%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : RNG130-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.kX5uO7F2i3 true
% Computer : n021.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 : Tue May 5 06:50:12 PM UTC 2026
% Result : Unsatisfiable 16.17s 2.95s
% Output : Refutation 16.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG130-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.kX5uO7F2i3 true
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 05:11:10 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 % Running portfolio for 300 s
% 0.16/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.34 % Number of cores: 8
% 0.16/0.35 % Python version: Python 3.6.8
% 0.16/0.35 % Running in FO mode
% 0.53/0.65 % Total configuration time : 435
% 0.53/0.65 % Estimated wc time : 1092
% 0.53/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 16.17/2.95 % Solved by fo/fo7.sh.
% 16.17/2.95 % done 761 iterations in 2.156s
% 16.17/2.95 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 16.17/2.95 % SZS output start Refutation
% 16.17/2.95 thf(a_type, type, a: $i).
% 16.17/2.95 thf(c_type, type, c: $i).
% 16.17/2.95 thf(zero_type, type, zero: $i).
% 16.17/2.95 thf(n_type, type, n: $i).
% 16.17/2.95 thf(plus_type, type, plus: $i > $i > $i).
% 16.17/2.95 thf(minus_type, type, minus: $i > $i).
% 16.17/2.95 thf(times_type, type, times: $i > $i > $i).
% 16.17/2.95 thf(d_type, type, d: $i).
% 16.17/2.95 thf(b_type, type, b: $i).
% 16.17/2.95 thf(sq_type, type, sq: $i > $i).
% 16.17/2.95 thf(goals, conjecture,
% 16.17/2.95 (( times @
% 16.17/2.95 ( plus @ ( sq @ a ) @ ( times @ n @ ( sq @ b ) ) ) @
% 16.17/2.95 ( plus @ ( sq @ c ) @ ( times @ n @ ( sq @ d ) ) ) ) =
% 16.17/2.95 ( plus @
% 16.17/2.95 ( sq @
% 16.17/2.95 ( plus @
% 16.17/2.95 ( times @ a @ c ) @ ( times @ ( minus @ n ) @ ( times @ b @ d ) ) ) ) @
% 16.17/2.95 ( times @ n @ ( sq @ ( plus @ ( times @ a @ d ) @ ( times @ b @ c ) ) ) ) ))).
% 16.17/2.95 thf(zf_stmt_0, negated_conjecture,
% 16.17/2.95 (( times @
% 16.17/2.95 ( plus @ ( sq @ a ) @ ( times @ n @ ( sq @ b ) ) ) @
% 16.17/2.95 ( plus @ ( sq @ c ) @ ( times @ n @ ( sq @ d ) ) ) ) !=
% 16.17/2.95 ( plus @
% 16.17/2.95 ( sq @
% 16.17/2.95 ( plus @
% 16.17/2.95 ( times @ a @ c ) @ ( times @ ( minus @ n ) @ ( times @ b @ d ) ) ) ) @
% 16.17/2.95 ( times @ n @ ( sq @ ( plus @ ( times @ a @ d ) @ ( times @ b @ c ) ) ) ) )),
% 16.17/2.95 inference('cnf.neg', [status(esa)], [goals])).
% 16.17/2.95 thf(zip_derived_cl9, plain,
% 16.17/2.95 (((times @ (plus @ (sq @ a) @ (times @ n @ (sq @ b))) @
% 16.17/2.95 (plus @ (sq @ c) @ (times @ n @ (sq @ d))))
% 16.17/2.95 != (plus @
% 16.17/2.95 (sq @
% 16.17/2.95 (plus @ (times @ a @ c) @ (times @ (minus @ n) @ (times @ b @ d)))) @
% 16.17/2.95 (times @ n @ (sq @ (plus @ (times @ a @ d) @ (times @ b @ c))))))),
% 16.17/2.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.17/2.95 thf(square, axiom, (( sq @ X ) = ( times @ X @ X ))).
% 16.17/2.95 thf(zip_derived_cl6, plain, (![X0 : $i]: ((sq @ X0) = (times @ X0 @ X0))),
% 16.17/2.95 inference('cnf', [status(esa)], [square])).
