%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP436-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.f0cxjGKA3u 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 : Thu Oct 2 04:36:26 PM UTC 2025
% Result : Unsatisfiable 30.54s 4.96s
% Output : Refutation 30.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP436-1 : TPTP v9.2.0. Released v2.6.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.f0cxjGKA3u true
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 14:11:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.56/0.64 % Total configuration time : 435
% 0.56/0.64 % Estimated wc time : 1092
% 0.56/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 30.54/4.96 % Solved by fo/fo4.sh.
% 30.54/4.96 % done 408 iterations in 4.170s
% 30.54/4.96 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 30.54/4.96 % SZS output start Refutation
% 30.54/4.96 thf(inverse_type, type, inverse: $i > $i).
% 30.54/4.96 thf(a1_type, type, a1: $i).
% 30.54/4.96 thf(b1_type, type, b1: $i).
% 30.54/4.96 thf(multiply_type, type, multiply: $i > $i > $i).
% 30.54/4.96 thf(single_axiom, axiom,
% 30.54/4.96 (( multiply @
% 30.54/4.96 A @
% 30.54/4.96 ( inverse @
% 30.54/4.96 ( multiply @
% 30.54/4.96 B @
% 30.54/4.96 ( multiply @
% 30.54/4.96 C @
% 30.54/4.96 ( multiply @
% 30.54/4.96 ( multiply @
% 30.54/4.96 ( inverse @ C ) @ ( inverse @ ( multiply @ D @ B ) ) ) @
% 30.54/4.96 A ) ) ) ) ) =
% 30.54/4.96 ( D ))).
% 30.54/4.96 thf(zip_derived_cl0, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 30.54/4.96 X1)))))
% 30.54/4.96 = (X0))),
% 30.54/4.96 inference('cnf', [status(esa)], [single_axiom])).
% 30.54/4.96 thf(zip_derived_cl0, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 30.54/4.96 X1)))))
% 30.54/4.96 = (X0))),
% 30.54/4.96 inference('cnf', [status(esa)], [single_axiom])).
% 30.54/4.96 thf(zip_derived_cl0, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 30.54/4.96 X1)))))
% 30.54/4.96 = (X0))),
% 30.54/4.96 inference('cnf', [status(esa)], [single_axiom])).
% 30.54/4.96 thf(zip_derived_cl4, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X2 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 (inverse @ X3))) @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl0, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 30.54/4.96 X1)))))
% 30.54/4.96 = (X0))),
% 30.54/4.96 inference('cnf', [status(esa)], [single_axiom])).
% 30.54/4.96 thf(zip_derived_cl13, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 30.54/4.96 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 30.54/4.96 = (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 30.54/4.96 (inverse @ X1))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl0, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 30.54/4.96 X1)))))
% 30.54/4.96 = (X0))),
% 30.54/4.96 inference('cnf', [status(esa)], [single_axiom])).
% 30.54/4.96 thf(zip_derived_cl28, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X4) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @ (multiply @ X3 @ (inverse @ X2))) @
% 30.54/4.96 (multiply @ X2 @ (multiply @ X1 @ X0))))))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl297, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X4) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (multiply @ X4 @ (multiply @ X1 @ (inverse @ X3)))))) @
% 30.54/4.96 X0)))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 30.54/4.96 thf(zip_derived_cl0, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 30.54/4.96 X1)))))
% 30.54/4.96 = (X0))),
% 30.54/4.96 inference('cnf', [status(esa)], [single_axiom])).
% 30.54/4.96 thf(zip_derived_cl338, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X0 @ X4)))))
% 30.54/4.96 = (multiply @ (inverse @ X1) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @ X2 @ (multiply @ X0 @ (inverse @ X1)))))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl297, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl338, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X0 @ X4)))))
% 30.54/4.96 = (multiply @ (inverse @ X1) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @ X2 @ (multiply @ X0 @ (inverse @ X1)))))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl297, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl397, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X4)))))
% 30.54/4.96 = (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl338, zip_derived_cl338])).
% 30.54/4.96 thf(zip_derived_cl297, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X4) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (multiply @ X4 @ (multiply @ X1 @ (inverse @ X3)))))) @
% 30.54/4.96 X0)))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 30.54/4.96 thf(zip_derived_cl507, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X2) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 30.54/4.96 X3)))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl397, zip_derived_cl297])).
