%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP109-1 : TPTP v9.2.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ojoKwTjRXr true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:35:38 PM UTC 2025
% Result : Unsatisfiable 0.57s 0.91s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP109-1 : TPTP v9.2.0. Bugfixed v2.7.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ojoKwTjRXr true
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 14:24:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.57/0.65 % Total configuration time : 435
% 0.57/0.65 % Estimated wc time : 1092
% 0.57/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.57/0.91 % Solved by fo/fo1_av.sh.
% 0.57/0.91 % done 77 iterations in 0.154s
% 0.57/0.91 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.57/0.91 % SZS output start Refutation
% 0.57/0.91 thf(b3_type, type, b3: $i).
% 0.57/0.91 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.57/0.91 thf(b1_type, type, b1: $i).
% 0.57/0.91 thf(inverse_type, type, inverse: $i > $i).
% 0.57/0.91 thf(a4_type, type, a4: $i).
% 0.57/0.91 thf(a3_type, type, a3: $i).
% 0.57/0.91 thf(a2_type, type, a2: $i).
% 0.57/0.91 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 0.57/0.91 thf(a1_type, type, a1: $i).
% 0.57/0.91 thf(b2_type, type, b2: $i).
% 0.57/0.91 thf(b4_type, type, b4: $i).
% 0.57/0.91 thf(c3_type, type, c3: $i).
% 0.57/0.91 thf(multiply, axiom,
% 0.57/0.91 (( multiply @ X @ Y ) = ( inverse @ ( double_divide @ Y @ X ) ))).
% 0.57/0.91 thf(zip_derived_cl1, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [multiply])).
% 0.57/0.91 thf(single_axiom, axiom,
% 0.57/0.91 (( double_divide @
% 0.57/0.91 ( inverse @
% 0.57/0.91 ( double_divide @
% 0.57/0.91 X @
% 0.57/0.91 ( inverse @
% 0.57/0.91 ( double_divide @ ( inverse @ Y ) @ ( double_divide @ X @ Z ) ) ) ) ) @
% 0.57/0.91 Z ) =
% 0.57/0.91 ( Y ))).
% 0.57/0.91 thf(zip_derived_cl0, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (inverse @
% 0.57/0.91 (double_divide @ X1 @
% 0.57/0.91 (inverse @
% 0.57/0.91 (double_divide @ (inverse @ X0) @ (double_divide @ X1 @ X2))))) @
% 0.57/0.91 X2) = (X0))),
% 0.57/0.91 inference('cnf', [status(esa)], [single_axiom])).
% 0.57/0.91 thf(zip_derived_cl1, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [multiply])).
% 0.57/0.91 thf(zip_derived_cl1, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [multiply])).
% 0.57/0.91 thf(zip_derived_cl7, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X1 @ X2) @ (inverse @ X0)) @ X1) @
% 0.57/0.91 X2) = (X0))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl1, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [multiply])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X1 @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X2 @ X1) @ (inverse @ X0)) @ X2))
% 0.57/0.91 = (inverse @ X0))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl7, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X1 @ X2) @ (inverse @ X0)) @ X1) @
% 0.57/0.91 X2) = (X0))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X1 @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X2 @ X1) @ (inverse @ X0)) @ X2))
% 0.57/0.91 = (inverse @ X0))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl13, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ((multiply @ X3 @
% 0.57/0.91 (multiply @ (multiply @ X0 @ (inverse @ X1)) @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X2 @ X3) @ (inverse @ X0)) @ X2)))
% 0.57/0.91 = (inverse @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 0.57/0.91 thf(zip_derived_cl39, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ (multiply @ X0 @ (inverse @ X1)) @ (inverse @ X0))
% 0.57/0.91 = (inverse @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl39, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ (multiply @ X0 @ (inverse @ X1)) @ (inverse @ X0))
% 0.57/0.91 = (inverse @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl48, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ (inverse @ X0) @
% 0.57/0.91 (inverse @ (multiply @ X1 @ (inverse @ X0)))) = (inverse @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl39])).
% 0.57/0.91 thf(zip_derived_cl39, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ (multiply @ X0 @ (inverse @ X1)) @ (inverse @ X0))
% 0.57/0.91 = (inverse @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl1, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [multiply])).
% 0.57/0.91 thf(zip_derived_cl7, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X1 @ X2) @ (inverse @ X0)) @ X1) @
% 0.57/0.91 X2) = (X0))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl10, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X3 @ X2) @ (multiply @ X1 @ X0)) @ X3) @
% 0.57/0.91 X2) = (double_divide @ X0 @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 0.57/0.91 thf(zip_derived_cl45, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X3 @ X2) @ (inverse @ X0)) @ X3) @
% 0.57/0.91 X2)
% 0.57/0.91 = (double_divide @ (inverse @ X1) @ (multiply @ X1 @ (inverse @ X0))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl10])).