% 16.17/2.95 thf(zip_derived_cl6, plain, (![X0 : $i]: ((sq @ X0) = (times @ X0 @ X0))),
% 16.17/2.95 inference('cnf', [status(esa)], [square])).
% 16.17/2.95 thf(zip_derived_cl6, plain, (![X0 : $i]: ((sq @ X0) = (times @ X0 @ X0))),
% 16.17/2.95 inference('cnf', [status(esa)], [square])).
% 16.17/2.95 thf(zip_derived_cl6, plain, (![X0 : $i]: ((sq @ X0) = (times @ X0 @ X0))),
% 16.17/2.95 inference('cnf', [status(esa)], [square])).
% 16.17/2.95 thf(zip_derived_cl6, plain, (![X0 : $i]: ((sq @ X0) = (times @ X0 @ X0))),
% 16.17/2.95 inference('cnf', [status(esa)], [square])).
% 16.17/2.95 thf(zip_derived_cl6, plain, (![X0 : $i]: ((sq @ X0) = (times @ X0 @ X0))),
% 16.17/2.95 inference('cnf', [status(esa)], [square])).
% 16.17/2.95 thf(zip_derived_cl10, plain,
% 16.17/2.95 (((times @ (plus @ (times @ a @ a) @ (times @ n @ (times @ b @ b))) @
% 16.17/2.95 (plus @ (times @ c @ c) @ (times @ n @ (times @ d @ d))))
% 16.17/2.95 != (plus @
% 16.17/2.95 (times @
% 16.17/2.95 (plus @ (times @ a @ c) @ (times @ (minus @ n) @ (times @ b @ d))) @
% 16.17/2.95 (plus @ (times @ a @ c) @ (times @ (minus @ n) @ (times @ b @ d)))) @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ (plus @ (times @ a @ d) @ (times @ b @ c)) @
% 16.17/2.95 (plus @ (times @ a @ d) @ (times @ b @ c))))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl9, zip_derived_cl6, zip_derived_cl6,
% 16.17/2.95 zip_derived_cl6, zip_derived_cl6, zip_derived_cl6,
% 16.17/2.95 zip_derived_cl6])).
% 16.17/2.95 thf(plus_comm, axiom, (( plus @ X @ Y ) = ( plus @ Y @ X ))).
% 16.17/2.95 thf(zip_derived_cl0, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ X0) = (plus @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_comm])).
% 16.17/2.95 thf(zip_derived_cl0, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ X0) = (plus @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_comm])).
% 16.17/2.95 thf(zip_derived_cl0, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ X0) = (plus @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_comm])).
% 16.17/2.95 thf(zip_derived_cl13, plain,
% 16.17/2.95 (((times @ (plus @ (times @ a @ a) @ (times @ n @ (times @ b @ b))) @
% 16.17/2.95 (plus @ (times @ c @ c) @ (times @ n @ (times @ d @ d))))
% 16.17/2.95 != (plus @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ (plus @ (times @ b @ c) @ (times @ a @ d)) @
% 16.17/2.95 (plus @ (times @ b @ c) @ (times @ a @ d)))) @
% 16.17/2.95 (times @
% 16.17/2.95 (plus @ (times @ a @ c) @ (times @ (minus @ n) @ (times @ b @ d))) @
% 16.17/2.95 (plus @ (times @ a @ c) @ (times @ (minus @ n) @ (times @ b @ d))))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl10, zip_derived_cl0, zip_derived_cl0,
% 16.17/2.95 zip_derived_cl0])).
