TSTP Solution File: GRP405-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP405-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VCusRW8WCw true
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:51:31 EDT 2023
% Result : Unsatisfiable 80.14s 12.18s
% Output : Refutation 80.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP405-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VCusRW8WCw true
% 0.18/0.35 % Computer : n031.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Aug 29 01:36:55 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.18/0.35 % Running portfolio for 300 s
% 0.18/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.35 % Number of cores: 8
% 0.18/0.35 % Python version: Python 3.6.8
% 0.18/0.35 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 80.14/12.18 % Solved by fo/fo7.sh.
% 80.14/12.18 % done 607 iterations in 11.417s
% 80.14/12.18 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 80.14/12.18 % SZS output start Refutation
% 80.14/12.18 thf(inverse_type, type, inverse: $i > $i).
% 80.14/12.18 thf(b3_type, type, b3: $i).
% 80.14/12.18 thf(c3_type, type, c3: $i).
% 80.14/12.18 thf(multiply_type, type, multiply: $i > $i > $i).
% 80.14/12.18 thf(a3_type, type, a3: $i).
% 80.14/12.18 thf(prove_these_axioms_3, conjecture,
% 80.14/12.18 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 80.14/12.18 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 80.14/12.18 thf(zf_stmt_0, negated_conjecture,
% 80.14/12.18 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 80.14/12.18 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 80.14/12.18 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 80.14/12.18 thf(zip_derived_cl1, plain,
% 80.14/12.18 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 80.14/12.18 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 80.14/12.18 inference('cnf', [status(esa)], [zf_stmt_0])).
% 80.14/12.18 thf(single_axiom, axiom,
% 80.14/12.18 (( multiply @
% 80.14/12.18 A @
% 80.14/12.18 ( inverse @
% 80.14/12.18 ( multiply @
% 80.14/12.18 ( inverse @ ( multiply @ ( inverse @ ( multiply @ A @ B ) ) @ C ) ) @
% 80.14/12.18 ( inverse @ ( multiply @ B @ ( multiply @ ( inverse @ B ) @ B ) ) ) ) ) ) =
% 80.14/12.18 ( C ))).
% 80.14/12.18 thf(zip_derived_cl0, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (X0))),
% 80.14/12.18 inference('cnf', [status(esa)], [single_axiom])).
% 80.14/12.18 thf(zip_derived_cl0, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (X0))),
% 80.14/12.18 inference('cnf', [status(esa)], [single_axiom])).
% 80.14/12.18 thf(zip_derived_cl0, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (X0))),
% 80.14/12.18 inference('cnf', [status(esa)], [single_axiom])).
% 80.14/12.18 thf(zip_derived_cl3, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ X3 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X0) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X1)) @
% 80.14/12.18 X0)) @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl3, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ X3 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X0) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X1)) @
% 80.14/12.18 X0)) @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl0, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (X0))),
% 80.14/12.18 inference('cnf', [status(esa)], [single_axiom])).
% 80.14/12.18 thf(zip_derived_cl13, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0)))))))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl30, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @
% 80.14/12.18 (multiply @ X4 @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))))))
% 80.14/12.18 = (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X0)) @ X3)) @
% 80.14/12.18 X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 80.14/12.18 thf(zip_derived_cl75, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 80.14/12.18 = (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X3)) @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl30])).
% 80.14/12.18 thf(zip_derived_cl75, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 80.14/12.18 = (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X3)) @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl30])).
% 80.14/12.18 thf(zip_derived_cl147, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X3 @ X2)) @ (multiply @ X3 @ X0))
% 80.14/12.18 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 80.14/12.18 (multiply @ X1 @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl75])).
% 80.14/12.18 thf(zip_derived_cl0, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (X0))),
% 80.14/12.18 inference('cnf', [status(esa)], [single_axiom])).
% 80.14/12.18 thf(zip_derived_cl254, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ X3 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 80.14/12.18 (multiply @ X1 @ X0))) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (multiply @ X3 @ X0))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl147, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl30, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @
% 80.14/12.18 (multiply @ X4 @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))))))
% 80.14/12.18 = (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X0)) @ X3)) @
% 80.14/12.18 X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 80.14/12.18 thf(zip_derived_cl0, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (X0))),
% 80.14/12.18 inference('cnf', [status(esa)], [single_axiom])).
% 80.14/12.18 thf(zip_derived_cl56, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X3)) @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0)))) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))))))))
% 80.14/12.18 = (X3))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl5423, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 80.14/12.18 ((multiply @ X5 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X1 @ X0)) @
% 80.14/12.18 (multiply @ X1 @
% 80.14/12.18 (multiply @ X5 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (inverse @ (multiply @ X4 @ (multiply @ (inverse @ X4) @ X4)))) @
% 80.14/12.18 (inverse @ (multiply @ X4 @ (multiply @ (inverse @ X4) @ X4))))))))))
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 80.14/12.18 (multiply @ X3 @ X0))) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl56])).
