(zip_derived_cl7771, plain,
% 10.24/3.07 (((mult @ op_d @ (mult @ op_c @ (mult @ op_c @ op_d)))
% 10.24/3.07 = (i @ (mult @ op_c @ (mult @ op_c @ op_d))))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl7395, zip_derived_cl7461])).
% 10.24/3.07 thf(zip_derived_cl6, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (mult @ X0 @ X2)))
% 10.24/3.07 = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ X2))),
% 10.24/3.07 inference('cnf', [status(esa)], [c07])).
% 10.24/3.07 thf(zip_derived_cl32, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (mult @ X1 @ X0)) = (i @ X1))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl243, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((rd @ X0 @ (mult @ X1 @ (mult @ X2 @ (mult @ X1 @ X0))))
% 10.24/3.07 = (i @ (mult @ X1 @ (mult @ X2 @ X1))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl32])).
% 10.24/3.07 thf(zip_derived_cl7806, plain,
% 10.24/3.07 (((rd @ (mult @ op_c @ op_d) @
% 10.24/3.07 (mult @ op_c @ (i @ (mult @ op_c @ (mult @ op_c @ op_d)))))
% 10.24/3.07 = (i @ (mult @ op_c @ (mult @ op_d @ op_c))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7771, zip_derived_cl243])).
% 10.24/3.07 thf(zip_derived_cl410, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (i @ (mult @ X1 @ X0))) = (i @ X0))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl5333, plain,
% 10.24/3.07 (![X0 : $i]: ((rd @ X0 @ (i @ X0)) = (mult @ X0 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl5274, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl7836, plain,
% 10.24/3.07 (((mult @ (mult @ op_c @ op_d) @ (mult @ op_c @ op_d))
% 10.24/3.07 = (i @ (mult @ op_c @ (mult @ op_d @ op_c))))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl7806, zip_derived_cl410, zip_derived_cl5333])).
% 10.24/3.07 thf(zip_derived_cl42, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((ld @ (i @ X1) @ (i @ (mult @ X1 @ X0))) = (i @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl8237, plain,
% 10.24/3.07 (((ld @ (i @ (mult @ op_c @ op_d)) @
% 10.24/3.07 (i @ (i @ (mult @ op_c @ (mult @ op_d @ op_c)))))
% 10.24/3.07 = (i @ (mult @ op_c @ op_d)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7836, zip_derived_cl42])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl30, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ (i @ X1) @ X0) = (mult @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl8284, plain,
% 10.24/3.07 (((mult @ (mult @ op_c @ op_d) @ (mult @ op_c @ (mult @ op_d @ op_c)))
% 10.24/3.07 = (i @ (mult @ op_c @ op_d)))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl8237, zip_derived_cl196, zip_derived_cl30])).
% 10.24/3.07 thf(zip_derived_cl62, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((rd @ (mult @ X1 @ (mult @ X2 @ (mult @ X1 @ X0))) @ X0)
% 10.24/3.07 = (mult @ X1 @ (mult @ X2 @ X1)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl9001, plain,
% 10.24/3.07 (((rd @ (mult @ op_c @ (i @ (mult @ op_c @ op_d))) @ (mult @ op_d @ op_c))
% 10.24/3.07 = (mult @ op_c @ (mult @ (mult @ op_c @ op_d) @ op_c)))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8284, zip_derived_cl62])).
% 10.24/3.07 thf(zip_derived_cl410, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (i @ (mult @ X1 @ X0))) = (i @ X0))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl2187, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((rd @ X0 @ X1)
% 10.24/3.07 = (mult @ X0 @ (i @ (mult @ (mult @ X0 @ X1) @ (i @ X0)))))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl1029, zip_derived_cl201])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl8, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((i @ (mult @ X0 @ X1)) = (mult @ (i @ X0) @ (i @ X1)))),
% 10.24/3.07 inference('cnf', [status(esa)], [c09])).
% 10.24/3.07 thf(zip_derived_cl9033, plain,
% 10.24/3.07 (((i @ (mult @ op_d @ (mult @ op_c @ op_d)))
% 10.24/3.07 = (mult @ op_c @ (mult @ (mult @ op_c @ op_d) @ op_c)))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl9001, zip_derived_cl410, zip_derived_cl2187,
% 10.24/3.07 zip_derived_cl7, zip_derived_cl196, zip_derived_cl8])).
% 10.24/3.07 thf(zip_derived_cl221, plain,
% 10.24/3.07 (((i @ (mult @ op_c @ op_c)) = (mult @ op_c @ op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl8])).