% 0.57/0.91 thf(zip_derived_cl7, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X1 @ X2) @ (inverse @ X0)) @ X1) @
% 0.57/0.91 X2) = (X0))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl52, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X0)
% 0.57/0.91 = (double_divide @ (inverse @ X1) @ (multiply @ X1 @ (inverse @ X0))))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl7])).
% 0.57/0.91 thf(zip_derived_cl85, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X0 @ (inverse @ X1))
% 0.57/0.91 = (double_divide @ (inverse @ (inverse @ X1)) @ (inverse @ X0)))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl52])).
% 0.57/0.91 thf(zip_derived_cl97, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 0.57/0.91 = (double_divide @ (inverse @ (multiply @ X1 @ X0)) @ (inverse @ X2)))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl85])).
% 0.57/0.91 thf(zip_derived_cl48, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ (inverse @ X0) @
% 0.57/0.91 (inverse @ (multiply @ X1 @ (inverse @ X0)))) = (inverse @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl39])).
% 0.57/0.91 thf(zip_derived_cl10, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X3 @ X2) @ (multiply @ X1 @ X0)) @ X3) @
% 0.57/0.91 X2) = (double_divide @ X0 @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 0.57/0.91 thf(zip_derived_cl53, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X3 @ X2) @ (inverse @ X0)) @ X3) @
% 0.57/0.91 X2)
% 0.57/0.91 = (double_divide @ (inverse @ (multiply @ X0 @ (inverse @ X1))) @
% 0.57/0.91 (inverse @ X1)))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl10])).
% 0.57/0.91 thf(zip_derived_cl7, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((double_divide @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X1 @ X2) @ (inverse @ X0)) @ X1) @
% 0.57/0.91 X2) = (X0))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl62, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X0)
% 0.57/0.91 = (double_divide @ (inverse @ (multiply @ X0 @ (inverse @ X1))) @
% 0.57/0.91 (inverse @ X1)))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl7])).
% 0.57/0.91 thf(zip_derived_cl383, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X1) = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl97, zip_derived_cl62])).
% 0.57/0.91 thf(zip_derived_cl1, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [multiply])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X1 @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X2 @ X1) @ (inverse @ X0)) @ X2))
% 0.57/0.91 = (inverse @ X0))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl12, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ((multiply @ X3 @
% 0.57/0.91 (multiply @
% 0.57/0.91 (multiply @ (double_divide @ X2 @ X3) @ (multiply @ X1 @ X0)) @ X2))
% 0.57/0.91 = (multiply @ X1 @ X0))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.57/0.91 thf(zip_derived_cl408, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X1 @ (multiply @ X0 @ X2))
% 0.57/0.91 = (multiply @ X0 @ (inverse @ (double_divide @ X2 @ X1))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl383, zip_derived_cl12])).
% 0.57/0.91 thf(zip_derived_cl1, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [multiply])).
% 0.57/0.91 thf(zip_derived_cl425, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X1 @ (multiply @ X0 @ X2))
% 0.57/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl408, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl383, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X1) = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl97, zip_derived_cl62])).
% 0.57/0.91 thf(zip_derived_cl468, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X1) = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl383])).
% 0.57/0.91 thf(zip_derived_cl383, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X1) = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl97, zip_derived_cl62])).
% 0.57/0.91 thf(zip_derived_cl1, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [multiply])).
% 0.57/0.91 thf(zip_derived_cl39, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ (multiply @ X0 @ (inverse @ X1)) @ (inverse @ X0))
% 0.57/0.91 = (inverse @ X1))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl51, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ (inverse @ X2))
% 0.57/0.91 = (multiply @ X1 @ X0))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl39])).
% 0.57/0.91 thf(zip_derived_cl397, plain,
% 0.57/0.91 (![X0 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ (multiply @ X2 @ X0) @ (inverse @ X2)) = (X0))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl383, zip_derived_cl51])).
% 0.57/0.91 thf(zip_derived_cl581, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl397])).
% 0.57/0.91 thf(zip_derived_cl468, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X1) = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl383])).
% 0.57/0.91 thf(zip_derived_cl425, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X1 @ (multiply @ X0 @ X2))
% 0.57/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl408, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl580, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X0 @ (multiply @ X2 @ (multiply @ X1 @ (inverse @ X1))))
% 0.57/0.91 = (multiply @ X2 @ X0))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl425])).
% 0.57/0.91 thf(zip_derived_cl468, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X1) = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl425, zip_derived_cl383])).