% 80.14/12.18 thf(zip_derived_cl56, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X3)) @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0)))) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))))))))
% 80.14/12.18 = (X3))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl5492, plain,
% 80.14/12.18 (![X0 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((X0)
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 80.14/12.18 (multiply @ X3 @ X0))) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))),
% 80.14/12.18 inference('demod', [status(thm)], [zip_derived_cl5423, zip_derived_cl56])).
% 80.14/12.18 thf(zip_derived_cl0, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (X0))),
% 80.14/12.18 inference('cnf', [status(esa)], [single_axiom])).
% 80.14/12.18 thf(zip_derived_cl5558, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ X0 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (multiply @ X2 @ X0) @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 80.14/12.18 (multiply @ X2 @ X0)))))))
% 80.14/12.18 = (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl5492, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl13, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0)))))))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl5823, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 80.14/12.18 (multiply @ X2 @ (inverse @ X1)))) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl5558, zip_derived_cl13])).
% 80.14/12.18 thf(zip_derived_cl5492, plain,
% 80.14/12.18 (![X0 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((X0)
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 80.14/12.18 (multiply @ X3 @ X0))) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))),
% 80.14/12.18 inference('demod', [status(thm)], [zip_derived_cl5423, zip_derived_cl56])).
% 80.14/12.18 thf(zip_derived_cl147, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X3 @ X2)) @ (multiply @ X3 @ X0))
% 80.14/12.18 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 80.14/12.18 (multiply @ X1 @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl75])).
% 80.14/12.18 thf(zip_derived_cl5523, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ X4 @
% 80.14/12.18 (inverse @ (multiply @ X3 @ (multiply @ (inverse @ X3) @ X3))))) @
% 80.14/12.18 (multiply @ X4 @ X1))
% 80.14/12.18 = (multiply @ X0 @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X3)) @
% 80.14/12.18 (multiply @ X2 @ X0))) @
% 80.14/12.18 X1)))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl5492, zip_derived_cl147])).
% 80.14/12.18 thf(zip_derived_cl6674, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ X3 @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))) @
% 80.14/12.18 (multiply @ X3 @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1)))))
% 80.14/12.18 = (multiply @ (inverse @ X0) @ X0))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl5823, zip_derived_cl5523])).
% 80.14/12.18 thf(zip_derived_cl6674, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ X3 @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))) @
% 80.14/12.18 (multiply @ X3 @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1)))))
% 80.14/12.18 = (multiply @ (inverse @ X0) @ X0))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl5823, zip_derived_cl5523])).
% 80.14/12.18 thf(zip_derived_cl7165, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl6674, zip_derived_cl6674])).
% 80.14/12.18 thf(zip_derived_cl7165, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl6674, zip_derived_cl6674])).
% 80.14/12.18 thf(zip_derived_cl6674, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ X3 @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))) @
% 80.14/12.18 (multiply @ X3 @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1)))))
% 80.14/12.18 = (multiply @ (inverse @ X0) @ X0))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl5823, zip_derived_cl5523])).
% 80.14/12.18 thf(zip_derived_cl3, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ X3 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X0) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X1)) @
% 80.14/12.18 X0)) @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl6968, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ X4 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X4 @ X3)) @ X2)) @
% 80.14/12.18 (inverse @ (multiply @ X3 @ (multiply @ (inverse @ X3) @ X3))))))
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))) @
% 80.14/12.18 (multiply @ X1 @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0)))))) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl6674, zip_derived_cl3])).
% 80.14/12.18 thf(zip_derived_cl30, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @
% 80.14/12.18 (multiply @ X4 @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))))))
% 80.14/12.18 = (multiply @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X0)) @ X3)) @
% 80.14/12.18 X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 80.14/12.18 thf(zip_derived_cl56, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X3)) @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0)))) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))))))))
% 80.14/12.18 = (X3))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl6674, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ X3 @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))) @
% 80.14/12.18 (multiply @ X3 @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1)))))
% 80.14/12.18 = (multiply @ (inverse @ X0) @ X0))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl5823, zip_derived_cl5523])).
% 80.14/12.18 thf(zip_derived_cl7401, plain,
% 80.14/12.18 (![X0 : $i, X2 : $i]:
% 80.14/12.18 ((X2)
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X2))))))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl6968, zip_derived_cl30, zip_derived_cl56,
% 80.14/12.18 zip_derived_cl6674])).
