%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP061-1 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7O7nrCSw6X true
% Computer : n018.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 04:35:33 PM UTC 2025
% Result : Unsatisfiable 77.17s 11.78s
% Output : Refutation 77.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP061-1 : TPTP v9.2.0. Released v1.0.0.
% 0.10/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7O7nrCSw6X true
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 14:24:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in FO mode
% 0.70/0.62 % Total configuration time : 435
% 0.70/0.62 % Estimated wc time : 1092
% 0.70/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.73/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 1.24/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 1.24/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.24/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.24/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.24/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.24/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 77.17/11.78 % Solved by fo/fo4.sh.
% 77.17/11.78 % done 675 iterations in 10.971s
% 77.17/11.78 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 77.17/11.78 % SZS output start Refutation
% 77.17/11.78 thf(a1_type, type, a1: $i).
% 77.17/11.78 thf(a3_type, type, a3: $i).
% 77.17/11.78 thf(b1_type, type, b1: $i).
% 77.17/11.78 thf(inverse_type, type, inverse: $i > $i).
% 77.17/11.78 thf(multiply_type, type, multiply: $i > $i > $i).
% 77.17/11.78 thf(c3_type, type, c3: $i).
% 77.17/11.78 thf(a2_type, type, a2: $i).
% 77.17/11.78 thf(b3_type, type, b3: $i).
% 77.17/11.78 thf(b2_type, type, b2: $i).
% 77.17/11.78 thf(single_axiom, axiom,
% 77.17/11.78 (( inverse @
% 77.17/11.78 ( multiply @
% 77.17/11.78 X @
% 77.17/11.78 ( multiply @
% 77.17/11.78 Y @
% 77.17/11.78 ( multiply @
% 77.17/11.78 ( multiply @ ( inverse @ Y ) @ Z ) @
% 77.17/11.78 ( inverse @ ( multiply @ U @ ( multiply @ X @ Z ) ) ) ) ) ) ) =
% 77.17/11.78 ( U ))).
% 77.17/11.78 thf(zip_derived_cl0, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X1 @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 77.17/11.78 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X3)))))))
% 77.17/11.78 = (X0))),
% 77.17/11.78 inference('cnf', [status(esa)], [single_axiom])).
% 77.17/11.78 thf(zip_derived_cl0, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X1 @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 77.17/11.78 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X3)))))))
% 77.17/11.78 = (X0))),
% 77.17/11.78 inference('cnf', [status(esa)], [single_axiom])).
% 77.17/11.78 thf(zip_derived_cl0, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X1 @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 77.17/11.78 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X3)))))))
% 77.17/11.78 = (X0))),
% 77.17/11.78 inference('cnf', [status(esa)], [single_axiom])).
% 77.17/11.78 thf(zip_derived_cl3, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X2) @
% 77.17/11.78 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2))))) @
% 77.17/11.78 X0))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 77.17/11.78 thf(zip_derived_cl0, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X1 @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 77.17/11.78 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X3)))))))
% 77.17/11.78 = (X0))),
% 77.17/11.78 inference('cnf', [status(esa)], [single_axiom])).
% 77.17/11.78 thf(zip_derived_cl9, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X1) @ X3) @
% 77.17/11.78 (inverse @ (multiply @ X2 @ (multiply @ X0 @ X3))))) @
% 77.17/11.78 X2)) @
% 77.17/11.78 X0))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 77.17/11.78 thf(zip_derived_cl29, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 77.17/11.78 X7 : $i, X8 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X7 @
% 77.17/11.78 (multiply @ X8 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X8) @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X7) @
% 77.17/11.78 (multiply @ (multiply @ X0 @ X6) @
% 77.17/11.78 (inverse @ (multiply @ X5 @ (multiply @ X4 @ X6))))) @
% 77.17/11.78 X5)) @
% 77.17/11.78 X4))))
% 77.17/11.78 = (multiply @ X2 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X1) @
% 77.17/11.78 (inverse @ (multiply @ X0 @ (multiply @ X2 @ X1)))))))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 77.17/11.78 thf(zip_derived_cl9, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X1) @ X3) @
% 77.17/11.78 (inverse @ (multiply @ X2 @ (multiply @ X0 @ X3))))) @
% 77.17/11.78 X2)) @
% 77.17/11.78 X0))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 77.17/11.78 thf(zip_derived_cl203, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X0) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X2) @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X2))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl9])).