% 30.54/4.96 thf(zip_derived_cl13, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 30.54/4.96 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 30.54/4.96 = (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 30.54/4.96 (inverse @ X1))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl4, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X2 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 (inverse @ X3))) @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl41, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 30.54/4.96 X1))) @
% 30.54/4.96 (inverse @ X0)))
% 30.54/4.96 = (X2))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl702, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @ (multiply @ X2 @ (multiply @ X0 @ X3)))))))) @
% 30.54/4.96 (inverse @ X2)))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl507, zip_derived_cl41])).
% 30.54/4.96 thf(zip_derived_cl41, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 30.54/4.96 X1))) @
% 30.54/4.96 (inverse @ X0)))
% 30.54/4.96 = (X2))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl13, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 30.54/4.96 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 30.54/4.96 = (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 30.54/4.96 (inverse @ X1))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl13, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 30.54/4.96 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 30.54/4.96 = (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 30.54/4.96 (inverse @ X1))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl43, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X1))) @
% 30.54/4.96 (inverse @ X0)))
% 30.54/4.96 = (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X2 @ X1))) @
% 30.54/4.96 (inverse @ X0))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 30.54/4.96 thf(zip_derived_cl137, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 30.54/4.96 ((multiply @ X6 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X6) @ (inverse @ X0)) @
% 30.54/4.96 (inverse @ X1)))
% 30.54/4.96 = (multiply @ X5 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X5) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @
% 30.54/4.96 (inverse @ (multiply @ X3 @ X0))) @
% 30.54/4.96 X3))) @
% 30.54/4.96 (inverse @ X2))))) @
% 30.54/4.96 (inverse @ X1))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl43])).
% 30.54/4.96 thf(zip_derived_cl41, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 30.54/4.96 X1))) @
% 30.54/4.96 (inverse @ X0)))
% 30.54/4.96 = (X2))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl158, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X5 : $i, X6 : $i]:
% 30.54/4.96 ((multiply @ X6 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X6) @ (inverse @ X0)) @
% 30.54/4.96 (inverse @ X1)))
% 30.54/4.96 = (multiply @ X5 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 30.54/4.96 (inverse @ X1))))),
% 30.54/4.96 inference('demod', [status(thm)], [zip_derived_cl137, zip_derived_cl41])).
% 30.54/4.96 thf(zip_derived_cl507, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X2) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 30.54/4.96 X3)))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl397, zip_derived_cl297])).
% 30.54/4.96 thf(zip_derived_cl713, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X0) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X1)) @
% 30.54/4.96 (inverse @ X0)))))) @
% 30.54/4.96 X4)))
% 30.54/4.96 = (multiply @ (inverse @ X3) @ (inverse @ X1)))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl158, zip_derived_cl507])).
% 30.54/4.96 thf(zip_derived_cl397, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X4 @
% 30.54/4.96 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X4)))))
% 30.54/4.96 = (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl338, zip_derived_cl338])).
% 30.54/4.96 thf(zip_derived_cl730, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X1)) @ X0))))) @
% 30.54/4.96 X4)))
% 30.54/4.96 = (multiply @ (inverse @ X3) @ (inverse @ X1)))),
% 30.54/4.96 inference('demod', [status(thm)], [zip_derived_cl713, zip_derived_cl397])).
% 30.54/4.96 thf(zip_derived_cl41, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 30.54/4.96 X1))) @
% 30.54/4.96 (inverse @ X0)))
% 30.54/4.96 = (X2))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl952, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 30.54/4.96 ((multiply @ X6 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X6) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X5) @
% 30.54/4.96 (inverse @ (multiply @ (inverse @ X1) @ (inverse @ X0)))) @
% 30.54/4.96 (inverse @ X1)))) @
% 30.54/4.96 (inverse @ X5)))
% 30.54/4.96 = (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 30.54/4.96 X3))))) @
% 30.54/4.96 X2)))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl730, zip_derived_cl41])).
% 30.54/4.96 thf(zip_derived_cl41, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 30.54/4.96 X1))) @
% 30.54/4.96 (inverse @ X0)))
% 30.54/4.96 = (X2))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl507, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X2) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 30.54/4.96 X3)))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl397, zip_derived_cl297])).