% 80.14/12.18 thf(zip_derived_cl7964, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((X1)
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X0) @ X0))))))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl7165, zip_derived_cl7401])).
% 80.14/12.18 thf(zip_derived_cl7165, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl6674, zip_derived_cl6674])).
% 80.14/12.18 thf(zip_derived_cl7165, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl6674, zip_derived_cl6674])).
% 80.14/12.18 thf(zip_derived_cl5823, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 80.14/12.18 (multiply @ X2 @ (inverse @ X1)))) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl5558, zip_derived_cl13])).
% 80.14/12.18 thf(zip_derived_cl7624, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @
% 80.14/12.18 (multiply @ (inverse @ (inverse @ X1)) @ (inverse @ X1)))))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl7165, zip_derived_cl5823])).
% 80.14/12.18 thf(zip_derived_cl7165, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl6674, zip_derived_cl6674])).
% 80.14/12.18 thf(zip_derived_cl7847, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1))))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl7624, zip_derived_cl7165])).
% 80.14/12.18 thf(zip_derived_cl8176, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl7165, zip_derived_cl7847])).
% 80.14/12.18 thf(zip_derived_cl56, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ X2 @ X3)) @
% 80.14/12.18 (multiply @ X2 @
% 80.14/12.18 (multiply @ X1 @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0)))) @
% 80.14/12.18 (inverse @ (multiply @ X0 @ (multiply @ (inverse @ X0) @ X0))))))))))
% 80.14/12.18 = (X3))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl0])).
% 80.14/12.18 thf(zip_derived_cl10533, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1)))) @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X1))))))) @
% 80.14/12.18 X0) = (X0))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl8176, zip_derived_cl56])).
% 80.14/12.18 thf(zip_derived_cl7165, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl6674, zip_derived_cl6674])).
% 80.14/12.18 thf(zip_derived_cl10745, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ X1) @ X1)))) @
% 80.14/12.18 X0) = (X0))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10533, zip_derived_cl7165])).
% 80.14/12.18 thf(zip_derived_cl10965, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @ X1) = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl7964, zip_derived_cl10745])).
% 80.14/12.18 thf(zip_derived_cl8176, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl7165, zip_derived_cl7847])).
% 80.14/12.18 thf(zip_derived_cl11464, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((inverse @
% 80.14/12.18 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0)))
% 80.14/12.18 = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl10965, zip_derived_cl8176])).
% 80.14/12.18 thf(zip_derived_cl10745, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ X1) @ X1)))) @
% 80.14/12.18 X0) = (X0))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10533, zip_derived_cl7165])).
% 80.14/12.18 thf(zip_derived_cl147, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X3 @ X2)) @ (multiply @ X3 @ X0))
% 80.14/12.18 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 80.14/12.18 (multiply @ X1 @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl75])).
% 80.14/12.18 thf(zip_derived_cl10749, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X0)) @ (multiply @ X4 @ X1))
% 80.14/12.18 = (multiply @ (inverse @ X0) @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X3)) @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ X2) @ X2)))) @
% 80.14/12.18 X1)))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl10745, zip_derived_cl147])).
% 80.14/12.18 thf(zip_derived_cl10745, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ X1) @ X1)))) @
% 80.14/12.18 X0) = (X0))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10533, zip_derived_cl7165])).
% 80.14/12.18 thf(zip_derived_cl11084, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X0)) @ (multiply @ X4 @ X1))
% 80.14/12.18 = (multiply @ (inverse @ X0) @ X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10749, zip_derived_cl10745])).
% 80.14/12.18 thf(zip_derived_cl13243, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1))
% 80.14/12.18 = (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl11464, zip_derived_cl11084])).
% 80.14/12.18 thf(zip_derived_cl10965, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @ X1) = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl7964, zip_derived_cl10745])).
% 80.14/12.18 thf(zip_derived_cl13275, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl13243, zip_derived_cl10965])).
% 80.14/12.18 thf(zip_derived_cl13346, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ X1 @ (multiply @ (inverse @ X0) @ X0)) = (X1))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl7165, zip_derived_cl13275])).
% 80.14/12.18 thf(zip_derived_cl13275, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl13243, zip_derived_cl10965])).
% 80.14/12.18 thf(zip_derived_cl10745, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ X1) @ X1)))) @
% 80.14/12.18 X0) = (X0))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10533, zip_derived_cl7165])).
% 80.14/12.18 thf(zip_derived_cl7964, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((X1)
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X0) @ X0))))))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl7165, zip_derived_cl7401])).