% 77.17/11.78 thf(zip_derived_cl203, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X0) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X2) @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X2))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl9])).
% 77.17/11.78 thf(zip_derived_cl0, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X1 @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 77.17/11.78 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X3)))))))
% 77.17/11.78 = (X0))),
% 77.17/11.78 inference('cnf', [status(esa)], [single_axiom])).
% 77.17/11.78 thf(zip_derived_cl408, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X4) @ X2) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X0) @ (multiply @ X3 @ X2)))))) @
% 77.17/11.78 (inverse @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl203, zip_derived_cl0])).
% 77.17/11.78 thf(zip_derived_cl938, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X3 @ (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl203, zip_derived_cl408])).
% 77.17/11.78 thf(zip_derived_cl203, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X0) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X2) @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X2))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl9])).
% 77.17/11.78 thf(zip_derived_cl1060, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 X0)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl1060, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 X0)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl0, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X1 @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 77.17/11.78 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X3)))))))
% 77.17/11.78 = (X0))),
% 77.17/11.78 inference('cnf', [status(esa)], [single_axiom])).
% 77.17/11.78 thf(zip_derived_cl1099, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X0 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @ X3 @ (inverse @ (multiply @ X2 @ X3)))) @
% 77.17/11.78 X2))) @
% 77.17/11.78 (inverse @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl1060, zip_derived_cl0])).
% 77.17/11.78 thf(zip_derived_cl1060, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 X0)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl1206, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X5 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X0 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @ (inverse @ X5) @ (inverse @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl1099, zip_derived_cl1060])).
% 77.17/11.78 thf(zip_derived_cl1060, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 X0)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl1280, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 X0)) @
% 77.17/11.78 X2)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl1206, zip_derived_cl1060])).
% 77.17/11.78 thf(zip_derived_cl4985, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 77.17/11.78 ((multiply @ X6 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ (inverse @ X4) @
% 77.17/11.78 (inverse @
% 77.17/11.78 (multiply @ X0 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X2)))) @
% 77.17/11.78 X1)))))) @
% 77.17/11.78 X0))))
% 77.17/11.78 = (X6))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl1060, zip_derived_cl1280])).
% 77.17/11.78 thf(zip_derived_cl1060, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 X0)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl5070, plain,
% 77.17/11.78 (![X0 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 77.17/11.78 ((multiply @ X6 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ X4 @ (multiply @ (inverse @ X4) @ (inverse @ X0))) @
% 77.17/11.78 X0))))
% 77.17/11.78 = (X6))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl4985, zip_derived_cl1060])).
% 77.17/11.78 thf(zip_derived_cl938, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X3 @ (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl203, zip_derived_cl408])).
% 77.17/11.78 thf(zip_derived_cl1060, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 X0)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl203, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X0) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X2) @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X2))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl9])).
% 77.17/11.78 thf(zip_derived_cl1120, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 77.17/11.78 ((multiply @ X0 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @ X3 @ (inverse @ (multiply @ X2 @ X3)))) @
% 77.17/11.78 X2))) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X1) @ X0)))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl1060, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl1060, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 X0)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl1226, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X5 : $i]:
% 77.17/11.78 ((multiply @ X0 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X1) @ X0)))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl1120, zip_derived_cl1060])).
% 77.17/11.78 thf(zip_derived_cl1402, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @
% 77.17/11.78 (multiply @ X1 @ (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))) @
% 77.17/11.78 (multiply @ X3 @ (multiply @ (inverse @ X3) @ X0))) = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl1226])).
% 77.17/11.78 thf(zip_derived_cl5263, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X3 @
% 77.17/11.78 (multiply @ X0 @
% 77.17/11.78 (inverse @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ X2 @ (multiply @ (inverse @ X2) @ (inverse @ X1))) @
% 77.17/11.78 X1) @
% 77.17/11.78 X0))))
% 77.17/11.78 = (X3))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl5070, zip_derived_cl1402])).