% 0.57/0.91 thf(zip_derived_cl603, plain,
% 0.57/0.91 (![X0 : $i, X2 : $i]: ((multiply @ X0 @ X2) = (multiply @ X2 @ X0))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl580, zip_derived_cl468])).
% 0.57/0.91 thf(prove_these_axioms, conjecture,
% 0.57/0.91 (~( ( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 0.57/0.91 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 0.57/0.91 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 0.57/0.91 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 0.57/0.91 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 0.57/0.91 ( multiply @ ( inverse @ b1 ) @ b1 ) ) ))).
% 0.57/0.91 thf(zf_stmt_0, negated_conjecture,
% 0.57/0.91 (( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 0.57/0.91 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 0.57/0.91 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 0.57/0.91 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 0.57/0.91 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 0.57/0.91 ( multiply @ ( inverse @ b1 ) @ b1 ) )),
% 0.57/0.91 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 0.57/0.91 thf(zip_derived_cl2, plain,
% 0.57/0.91 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 0.57/0.91 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.57/0.91 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.57/0.91 | ((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) != (a2))
% 0.57/0.91 | ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))),
% 0.57/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.91 thf(zip_derived_cl3, plain,
% 0.57/0.91 ((((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))
% 0.57/0.91 <= (~
% 0.57/0.91 (((multiply @ (inverse @ a1) @ a1)
% 0.57/0.91 = (multiply @ (inverse @ b1) @ b1))))),
% 0.57/0.91 inference('split', [status(esa)], [zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl737, plain,
% 0.57/0.91 ((((multiply @ (inverse @ a1) @ a1) != (multiply @ b1 @ (inverse @ b1))))
% 0.57/0.91 <= (~
% 0.57/0.91 (((multiply @ (inverse @ a1) @ a1)
% 0.57/0.91 = (multiply @ (inverse @ b1) @ b1))))),
% 0.57/0.91 inference('s_sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl603, plain,
% 0.57/0.91 (![X0 : $i, X2 : $i]: ((multiply @ X0 @ X2) = (multiply @ X2 @ X0))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl580, zip_derived_cl468])).
% 0.57/0.91 thf(zip_derived_cl767, plain,
% 0.57/0.91 ((((multiply @ a1 @ (inverse @ a1)) != (multiply @ b1 @ (inverse @ b1))))
% 0.57/0.91 <= (~
% 0.57/0.91 (((multiply @ (inverse @ a1) @ a1)
% 0.57/0.91 = (multiply @ (inverse @ b1) @ b1))))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl737, zip_derived_cl603])).
% 0.57/0.91 thf(zip_derived_cl603, plain,
% 0.57/0.91 (![X0 : $i, X2 : $i]: ((multiply @ X0 @ X2) = (multiply @ X2 @ X0))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl580, zip_derived_cl468])).
% 0.57/0.91 thf(zip_derived_cl5, plain,
% 0.57/0.91 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.57/0.91 != (multiply @ a3 @ (multiply @ b3 @ c3))))
% 0.57/0.91 <= (~
% 0.57/0.91 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.57/0.91 = (multiply @ a3 @ (multiply @ b3 @ c3)))))),
% 0.57/0.91 inference('split', [status(esa)], [zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl741, plain,
% 0.57/0.91 ((((multiply @ c3 @ (multiply @ a3 @ b3))
% 0.57/0.91 != (multiply @ a3 @ (multiply @ b3 @ c3))))
% 0.57/0.91 <= (~
% 0.57/0.91 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.57/0.91 = (multiply @ a3 @ (multiply @ b3 @ c3)))))),
% 0.57/0.91 inference('s_sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl5])).
% 0.57/0.91 thf(zip_derived_cl425, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X1 @ (multiply @ X0 @ X2))
% 0.57/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl408, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl603, plain,
% 0.57/0.91 (![X0 : $i, X2 : $i]: ((multiply @ X0 @ X2) = (multiply @ X2 @ X0))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl580, zip_derived_cl468])).
% 0.57/0.91 thf(zip_derived_cl772, plain,
% 0.57/0.91 ((((multiply @ a3 @ (multiply @ b3 @ c3))
% 0.57/0.91 != (multiply @ a3 @ (multiply @ b3 @ c3))))
% 0.57/0.91 <= (~
% 0.57/0.91 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.57/0.91 = (multiply @ a3 @ (multiply @ b3 @ c3)))))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl741, zip_derived_cl425, zip_derived_cl603])).
% 0.57/0.91 thf('0', plain,
% 0.57/0.91 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.57/0.91 = (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 0.57/0.91 inference('simplify', [status(thm)], [zip_derived_cl772])).
% 0.57/0.91 thf(zip_derived_cl603, plain,
% 0.57/0.91 (![X0 : $i, X2 : $i]: ((multiply @ X0 @ X2) = (multiply @ X2 @ X0))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl580, zip_derived_cl468])).