% 16.17/2.95 thf(distrib1, axiom,
% 16.17/2.95 (( times @ X @ ( plus @ Y @ Z ) ) =
% 16.17/2.95 ( plus @ ( times @ X @ Y ) @ ( times @ X @ Z ) ))).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(times_com, axiom, (( times @ X @ Y ) = ( times @ Y @ X ))).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(times_assoc, axiom,
% 16.17/2.95 (( times @ X @ ( times @ Y @ Z ) ) = ( times @ ( times @ X @ Y ) @ Z ))).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(plus_assoc, axiom,
% 16.17/2.95 (( plus @ X @ ( plus @ Y @ Z ) ) = ( plus @ ( plus @ X @ Y ) @ Z ))).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl1029, plain,
% 16.17/2.95 (((plus @
% 16.17/2.95 (times @ (plus @ (times @ a @ a) @ (times @ n @ (times @ b @ b))) @
% 16.17/2.95 (times @ c @ c)) @
% 16.17/2.95 (times @ (plus @ (times @ a @ a) @ (times @ n @ (times @ b @ b))) @
% 16.17/2.95 (times @ n @ (times @ d @ d))))
% 16.17/2.95 != (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ c @ (times @ b @ c)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ c @ (times @ a @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ b @ (times @ c @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ d @ (times @ a @ d)))) @
% 16.17/2.95 (plus @ (times @ a @ (times @ c @ (times @ a @ c))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ a @
% 16.17/2.95 (times @ c @ (times @ (minus @ n) @ (times @ b @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ (minus @ n) @
% 16.17/2.95 (times @ b @ (times @ a @ (times @ c @ d)))) @
% 16.17/2.95 (times @ (minus @ n) @
% 16.17/2.95 (times @ b @
% 16.17/2.95 (times @ d @ (times @ (minus @ n) @ (times @ b @ d)))))))))))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl13, zip_derived_cl7, zip_derived_cl7,
% 16.17/2.95 zip_derived_cl5, zip_derived_cl4, zip_derived_cl7,
% 16.17/2.95 zip_derived_cl7, zip_derived_cl5, zip_derived_cl4,
% 16.17/2.95 zip_derived_cl7, zip_derived_cl5, zip_derived_cl4,
% 16.17/2.95 zip_derived_cl7, zip_derived_cl1, zip_derived_cl7,
% 16.17/2.95 zip_derived_cl7, zip_derived_cl7, zip_derived_cl7,
% 16.17/2.95 zip_derived_cl5, zip_derived_cl4, zip_derived_cl7,
% 16.17/2.95 zip_derived_cl7, zip_derived_cl5, zip_derived_cl4,
% 16.17/2.95 zip_derived_cl4, zip_derived_cl7, zip_derived_cl5,
% 16.17/2.95 zip_derived_cl4, zip_derived_cl7, zip_derived_cl7,
% 16.17/2.95 zip_derived_cl1, zip_derived_cl1, zip_derived_cl1,
% 16.17/2.95 zip_derived_cl1])).
% 16.17/2.95 thf(distrib2, axiom,
% 16.17/2.95 (( times @ ( plus @ X @ Y ) @ Z ) =
% 16.17/2.95 ( plus @ ( times @ X @ Z ) @ ( times @ Y @ Z ) ))).
% 16.17/2.95 thf(zip_derived_cl8, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ (plus @ X0 @ X2) @ X1)
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X2 @ X1)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib2])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl8, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ (plus @ X0 @ X2) @ X1)
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X2 @ X1)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib2])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl1195, plain,
% 16.17/2.95 (((plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @ (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @ (times @ a @ (times @ a @ (times @ n @ (times @ d @ d)))) @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ b @ (times @ b @ (times @ n @ (times @ d @ d))))))))
% 16.17/2.95 != (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ c @ (times @ b @ c)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ c @ (times @ a @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ b @ (times @ c @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ d @ (times @ a @ d)))) @
% 16.17/2.95 (plus @ (times @ a @ (times @ c @ (times @ a @ c))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ a @
% 16.17/2.95 (times @ c @ (times @ (minus @ n) @ (times @ b @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ (minus @ n) @
% 16.17/2.95 (times @ b @ (times @ a @ (times @ c @ d)))) @
% 16.17/2.95 (times @ (minus @ n) @
% 16.17/2.95 (times @ b @
% 16.17/2.95 (times @ d @ (times @ (minus @ n) @ (times @ b @ d)))))))))))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl1029, zip_derived_cl8, zip_derived_cl4,
% 16.17/2.95 zip_derived_cl4, zip_derived_cl4, zip_derived_cl8,
% 16.17/2.95 zip_derived_cl4, zip_derived_cl4, zip_derived_cl4,
% 16.17/2.95 zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl109, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X0 @ X2)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl109, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X0 @ X2)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl109, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X0 @ X2)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl1288, plain,
% 16.17/2.95 (((plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @ (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @ (times @ a @ (times @ a @ (times @ n @ (times @ d @ d)))) @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ b @ (times @ b @ (times @ n @ (times @ d @ d))))))))
% 16.17/2.95 != (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ c @ (times @ a @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ b @ (times @ c @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ a @ (times @ d @ d)))) @
% 16.17/2.95 (plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ a @
% 16.17/2.95 (times @ c @ (times @ (minus @ n) @ (times @ b @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ (minus @ n) @
% 16.17/2.95 (times @ b @ (times @ a @ (times @ c @ d)))) @
% 16.17/2.95 (times @ (minus @ n) @
% 16.17/2.95 (times @ b @
% 16.17/2.95 (times @ d @ (times @ (minus @ n) @ (times @ b @ d)))))))))))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl1195, zip_derived_cl109, zip_derived_cl109,
% 16.17/2.95 zip_derived_cl109])).