% 30.54/4.96 thf(zip_derived_cl712, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X4 @ X0))) @
% 30.54/4.96 X4)))
% 30.54/4.96 = (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X0))) @
% 30.54/4.96 X1))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl507])).
% 30.54/4.96 thf(zip_derived_cl41, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 30.54/4.96 X1))) @
% 30.54/4.96 (inverse @ X0)))
% 30.54/4.96 = (X2))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl1032, plain,
% 30.54/4.96 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((inverse @ X0)
% 30.54/4.96 = (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 30.54/4.96 X3))))) @
% 30.54/4.96 X2)))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl952, zip_derived_cl712, zip_derived_cl41])).
% 30.54/4.96 thf(zip_derived_cl1101, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((inverse @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X0 @ (multiply @ X2 @ (multiply @ X4 @ X3)))))))
% 30.54/4.96 = (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X0))) @
% 30.54/4.96 X1)))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl702, zip_derived_cl1032])).
% 30.54/4.96 thf(zip_derived_cl4, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X2 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 (inverse @ X3))) @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl4, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X2 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 (inverse @ X3))) @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl10, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 30.54/4.96 ((multiply @ X5 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X7 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X7) @ (inverse @ X0)) @
% 30.54/4.96 (inverse @ X6))) @
% 30.54/4.96 (multiply @ X6 @ (multiply @ X1 @ X5)))))
% 30.54/4.96 = (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X2 @ X0))) @
% 30.54/4.96 (inverse @ X3))) @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X2 @ X1)))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl4, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X2 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 (inverse @ X3))) @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 30.54/4.96 = (X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl2580, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X3)) @
% 30.54/4.96 (inverse @ X2))) @
% 30.54/4.96 (multiply @ X2 @ (multiply @ X1 @ X0))))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl3018, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 30.54/4.96 X7 : $i, X8 : $i]:
% 30.54/4.96 ((multiply @ X6 @
% 30.54/4.96 (multiply @ X5 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X8 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X8) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0)))))))) @
% 30.54/4.96 (inverse @ X7))) @
% 30.54/4.96 (multiply @ X7 @ (multiply @ X6 @ X5))))))
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X4 @ X3))) @
% 30.54/4.96 X4))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl1101, zip_derived_cl2580])).
% 30.54/4.96 thf(zip_derived_cl1101, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((inverse @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X0 @ (multiply @ X2 @ (multiply @ X4 @ X3)))))))
% 30.54/4.96 = (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X0))) @
% 30.54/4.96 X1)))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl702, zip_derived_cl1032])).
% 30.54/4.96 thf(zip_derived_cl2580, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X3)) @
% 30.54/4.96 (inverse @ X2))) @
% 30.54/4.96 (multiply @ X2 @ (multiply @ X1 @ X0))))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl3041, plain,
% 30.54/4.96 (![X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X3))) @ X1)
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X4 @ X3))) @
% 30.54/4.96 X4))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl3018, zip_derived_cl1101, zip_derived_cl2580])).
% 30.54/4.96 thf(zip_derived_cl0, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 30.54/4.96 X1)))))
% 30.54/4.96 = (X0))),
% 30.54/4.96 inference('cnf', [status(esa)], [single_axiom])).
% 30.54/4.96 thf(zip_derived_cl3278, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 X0)))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3041, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl3278, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 X0)))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3041, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl158, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X5 : $i, X6 : $i]:
% 30.54/4.96 ((multiply @ X6 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X6) @ (inverse @ X0)) @
% 30.54/4.96 (inverse @ X1)))
% 30.54/4.96 = (multiply @ X5 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 30.54/4.96 (inverse @ X1))))),
% 30.54/4.96 inference('demod', [status(thm)], [zip_derived_cl137, zip_derived_cl41])).
% 30.54/4.96 thf(zip_derived_cl3573, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 30.54/4.96 ((multiply @ X5 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X2 @ X3))) @
% 30.54/4.96 X2))))))
% 30.54/4.96 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ (inverse @ X0))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3278, zip_derived_cl158])).
% 30.54/4.96 thf(zip_derived_cl3278, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 X0)))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3041, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl3677, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X5 : $i]:
% 30.54/4.96 ((multiply @ X5 @ (multiply @ (inverse @ X5) @ (inverse @ X0)))
% 30.54/4.96 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ (inverse @ X0))))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl3573, zip_derived_cl3278])).