% 77.17/11.78 thf(zip_derived_cl938, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X3 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X3 @ (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl203, zip_derived_cl408])).
% 77.17/11.78 thf(zip_derived_cl1226, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X5 : $i]:
% 77.17/11.78 ((multiply @ X0 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X1) @ X0)))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl1120, zip_derived_cl1060])).
% 77.17/11.78 thf(zip_derived_cl1422, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ X3 @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X3)))))
% 77.17/11.78 = (multiply @ (inverse @ X2) @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ X1 @ (inverse @ (multiply @ X0 @ X1))))))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl1226])).
% 77.17/11.78 thf(zip_derived_cl6375, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X0) @ X0)
% 77.17/11.78 = (multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ X1 @
% 77.17/11.78 (inverse @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (inverse @ X3) @ (inverse @ X2))) @
% 77.17/11.78 X2) @
% 77.17/11.78 X1))))))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl5263, zip_derived_cl1422])).
% 77.17/11.78 thf(zip_derived_cl5263, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X3 @
% 77.17/11.78 (multiply @ X0 @
% 77.17/11.78 (inverse @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ X2 @ (multiply @ (inverse @ X2) @ (inverse @ X1))) @
% 77.17/11.78 X1) @
% 77.17/11.78 X0))))
% 77.17/11.78 = (X3))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl5070, zip_derived_cl1402])).
% 77.17/11.78 thf(zip_derived_cl6586, plain,
% 77.17/11.78 (![X0 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X4) @ X4))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl6375, zip_derived_cl5263])).
% 77.17/11.78 thf(prove_these_axioms, conjecture,
% 77.17/11.78 (~( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 77.17/11.78 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 77.17/11.78 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 77.17/11.78 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 77.17/11.78 ( multiply @ ( inverse @ b1 ) @ b1 ) ) ))).
% 77.17/11.78 thf(zf_stmt_0, negated_conjecture,
% 77.17/11.78 (( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 77.17/11.78 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 77.17/11.78 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 77.17/11.78 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 77.17/11.78 ( multiply @ ( inverse @ b1 ) @ b1 ) )),
% 77.17/11.78 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 77.17/11.78 thf(zip_derived_cl1, plain,
% 77.17/11.78 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 77.17/11.78 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 77.17/11.78 | ((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) != (a2))
% 77.17/11.78 | ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))),
% 77.17/11.78 inference('cnf', [status(esa)], [zf_stmt_0])).
% 77.17/11.78 thf(zip_derived_cl6782, plain,
% 77.17/11.78 (![X0 : $i]:
% 77.17/11.78 (((multiply @ (multiply @ (inverse @ X0) @ X0) @ a2) != (a2))
% 77.17/11.78 | ((multiply @ (inverse @ a1) @ a1)
% 77.17/11.78 != (multiply @ (inverse @ b1) @ b1))
% 77.17/11.78 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 77.17/11.78 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 77.17/11.78 inference('sup-', [status(thm)], [zip_derived_cl6586, zip_derived_cl1])).
% 77.17/11.78 thf(zip_derived_cl6586, plain,
% 77.17/11.78 (![X0 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X4) @ X4))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl6375, zip_derived_cl5263])).
% 77.17/11.78 thf(zip_derived_cl7007, plain,
% 77.17/11.78 (![X0 : $i]:
% 77.17/11.78 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 77.17/11.78 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 77.17/11.78 | ((multiply @ (multiply @ (inverse @ X0) @ X0) @ a2) != (a2)))),
% 77.17/11.78 inference('simplify_reflect+', [status(thm)],
% 77.17/11.78 [zip_derived_cl6782, zip_derived_cl6586])).
% 77.17/11.78 thf(zip_derived_cl6586, plain,
% 77.17/11.78 (![X0 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X4) @ X4))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl6375, zip_derived_cl5263])).
% 77.17/11.78 thf(zip_derived_cl6586, plain,
% 77.17/11.78 (![X0 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X4) @ X4))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl6375, zip_derived_cl5263])).
% 77.17/11.78 thf(zip_derived_cl1206, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X5 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X0 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @ (inverse @ X5) @ (inverse @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl1099, zip_derived_cl1060])).