% 16.17/2.95 thf(zip_derived_cl0, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ X0) = (plus @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_comm])).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl23, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X1 @ X0) @ X2))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl273, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ X2 @ X0)) = (plus @ X2 @ (plus @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl1541, plain,
% 16.17/2.95 (((plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @ (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @ (times @ a @ (times @ a @ (times @ n @ (times @ d @ d)))) @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ b @ (times @ b @ (times @ n @ (times @ d @ d))))))))
% 16.17/2.95 != (plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ b @ (times @ c @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ (minus @ n) @
% 16.17/2.95 (times @ b @ (times @ a @ (times @ c @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ c @ (times @ a @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ a @
% 16.17/2.95 (times @ c @ (times @ (minus @ n) @ (times @ b @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ a @ (times @ d @ d)))) @
% 16.17/2.95 (times @ (minus @ n) @
% 16.17/2.95 (times @ b @
% 16.17/2.95 (times @ d @ (times @ (minus @ n) @ (times @ b @ d)))))))))))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl1288, zip_derived_cl273, zip_derived_cl273,
% 16.17/2.95 zip_derived_cl273, zip_derived_cl273, zip_derived_cl273,
% 16.17/2.95 zip_derived_cl273, zip_derived_cl273, zip_derived_cl273,
% 16.17/2.95 zip_derived_cl273])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(plus_inv, axiom, (( plus @ X @ ( minus @ X ) ) = ( zero ))).
% 16.17/2.95 thf(zip_derived_cl3, plain,
% 16.17/2.95 (![X0 : $i]: ((plus @ X0 @ (minus @ X0)) = (zero))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_inv])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl1044, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((times @ X1 @ zero)
% 16.17/2.95 = (plus @ (times @ X1 @ X0) @ (times @ X1 @ (minus @ X0))))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl7])).
% 16.17/2.95 thf(plus_zero, axiom, (( plus @ zero @ X ) = ( X ))).
% 16.17/2.95 thf(zip_derived_cl2, plain, (![X0 : $i]: ((plus @ zero @ X0) = (X0))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_zero])).
% 16.17/2.95 thf(zip_derived_cl0, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ X0) = (plus @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_comm])).
% 16.17/2.95 thf(zip_derived_cl14, plain, (![X0 : $i]: ((X0) = (plus @ X0 @ zero))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 16.17/2.95 thf(zip_derived_cl7, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (plus @ X1 @ X2))
% 16.17/2.95 = (plus @ (times @ X0 @ X1) @ (times @ X0 @ X2)))),
% 16.17/2.95 inference('cnf', [status(esa)], [distrib1])).
% 16.17/2.95 thf(zip_derived_cl1043, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((times @ X1 @ X0) = (plus @ (times @ X1 @ X0) @ (times @ X1 @ zero)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl7])).
% 16.17/2.95 thf(zip_derived_cl3, plain,
% 16.17/2.95 (![X0 : $i]: ((plus @ X0 @ (minus @ X0)) = (zero))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_inv])).
% 16.17/2.95 thf(zip_derived_cl3, plain,
% 16.17/2.95 (![X0 : $i]: ((plus @ X0 @ (minus @ X0)) = (zero))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_inv])).