% 0.57/0.91 thf(zip_derived_cl4, plain,
% 0.57/0.91 ((((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) != (a2)))
% 0.57/0.91 <= (~ (((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) = (a2))))),
% 0.57/0.91 inference('split', [status(esa)], [zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl738, plain,
% 0.57/0.91 ((((multiply @ (multiply @ b2 @ (inverse @ b2)) @ a2) != (a2)))
% 0.57/0.91 <= (~ (((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) = (a2))))),
% 0.57/0.91 inference('s_sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl603, plain,
% 0.57/0.91 (![X0 : $i, X2 : $i]: ((multiply @ X0 @ X2) = (multiply @ X2 @ X0))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl580, zip_derived_cl468])).
% 0.57/0.91 thf(zip_derived_cl425, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ((multiply @ X1 @ (multiply @ X0 @ X2))
% 0.57/0.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl408, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl383, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((X1) = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl97, zip_derived_cl62])).
% 0.57/0.91 thf(zip_derived_cl768, plain,
% 0.57/0.91 ((((a2) != (a2)))
% 0.57/0.91 <= (~ (((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) = (a2))))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl738, zip_derived_cl603, zip_derived_cl425,
% 0.57/0.91 zip_derived_cl383])).
% 0.57/0.91 thf('1', plain,
% 0.57/0.91 ((((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) = (a2)))),
% 0.57/0.91 inference('simplify', [status(thm)], [zip_derived_cl768])).
% 0.57/0.91 thf(zip_derived_cl603, plain,
% 0.57/0.91 (![X0 : $i, X2 : $i]: ((multiply @ X0 @ X2) = (multiply @ X2 @ X0))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl580, zip_derived_cl468])).
% 0.57/0.91 thf(zip_derived_cl6, plain,
% 0.57/0.91 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))
% 0.57/0.91 <= (~ (((multiply @ a4 @ b4) = (multiply @ b4 @ a4))))),
% 0.57/0.91 inference('split', [status(esa)], [zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl742, plain,
% 0.57/0.91 ((((multiply @ a4 @ b4) != (multiply @ a4 @ b4)))
% 0.57/0.91 <= (~ (((multiply @ a4 @ b4) = (multiply @ b4 @ a4))))),
% 0.57/0.91 inference('s_sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl6])).
% 0.57/0.91 thf('2', plain, ((((multiply @ a4 @ b4) = (multiply @ b4 @ a4)))),
% 0.57/0.91 inference('simplify', [status(thm)], [zip_derived_cl742])).
% 0.57/0.91 thf('3', plain,
% 0.57/0.91 (~
% 0.57/0.91 (((multiply @ (inverse @ a1) @ a1) = (multiply @ (inverse @ b1) @ b1))) |
% 0.57/0.91 ~ (((multiply @ a4 @ b4) = (multiply @ b4 @ a4))) |
% 0.57/0.91 ~ (((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) = (a2))) |
% 0.57/0.91 ~
% 0.57/0.91 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.57/0.91 = (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 0.57/0.91 inference('split', [status(esa)], [zip_derived_cl2])).
% 0.57/0.91 thf('4', plain,
% 0.57/0.91 (~
% 0.57/0.91 (((multiply @ (inverse @ a1) @ a1) = (multiply @ (inverse @ b1) @ b1)))),
% 0.57/0.91 inference('sat_resolution*', [status(thm)], ['0', '1', '2', '3'])).
% 0.57/0.91 thf(zip_derived_cl783, plain,
% 0.57/0.91 (((multiply @ a1 @ (inverse @ a1)) != (multiply @ b1 @ (inverse @ b1)))),
% 0.57/0.91 inference('simpl_trail', [status(thm)], [zip_derived_cl767, '4'])).
% 0.57/0.91 thf(zip_derived_cl854, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ((multiply @ a1 @ (inverse @ a1)) != (multiply @ X0 @ (inverse @ X0)))),
% 0.57/0.91 inference('s_sup-', [status(thm)], [zip_derived_cl581, zip_derived_cl783])).
% 0.57/0.91 thf(zip_derived_cl581, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 0.57/0.91 inference('s_sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl397])).
% 0.57/0.91 thf(zip_derived_cl885, plain, ($false),
% 0.57/0.91 inference('simplify_reflect+', [status(thm)],
% 0.57/0.91 [zip_derived_cl854, zip_derived_cl581])).
% 0.57/0.91
% 0.57/0.91 % SZS output end Refutation
% 0.57/0.91
% 0.57/0.91
% 0.57/0.91 % Terminating...
% 0.61/0.95 % Runner terminated.
% 1.79/0.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------