% 30.54/4.96 thf(zip_derived_cl4031, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X0 @ (inverse @ X0))
% 30.54/4.96 = (multiply @ X4 @
% 30.54/4.96 (multiply @ (inverse @ X4) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @
% 30.54/4.96 (inverse @ (multiply @ X1 @ X2))) @
% 30.54/4.96 X1)))))))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3278, zip_derived_cl3677])).
% 30.54/4.96 thf(zip_derived_cl3278, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 X0)))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3041, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl4075, plain,
% 30.54/4.96 (![X0 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl4031, zip_derived_cl3278])).
% 30.54/4.96 thf(zip_derived_cl4075, plain,
% 30.54/4.96 (![X0 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl4031, zip_derived_cl3278])).
% 30.54/4.96 thf(zip_derived_cl3278, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 X0)))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3041, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl3041, plain,
% 30.54/4.96 (![X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X3))) @ X1)
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X4 @ X3))) @
% 30.54/4.96 X4))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl3018, zip_derived_cl1101, zip_derived_cl2580])).
% 30.54/4.96 thf(zip_derived_cl3533, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 30.54/4.96 ((multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @ X0)
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ (inverse @ X5) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X4) @
% 30.54/4.96 (inverse @ (multiply @ X2 @ X3))) @
% 30.54/4.96 X2))))))) @
% 30.54/4.96 X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3278, zip_derived_cl3041])).
% 30.54/4.96 thf(zip_derived_cl3278, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 30.54/4.96 X0)))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3041, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl3670, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X5 : $i]:
% 30.54/4.96 ((multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @ X0)
% 30.54/4.96 = (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X1)) @ X1))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl3533, zip_derived_cl3278])).
% 30.54/4.96 thf(zip_derived_cl0, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 30.54/4.96 X1)))))
% 30.54/4.96 = (X0))),
% 30.54/4.96 inference('cnf', [status(esa)], [single_axiom])).
% 30.54/4.96 thf(zip_derived_cl3744, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ (multiply @ X2 @ X3) @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X1) @ (inverse @ X0)) @ X0)))))
% 30.54/4.96 = (X2))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl3670, zip_derived_cl0])).
% 30.54/4.96 thf(zip_derived_cl7412, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.54/4.96 ((multiply @ X0 @ (inverse @ X0))
% 30.54/4.96 = (multiply @ X2 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X1)) @ X1)))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl4075, zip_derived_cl3744])).
% 30.54/4.96 thf(zip_derived_cl1032, plain,
% 30.54/4.96 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((inverse @ X0)
% 30.54/4.96 = (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 30.54/4.96 X3))))) @
% 30.54/4.96 X2)))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl952, zip_derived_cl712, zip_derived_cl41])).
% 30.54/4.96 thf(zip_derived_cl2580, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X3)) @
% 30.54/4.96 (inverse @ X2))) @
% 30.54/4.96 (multiply @ X2 @ (multiply @ X1 @ X0))))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl3020, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 30.54/4.96 ((multiply @ X5 @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X7 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X7) @ (inverse @ X0)) @
% 30.54/4.96 (inverse @ X6))) @
% 30.54/4.96 (multiply @ X6 @ (multiply @ X5 @ X4))))))
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X0)) @ X2))))) @
% 30.54/4.96 X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl1032, zip_derived_cl2580])).
% 30.54/4.96 thf(zip_derived_cl2580, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 30.54/4.96 ((multiply @ X1 @
% 30.54/4.96 (multiply @ X0 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @
% 30.54/4.96 (multiply @ X4 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X3)) @
% 30.54/4.96 (inverse @ X2))) @
% 30.54/4.96 (multiply @ X2 @ (multiply @ X1 @ X0))))))
% 30.54/4.96 = (X3))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl4])).
% 30.54/4.96 thf(zip_derived_cl3042, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((X0)
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X0)) @ X2))))) @
% 30.54/4.96 X1))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl3020, zip_derived_cl2580])).
% 30.54/4.96 thf(zip_derived_cl7620, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.54/4.96 ((X2)
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))) @
% 30.54/4.96 X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl7412, zip_derived_cl3042])).