% 16.17/2.95 thf(zip_derived_cl1, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_assoc])).
% 16.17/2.95 thf(zip_derived_cl26, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((plus @ X1 @ (plus @ (minus @ X1) @ X0)) = (plus @ zero @ X0))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 16.17/2.95 thf(zip_derived_cl2, plain, (![X0 : $i]: ((plus @ zero @ X0) = (X0))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_zero])).
% 16.17/2.95 thf(zip_derived_cl31, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ (plus @ (minus @ X1) @ X0)) = (X0))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl2])).
% 16.17/2.95 thf(zip_derived_cl42, plain,
% 16.17/2.95 (![X0 : $i]: ((plus @ X0 @ zero) = (minus @ (minus @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl31])).
% 16.17/2.95 thf(zip_derived_cl14, plain, (![X0 : $i]: ((X0) = (plus @ X0 @ zero))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 16.17/2.95 thf(zip_derived_cl44, plain, (![X0 : $i]: ((X0) = (minus @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl31, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ (plus @ (minus @ X1) @ X0)) = (X0))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl2])).
% 16.17/2.95 thf(zip_derived_cl50, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ (minus @ X0) @ (plus @ X0 @ X1)) = (X1))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl31])).
% 16.17/2.95 thf(zip_derived_cl1735, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((plus @ (minus @ (times @ X1 @ X0)) @ (times @ X1 @ X0))
% 16.17/2.95 = (times @ X1 @ zero))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl1043, zip_derived_cl50])).
% 16.17/2.95 thf(zip_derived_cl44, plain, (![X0 : $i]: ((X0) = (minus @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl3, plain,
% 16.17/2.95 (![X0 : $i]: ((plus @ X0 @ (minus @ X0)) = (zero))),
% 16.17/2.95 inference('cnf', [status(esa)], [plus_inv])).
% 16.17/2.95 thf(zip_derived_cl48, plain,
% 16.17/2.95 (![X0 : $i]: ((plus @ (minus @ X0) @ X0) = (zero))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl3])).
% 16.17/2.95 thf(zip_derived_cl1781, plain, (![X1 : $i]: ((zero) = (times @ X1 @ zero))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl1735, zip_derived_cl48])).
% 16.17/2.95 thf(zip_derived_cl5428, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((zero) = (plus @ (times @ X1 @ X0) @ (times @ X1 @ (minus @ X0))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl1044, zip_derived_cl1781])).
% 16.17/2.95 thf(zip_derived_cl50, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ (minus @ X0) @ (plus @ X0 @ X1)) = (X1))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl31])).
% 16.17/2.95 thf(zip_derived_cl5430, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((plus @ (minus @ (times @ X1 @ X0)) @ zero)
% 16.17/2.95 = (times @ X1 @ (minus @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5428, zip_derived_cl50])).
% 16.17/2.95 thf(zip_derived_cl14, plain, (![X0 : $i]: ((X0) = (plus @ X0 @ zero))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 16.17/2.95 thf(zip_derived_cl5512, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((minus @ (times @ X1 @ X0)) = (times @ X1 @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl5430, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(zip_derived_cl5539, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((times @ (minus @ X0) @ X1) = (minus @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5512, zip_derived_cl5])).
% 16.17/2.95 thf(zip_derived_cl5644, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((times @ (minus @ X1) @ X0) = (minus @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl5539])).
% 16.17/2.95 thf(zip_derived_cl5644, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((times @ (minus @ X1) @ X0) = (minus @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl5539])).
% 16.17/2.95 thf(zip_derived_cl5512, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((minus @ (times @ X1 @ X0)) = (times @ X1 @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl5430, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl5512, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((minus @ (times @ X1 @ X0)) = (times @ X1 @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl5430, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl5644, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((times @ (minus @ X1) @ X0) = (minus @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl5539])).
% 16.17/2.95 thf(zip_derived_cl5512, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((minus @ (times @ X1 @ X0)) = (times @ X1 @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl5430, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl5512, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((minus @ (times @ X1 @ X0)) = (times @ X1 @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl5430, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl5644, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((times @ (minus @ X1) @ X0) = (minus @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl5539])).