% 10.24/3.07 thf(zip_derived_cl34, plain, (![X0 : $i]: ((mult @ (i @ X0) @ X0) = (unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl7])).
% 10.24/3.07 thf(zip_derived_cl229, plain,
% 10.24/3.07 (((mult @ (mult @ op_c @ op_c) @ (mult @ op_c @ op_c)) = (unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl34])).
% 10.24/3.07 thf(zip_derived_cl6, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (mult @ X0 @ X2)))
% 10.24/3.07 = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ X2))),
% 10.24/3.07 inference('cnf', [status(esa)], [c07])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl59, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((ld @ (mult @ X1 @ (mult @ X2 @ X1)) @
% 10.24/3.07 (mult @ X1 @ (mult @ X2 @ (mult @ X1 @ X0)))) = (X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl557, plain,
% 10.24/3.07 (((ld @ (mult @ op_c @ (mult @ (mult @ op_c @ op_c) @ op_c)) @
% 10.24/3.07 (mult @ op_c @ unit)) = (op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl229, zip_derived_cl59])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(c01, axiom, (( mult @ A @ ( ld @ A @ B ) ) = ( B ))).
% 10.24/3.07 thf(zip_derived_cl0, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (ld @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c01])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl33, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ X0) = (ld @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl7])).
% 10.24/3.07 thf(zip_derived_cl616, plain,
% 10.24/3.07 (((mult @ (i @ (mult @ op_c @ (mult @ (mult @ op_c @ op_c) @ op_c))) @
% 10.24/3.07 op_c) = (op_c))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl557, zip_derived_cl4, zip_derived_cl33])).
% 10.24/3.07 thf(zip_derived_cl32, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ X0 @ (mult @ X1 @ X0)) = (i @ X1))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl748, plain,
% 10.24/3.07 (((rd @ op_c @ op_c)
% 10.24/3.07 = (i @ (i @ (mult @ op_c @ (mult @ (mult @ op_c @ op_c) @ op_c)))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl616, zip_derived_cl32])).
% 10.24/3.07 thf(zip_derived_cl5, plain, (![X0 : $i]: ((mult @ unit @ X0) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c06])).
% 10.24/3.07 thf(zip_derived_cl3, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((rd @ (mult @ X0 @ X1) @ X1) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c04])).
% 10.24/3.07 thf(zip_derived_cl27, plain, (![X0 : $i]: ((rd @ X0 @ X0) = (unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl757, plain,
% 10.24/3.07 (((unit) = (mult @ op_c @ (mult @ (mult @ op_c @ op_c) @ op_c)))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl748, zip_derived_cl27, zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl6, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (mult @ X0 @ X2)))
% 10.24/3.07 = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ X2))),
% 10.24/3.07 inference('cnf', [status(esa)], [c07])).
% 10.24/3.07 thf(zip_derived_cl7, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ (i @ X1) @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c08])).
% 10.24/3.07 thf(zip_derived_cl61, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ (i @ (mult @ X1 @ (mult @ X2 @ X1))) @
% 10.24/3.07 (mult @ X1 @ (mult @ X2 @ (mult @ X1 @ X0)))) = (X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl7])).
% 10.24/3.07 thf(zip_derived_cl924, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((mult @ (i @ (mult @ op_c @ (mult @ X0 @ op_c))) @
% 10.24/3.07 (mult @ op_c @ (mult @ X0 @ unit)))
% 10.24/3.07 = (mult @ (mult @ op_c @ op_c) @ op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl757, zip_derived_cl61])).
% 10.24/3.07 thf(zip_derived_cl4, plain, (![X0 : $i]: ((mult @ X0 @ unit) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c05])).
% 10.24/3.07 thf(zip_derived_cl940, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((mult @ (i @ (mult @ op_c @ (mult @ X0 @ op_c))) @ (mult @ op_c @ X0))
% 10.24/3.07 = (mult @ (mult @ op_c @ op_c) @ op_c))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl924, zip_derived_cl4])).
% 10.24/3.07 thf(zip_derived_cl757, plain,
% 10.24/3.07 (((unit) = (mult @ op_c @ (mult @ (mult @ op_c @ op_c) @ op_c)))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl748, zip_derived_cl27, zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl917, plain,
% 10.24/3.07 (((ld @ op_c @ unit) = (mult @ (mult @ op_c @ op_c) @ op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl757, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl155, plain,
% 10.24/3.07 (![X0 : $i]: ((mult @ X0 @ (i @ X0)) = (unit))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl17])).
% 10.24/3.07 thf(zip_derived_cl1, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ X1 @ (mult @ X1 @ X0)) = (X0))),
% 10.24/3.07 inference('cnf', [status(esa)], [c02])).