% 77.17/11.78 thf(zip_derived_cl6737, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 77.17/11.78 ((inverse @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 77.17/11.78 (multiply @ (inverse @ X0) @ X0))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl6586, zip_derived_cl1206])).
% 77.17/11.78 thf(zip_derived_cl7651, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((inverse @ (multiply @ X1 @ (multiply @ (inverse @ X0) @ X0)))
% 77.17/11.78 = (inverse @ X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl6586, zip_derived_cl6737])).
% 77.17/11.78 thf(zip_derived_cl203, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X0) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X2) @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X2))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl9])).
% 77.17/11.78 thf(zip_derived_cl7741, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ X3 @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X4) @ X2) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X0) @ (multiply @ X3 @ X2))))))
% 77.17/11.78 = (multiply @ X0 @ (multiply @ (inverse @ X1) @ X1)))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl7651, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl203, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X0) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X2) @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X2))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl9])).
% 77.17/11.78 thf(zip_derived_cl7929, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((X0) = (multiply @ X0 @ (multiply @ (inverse @ X1) @ X1)))),
% 77.17/11.78 inference('demod', [status(thm)], [zip_derived_cl7741, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl5070, plain,
% 77.17/11.78 (![X0 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 77.17/11.78 ((multiply @ X6 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (multiply @
% 77.17/11.78 (multiply @ X4 @ (multiply @ (inverse @ X4) @ (inverse @ X0))) @
% 77.17/11.78 X0))))
% 77.17/11.78 = (X6))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl4985, zip_derived_cl1060])).
% 77.17/11.78 thf(zip_derived_cl8024, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X0) @ X0))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl7929, zip_derived_cl5070])).
% 77.17/11.78 thf(zip_derived_cl7929, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((X0) = (multiply @ X0 @ (multiply @ (inverse @ X1) @ X1)))),
% 77.17/11.78 inference('demod', [status(thm)], [zip_derived_cl7741, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl8172, plain,
% 77.17/11.78 (![X1 : $i, X2 : $i]:
% 77.17/11.78 ((multiply @ X1 @ (multiply @ X2 @ (inverse @ X2))) = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8024, zip_derived_cl7929])).
% 77.17/11.78 thf(zip_derived_cl7929, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((X0) = (multiply @ X0 @ (multiply @ (inverse @ X1) @ X1)))),
% 77.17/11.78 inference('demod', [status(thm)], [zip_derived_cl7741, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl6586, plain,
% 77.17/11.78 (![X0 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X4) @ X4))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl6375, zip_derived_cl5263])).
% 77.17/11.78 thf(zip_derived_cl8054, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 77.17/11.78 = (multiply @ (inverse @ X1) @ X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl7929, zip_derived_cl6586])).
% 77.17/11.78 thf(zip_derived_cl1422, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ X3 @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X3)))))
% 77.17/11.78 = (multiply @ (inverse @ X2) @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ X1 @ (inverse @ (multiply @ X0 @ X1))))))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl1226])).
% 77.17/11.78 thf(zip_derived_cl1422, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ X3 @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X3)))))
% 77.17/11.78 = (multiply @ (inverse @ X2) @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ X1 @ (inverse @ (multiply @ X0 @ X1))))))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl1226])).
% 77.17/11.78 thf(zip_derived_cl1946, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X2) @
% 77.17/11.78 (multiply @ X2 @ (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0)))))
% 77.17/11.78 = (multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ X3 @ (inverse @ (multiply @ X1 @ X3))))))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl1422, zip_derived_cl1422])).
% 77.17/11.78 thf(zip_derived_cl8469, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X4) @
% 77.17/11.78 (multiply @ X4 @ (multiply @ X2 @ (multiply @ (inverse @ X0) @ X0))))
% 77.17/11.78 = (multiply @ (inverse @ X3) @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X2) @ X1))))))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl8054, zip_derived_cl1946])).