% 16.17/2.95 thf(zip_derived_cl5512, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]:
% 16.17/2.95 ((minus @ (times @ X1 @ X0)) = (times @ X1 @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl5430, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl44, plain, (![X0 : $i]: ((X0) = (minus @ (minus @ X0)))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl14])).
% 16.17/2.95 thf(zip_derived_cl5679, plain,
% 16.17/2.95 (((plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @ (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @ (times @ a @ (times @ a @ (times @ n @ (times @ d @ d)))) @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ b @ (times @ b @ (times @ n @ (times @ d @ d))))))))
% 16.17/2.95 != (plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ b @ (times @ c @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (minus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ a @ (times @ c @ d))))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ c @ (times @ a @ d)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (minus @
% 16.17/2.95 (times @ a @ (times @ c @ (times @ n @ (times @ b @ d))))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ a @ (times @ a @ (times @ d @ d)))) @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ b @ (times @ d @ (times @ n @ (times @ b @ d)))))))))))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl1541, zip_derived_cl5644, zip_derived_cl5644,
% 16.17/2.95 zip_derived_cl5512, zip_derived_cl5512, zip_derived_cl5644,
% 16.17/2.95 zip_derived_cl5512, zip_derived_cl5512, zip_derived_cl5644,
% 16.17/2.95 zip_derived_cl5512, zip_derived_cl44])).
% 16.17/2.95 thf(zip_derived_cl5, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((times @ X1 @ X0) = (times @ X0 @ X1))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_com])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl111, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X1 @ X0) @ X2))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl4, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X0 @ (times @ X1 @ X2)) = (times @ (times @ X0 @ X1) @ X2))),
% 16.17/2.95 inference('cnf', [status(esa)], [times_assoc])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl575, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.17/2.95 ((times @ X1 @ (times @ X2 @ X0)) = (times @ X2 @ (times @ X1 @ X0)))),
% 16.17/2.95 inference('sup+', [status(thm)], [zip_derived_cl111, zip_derived_cl4])).
% 16.17/2.95 thf(zip_derived_cl31, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ (plus @ (minus @ X1) @ X0)) = (X0))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl2])).
% 16.17/2.95 thf(zip_derived_cl31, plain,
% 16.17/2.95 (![X0 : $i, X1 : $i]: ((plus @ X1 @ (plus @ (minus @ X1) @ X0)) = (X0))),
% 16.17/2.95 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl2])).
% 16.17/2.95 thf(zip_derived_cl8857, plain,
% 16.17/2.95 (((plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @ (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @ (times @ a @ (times @ a @ (times @ n @ (times @ d @ d)))) @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ b @ (times @ d @ d))))))))
% 16.17/2.95 != (plus @ (times @ a @ (times @ a @ (times @ c @ c))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ b @ (times @ c @ c)))) @
% 16.17/2.95 (plus @
% 16.17/2.95 (times @ a @ (times @ a @ (times @ n @ (times @ d @ d)))) @
% 16.17/2.95 (times @ n @
% 16.17/2.95 (times @ n @ (times @ b @ (times @ b @ (times @ d @ d)))))))))),
% 16.17/2.95 inference('demod', [status(thm)],
% 16.17/2.95 [zip_derived_cl5679, zip_derived_cl575, zip_derived_cl575,
% 16.17/2.95 zip_derived_cl575, zip_derived_cl575, zip_derived_cl575,
% 16.17/2.95 zip_derived_cl575, zip_derived_cl575, zip_derived_cl575,
% 16.17/2.95 zip_derived_cl575, zip_derived_cl575, zip_derived_cl575,
% 16.17/2.95 zip_derived_cl575, zip_derived_cl575, zip_derived_cl575,
% 16.17/2.95 zip_derived_cl575, zip_derived_cl31, zip_derived_cl31])).
% 16.17/2.95 thf(zip_derived_cl8858, plain, ($false),
% 16.17/2.95 inference('simplify', [status(thm)], [zip_derived_cl8857])).
% 16.17/2.95
% 16.17/2.95 % SZS output end Refutation
% 16.17/2.95
% 16.17/2.95
% 16.17/2.95 % Terminating...
% 16.17/2.98 % Runner terminated.
% 16.17/2.99 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------