% 10.24/3.07 thf(zip_derived_cl165, plain, (![X0 : $i]: ((ld @ X0 @ unit) = (i @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl934, plain,
% 10.24/3.07 (((i @ op_c) = (mult @ (mult @ op_c @ op_c) @ op_c))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl917, zip_derived_cl165])).
% 10.24/3.07 thf(zip_derived_cl3449, plain,
% 10.24/3.07 (![X0 : $i]:
% 10.24/3.07 ((mult @ (i @ (mult @ op_c @ (mult @ X0 @ op_c))) @ (mult @ op_c @ X0))
% 10.24/3.07 = (i @ op_c))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl940, zip_derived_cl934])).
% 10.24/3.07 thf(zip_derived_cl9100, plain,
% 10.24/3.07 (((mult @ (i @ (i @ (mult @ op_d @ (mult @ op_c @ op_d)))) @
% 10.24/3.07 (mult @ op_c @ (mult @ op_c @ op_d))) = (i @ op_c))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl9033, zip_derived_cl3449])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl6, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.24/3.07 ((mult @ X0 @ (mult @ X1 @ (mult @ X0 @ X2)))
% 10.24/3.07 = (mult @ (mult @ X0 @ (mult @ X1 @ X0)) @ X2))),
% 10.24/3.07 inference('cnf', [status(esa)], [c07])).
% 10.24/3.07 thf(zip_derived_cl7771, plain,
% 10.24/3.07 (((mult @ op_d @ (mult @ op_c @ (mult @ op_c @ op_d)))
% 10.24/3.07 = (i @ (mult @ op_c @ (mult @ op_c @ op_d))))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl7395, zip_derived_cl7461])).
% 10.24/3.07 thf(zip_derived_cl410, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((mult @ X1 @ (i @ (mult @ X1 @ X0))) = (i @ X0))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl196])).
% 10.24/3.07 thf(zip_derived_cl9127, plain,
% 10.24/3.07 (((mult @ op_d @ (i @ (mult @ op_c @ op_d))) = (i @ op_c))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl9100, zip_derived_cl196, zip_derived_cl6,
% 10.24/3.07 zip_derived_cl7771, zip_derived_cl410])).
% 10.24/3.07 thf(zip_derived_cl42, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]:
% 10.24/3.07 ((ld @ (i @ X1) @ (i @ (mult @ X1 @ X0))) = (i @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl9197, plain,
% 10.24/3.07 (((ld @ (i @ op_d) @ (i @ (i @ op_c))) = (i @ (i @ (mult @ op_c @ op_d))))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl9127, zip_derived_cl42])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl30, plain,
% 10.24/3.07 (![X0 : $i, X1 : $i]: ((ld @ (i @ X1) @ X0) = (mult @ X1 @ X0))),
% 10.24/3.07 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 10.24/3.07 thf(zip_derived_cl196, plain, (![X1 : $i]: ((X1) = (i @ (i @ X1)))),
% 10.24/3.07 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl3])).
% 10.24/3.07 thf(zip_derived_cl9242, plain,
% 10.24/3.07 (((mult @ op_d @ op_c) = (mult @ op_c @ op_d))),
% 10.24/3.07 inference('demod', [status(thm)],
% 10.24/3.07 [zip_derived_cl9197, zip_derived_cl196, zip_derived_cl30,
% 10.24/3.07 zip_derived_cl196])).
% 10.24/3.07 thf(goals, conjecture, (( mult @ op_c @ op_d ) = ( mult @ op_d @ op_c ))).
% 10.24/3.07 thf(zf_stmt_0, negated_conjecture,
% 10.24/3.07 (( mult @ op_c @ op_d ) != ( mult @ op_d @ op_c )),
% 10.24/3.07 inference('cnf.neg', [status(esa)], [goals])).
% 10.24/3.07 thf(zip_derived_cl11, plain,
% 10.24/3.07 (((mult @ op_c @ op_d) != (mult @ op_d @ op_c))),
% 10.24/3.07 inference('cnf', [status(esa)], [zf_stmt_0])).
% 10.24/3.07 thf(zip_derived_cl9243, plain, ($false),
% 10.24/3.07 inference('simplify_reflect-', [status(thm)],
% 10.24/3.07 [zip_derived_cl9242, zip_derived_cl11])).
% 10.24/3.07
% 10.24/3.07 % SZS output end Refutation
% 10.24/3.07
% 10.24/3.07
% 10.24/3.07 % Terminating...
% 11.30/3.32 % Runner terminated.
% 11.30/3.34 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------