% 30.54/4.96 thf(zip_derived_cl7620, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.54/4.96 ((X2)
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))) @
% 30.54/4.96 X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl7412, zip_derived_cl3042])).
% 30.54/4.96 thf(zip_derived_cl3042, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((X0)
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (inverse @
% 30.54/4.96 (multiply @ X1 @
% 30.54/4.96 (multiply @ X3 @
% 30.54/4.96 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X0)) @ X2))))) @
% 30.54/4.96 X1))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl3020, zip_derived_cl2580])).
% 30.54/4.96 thf(zip_derived_cl8201, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X2 @ (multiply @ X3 @ (inverse @ X3)))
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))) @
% 30.54/4.96 X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl7620, zip_derived_cl3042])).
% 30.54/4.96 thf(zip_derived_cl7620, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.54/4.96 ((X2)
% 30.54/4.96 = (multiply @
% 30.54/4.96 (multiply @ X2 @
% 30.54/4.96 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))) @
% 30.54/4.96 X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl7412, zip_derived_cl3042])).
% 30.54/4.96 thf(zip_derived_cl8291, plain,
% 30.54/4.96 (![X2 : $i, X3 : $i]:
% 30.54/4.96 ((multiply @ X2 @ (multiply @ X3 @ (inverse @ X3))) = (X2))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl8201, zip_derived_cl7620])).
% 30.54/4.96 thf(zip_derived_cl8297, plain,
% 30.54/4.96 (![X1 : $i, X2 : $i]:
% 30.54/4.96 ((X2) = (multiply @ (multiply @ X2 @ (inverse @ X1)) @ X1))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl7620, zip_derived_cl8291])).
% 30.54/4.96 thf(zip_derived_cl8724, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i]:
% 30.54/4.96 ((X1) = (multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl4075, zip_derived_cl8297])).
% 30.54/4.96 thf(zip_derived_cl8297, plain,
% 30.54/4.96 (![X1 : $i, X2 : $i]:
% 30.54/4.96 ((X2) = (multiply @ (multiply @ X2 @ (inverse @ X1)) @ X1))),
% 30.54/4.96 inference('demod', [status(thm)],
% 30.54/4.96 [zip_derived_cl7620, zip_derived_cl8291])).
% 30.54/4.96 thf(zip_derived_cl8896, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i]:
% 30.54/4.96 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ (inverse @ X0) @ X0))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl8724, zip_derived_cl8297])).
% 30.54/4.96 thf(prove_these_axioms_1, conjecture,
% 30.54/4.96 (( multiply @ ( inverse @ a1 ) @ a1 ) =
% 30.54/4.96 ( multiply @ ( inverse @ b1 ) @ b1 ))).
% 30.54/4.96 thf(zf_stmt_0, negated_conjecture,
% 30.54/4.96 (( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 30.54/4.96 ( multiply @ ( inverse @ b1 ) @ b1 )),
% 30.54/4.96 inference('cnf.neg', [status(esa)], [prove_these_axioms_1])).
% 30.54/4.96 thf(zip_derived_cl1, plain,
% 30.54/4.96 (((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1))),
% 30.54/4.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 30.54/4.96 thf(zip_derived_cl10383, plain,
% 30.54/4.96 (![X0 : $i]:
% 30.54/4.96 ((multiply @ X0 @ (inverse @ X0)) != (multiply @ (inverse @ b1) @ b1))),
% 30.54/4.96 inference('sup-', [status(thm)], [zip_derived_cl8896, zip_derived_cl1])).
% 30.54/4.96 thf(zip_derived_cl8896, plain,
% 30.54/4.96 (![X0 : $i, X1 : $i]:
% 30.54/4.96 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ (inverse @ X0) @ X0))),
% 30.54/4.96 inference('sup+', [status(thm)], [zip_derived_cl8724, zip_derived_cl8297])).
% 30.54/4.96 thf(zip_derived_cl10626, plain, ($false),
% 30.54/4.96 inference('simplify_reflect+', [status(thm)],
% 30.54/4.96 [zip_derived_cl10383, zip_derived_cl8896])).
% 30.54/4.96
% 30.54/4.96 % SZS output end Refutation
% 30.54/4.96
% 30.54/4.96
% 30.54/4.96 % Terminating...
% 31.26/5.06 % Runner terminated.
% 31.26/5.08 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------