% 77.17/11.78 thf(zip_derived_cl7929, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((X0) = (multiply @ X0 @ (multiply @ (inverse @ X1) @ X1)))),
% 77.17/11.78 inference('demod', [status(thm)], [zip_derived_cl7741, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl1422, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ X3 @
% 77.17/11.78 (multiply @ X4 @
% 77.17/11.78 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X3)))))
% 77.17/11.78 = (multiply @ (inverse @ X2) @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ X1 @ (inverse @ (multiply @ X0 @ X1))))))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl1226])).
% 77.17/11.78 thf(zip_derived_cl1226, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X5 : $i]:
% 77.17/11.78 ((multiply @ X0 @
% 77.17/11.78 (multiply @ X5 @
% 77.17/11.78 (multiply @ (inverse @ X5) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X1) @ X0)))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl1120, zip_derived_cl1060])).
% 77.17/11.78 thf(zip_derived_cl1943, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X2) @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X0)))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl1422, zip_derived_cl1226])).
% 77.17/11.78 thf(zip_derived_cl8605, plain,
% 77.17/11.78 (![X2 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X2)) = (X2))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8469, zip_derived_cl7929, zip_derived_cl1943])).
% 77.17/11.78 thf(zip_derived_cl9610, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X0) @ X0) = (multiply @ X1 @ (inverse @ X1)))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl8172, zip_derived_cl8605])).
% 77.17/11.78 thf(zip_derived_cl8605, plain,
% 77.17/11.78 (![X2 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X2)) = (X2))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8469, zip_derived_cl7929, zip_derived_cl1943])).
% 77.17/11.78 thf(zip_derived_cl7929, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((X0) = (multiply @ X0 @ (multiply @ (inverse @ X1) @ X1)))),
% 77.17/11.78 inference('demod', [status(thm)], [zip_derived_cl7741, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl9524, plain,
% 77.17/11.78 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl8605, zip_derived_cl7929])).
% 77.17/11.78 thf(zip_derived_cl8605, plain,
% 77.17/11.78 (![X2 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X2)) = (X2))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8469, zip_derived_cl7929, zip_derived_cl1943])).
% 77.17/11.78 thf(zip_derived_cl9724, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl9524, zip_derived_cl8605])).
% 77.17/11.78 thf(zip_derived_cl1943, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X2) @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X0)))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl1422, zip_derived_cl1226])).
% 77.17/11.78 thf(zip_derived_cl9930, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X2) @
% 77.17/11.78 (multiply @ X2 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ (inverse @ X1)) @ X0) @
% 77.17/11.78 (inverse @ X0))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl9724, zip_derived_cl1943])).
% 77.17/11.78 thf(zip_derived_cl9524, plain,
% 77.17/11.78 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl8605, zip_derived_cl7929])).
% 77.17/11.78 thf(zip_derived_cl8605, plain,
% 77.17/11.78 (![X2 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X2)) = (X2))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8469, zip_derived_cl7929, zip_derived_cl1943])).
% 77.17/11.78 thf(zip_derived_cl10029, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl9930, zip_derived_cl9524, zip_derived_cl8605])).
% 77.17/11.78 thf(zip_derived_cl10443, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 77.17/11.78 (inverse @ (inverse @ X1))) = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)],
% 77.17/11.78 [zip_derived_cl9610, zip_derived_cl10029])).
% 77.17/11.78 thf(zip_derived_cl9524, plain,
% 77.17/11.78 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl8605, zip_derived_cl7929])).
% 77.17/11.78 thf(zip_derived_cl10468, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl10443, zip_derived_cl9524])).
% 77.17/11.78 thf(zip_derived_cl10596, plain,
% 77.17/11.78 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 77.17/11.78 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 77.17/11.78 | ((a2) != (a2)))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl7007, zip_derived_cl10468])).
% 77.17/11.78 thf(zip_derived_cl10597, plain,
% 77.17/11.78 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 77.17/11.78 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 77.17/11.78 inference('simplify', [status(thm)], [zip_derived_cl10596])).
% 77.17/11.78 thf(zip_derived_cl8605, plain,
% 77.17/11.78 (![X2 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X2)) = (X2))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8469, zip_derived_cl7929, zip_derived_cl1943])).
% 77.17/11.78 thf(zip_derived_cl8172, plain,
% 77.17/11.78 (![X1 : $i, X2 : $i]:
% 77.17/11.78 ((multiply @ X1 @ (multiply @ X2 @ (inverse @ X2))) = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8024, zip_derived_cl7929])).
% 77.17/11.78 thf(zip_derived_cl9724, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl9524, zip_derived_cl8605])).
% 77.17/11.78 thf(zip_derived_cl9951, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl8172, zip_derived_cl9724])).
% 77.17/11.78 thf(zip_derived_cl203, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X1 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ X0) @
% 77.17/11.78 (inverse @ (multiply @ (inverse @ X2) @ (multiply @ X1 @ X0))))))
% 77.17/11.78 = (X2))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl9])).
% 77.17/11.78 thf(zip_derived_cl13774, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X2 @
% 77.17/11.78 (multiply @ X3 @
% 77.17/11.78 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X2)) @
% 77.17/11.78 (inverse @
% 77.17/11.78 (multiply @ (inverse @ X1) @ (multiply @ X0 @ (inverse @ X0)))))))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl9951, zip_derived_cl203])).
% 77.17/11.78 thf(zip_derived_cl10029, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl9930, zip_derived_cl9524, zip_derived_cl8605])).
% 77.17/11.78 thf(zip_derived_cl8605, plain,
% 77.17/11.78 (![X2 : $i, X4 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X2)) = (X2))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8469, zip_derived_cl7929, zip_derived_cl1943])).
% 77.17/11.78 thf(zip_derived_cl10416, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 77.17/11.78 inference('sup+', [status(thm)],
% 77.17/11.78 [zip_derived_cl10029, zip_derived_cl8605])).
% 77.17/11.78 thf(zip_derived_cl10029, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl9930, zip_derived_cl9524, zip_derived_cl8605])).
% 77.17/11.78 thf(zip_derived_cl12187, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i]:
% 77.17/11.78 ((multiply @ (inverse @ X0) @ (inverse @ X1))
% 77.17/11.78 = (inverse @ (multiply @ X1 @ X0)))),
% 77.17/11.78 inference('sup+', [status(thm)],
% 77.17/11.78 [zip_derived_cl10416, zip_derived_cl10029])).
% 77.17/11.78 thf(zip_derived_cl8172, plain,
% 77.17/11.78 (![X1 : $i, X2 : $i]:
% 77.17/11.78 ((multiply @ X1 @ (multiply @ X2 @ (inverse @ X2))) = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl8024, zip_derived_cl7929])).
% 77.17/11.78 thf(zip_derived_cl9524, plain,
% 77.17/11.78 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 77.17/11.78 inference('sup+', [status(thm)], [zip_derived_cl8605, zip_derived_cl7929])).
% 77.17/11.78 thf(zip_derived_cl13974, plain,
% 77.17/11.78 (![X1 : $i, X2 : $i, X3 : $i]:
% 77.17/11.78 ((multiply @ X2 @
% 77.17/11.78 (multiply @ X3 @ (multiply @ (inverse @ (multiply @ X2 @ X3)) @ X1)))
% 77.17/11.78 = (X1))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl13774, zip_derived_cl12187, zip_derived_cl8172,
% 77.17/11.78 zip_derived_cl9524])).
% 77.17/11.78 thf(zip_derived_cl22144, plain,
% 77.17/11.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 77.17/11.78 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 77.17/11.78 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 77.17/11.78 inference('sup+', [status(thm)],
% 77.17/11.78 [zip_derived_cl8605, zip_derived_cl13974])).
% 77.17/11.78 thf(zip_derived_cl22328, plain,
% 77.17/11.78 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 77.17/11.78 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 77.17/11.78 inference('demod', [status(thm)],
% 77.17/11.78 [zip_derived_cl10597, zip_derived_cl22144])).
% 77.17/11.78 thf(zip_derived_cl22329, plain, ($false),
% 77.17/11.78 inference('simplify', [status(thm)], [zip_derived_cl22328])).
% 77.17/11.78
% 77.17/11.78 % SZS output end Refutation
% 77.17/11.78
% 77.17/11.78
% 77.17/11.78 % Terminating...
% 77.79/11.88 % Runner terminated.
% 77.79/11.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------