% 80.14/12.18 thf(zip_derived_cl10877, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 80.14/12.18 ((X3)
% 80.14/12.18 = (inverse @
% 80.14/12.18 (multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X1)) @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 80.14/12.18 (inverse @ (multiply @ X3 @ (multiply @ (inverse @ X2) @ X2))))))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl10745, zip_derived_cl7964])).
% 80.14/12.18 thf(zip_derived_cl10745, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @
% 80.14/12.18 (inverse @
% 80.14/12.18 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 80.14/12.18 (inverse @ (multiply @ (inverse @ X1) @ X1)))) @
% 80.14/12.18 X0) = (X0))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10533, zip_derived_cl7165])).
% 80.14/12.18 thf(zip_derived_cl11209, plain,
% 80.14/12.18 (![X2 : $i, X3 : $i]:
% 80.14/12.18 ((X3)
% 80.14/12.18 = (inverse @
% 80.14/12.18 (inverse @ (multiply @ X3 @ (multiply @ (inverse @ X2) @ X2)))))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10877, zip_derived_cl10745])).
% 80.14/12.18 thf(zip_derived_cl13333, plain,
% 80.14/12.18 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl13275, zip_derived_cl11209])).
% 80.14/12.18 thf(zip_derived_cl7165, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)], [zip_derived_cl6674, zip_derived_cl6674])).
% 80.14/12.18 thf(zip_derived_cl13377, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ (inverse @ X1) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl13333, zip_derived_cl7165])).
% 80.14/12.18 thf(zip_derived_cl13490, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl13346, zip_derived_cl13377])).
% 80.14/12.18 thf(zip_derived_cl11084, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X0)) @ (multiply @ X4 @ X1))
% 80.14/12.18 = (multiply @ (inverse @ X0) @ X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10749, zip_derived_cl10745])).
% 80.14/12.18 thf(zip_derived_cl13499, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X0 @ X2)) @ X0)
% 80.14/12.18 = (multiply @ (inverse @ X2) @ (multiply @ X1 @ (inverse @ X1))))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl13490, zip_derived_cl11084])).
% 80.14/12.18 thf(zip_derived_cl13490, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl13346, zip_derived_cl13377])).
% 80.14/12.18 thf(zip_derived_cl13547, plain,
% 80.14/12.18 (![X0 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X0 @ X2)) @ X0) = (inverse @ X2))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl13499, zip_derived_cl13490])).
% 80.14/12.18 thf(zip_derived_cl13547, plain,
% 80.14/12.18 (![X0 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X0 @ X2)) @ X0) = (inverse @ X2))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl13499, zip_derived_cl13490])).
% 80.14/12.18 thf(zip_derived_cl13715, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (inverse @ X0)) @
% 80.14/12.18 (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl13547, zip_derived_cl13547])).
% 80.14/12.18 thf(zip_derived_cl13333, plain,
% 80.14/12.18 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl13275, zip_derived_cl11209])).
% 80.14/12.18 thf(zip_derived_cl13730, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i]:
% 80.14/12.18 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl13715, zip_derived_cl13333])).
% 80.14/12.18 thf(zip_derived_cl11084, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X4 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (multiply @ X4 @ X0)) @ (multiply @ X4 @ X1))
% 80.14/12.18 = (multiply @ (inverse @ X0) @ X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl10749, zip_derived_cl10745])).
% 80.14/12.18 thf(zip_derived_cl14046, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ (inverse @ (inverse @ X0)) @ (multiply @ X2 @ X1))
% 80.14/12.18 = (multiply @ (inverse @ (inverse @ (multiply @ X0 @ X2))) @ X1))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl13730, zip_derived_cl11084])).
% 80.14/12.18 thf(zip_derived_cl13333, plain,
% 80.14/12.18 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl13275, zip_derived_cl11209])).
% 80.14/12.18 thf(zip_derived_cl13333, plain,
% 80.14/12.18 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 80.14/12.18 inference('sup+', [status(thm)],
% 80.14/12.18 [zip_derived_cl13275, zip_derived_cl11209])).
% 80.14/12.18 thf(zip_derived_cl14105, plain,
% 80.14/12.18 (![X0 : $i, X1 : $i, X2 : $i]:
% 80.14/12.18 ((multiply @ X0 @ (multiply @ X2 @ X1))
% 80.14/12.18 = (multiply @ (multiply @ X0 @ X2) @ X1))),
% 80.14/12.18 inference('demod', [status(thm)],
% 80.14/12.18 [zip_derived_cl14046, zip_derived_cl13333, zip_derived_cl13333])).
% 80.14/12.18 thf(zip_derived_cl14204, plain,
% 80.14/12.18 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 80.14/12.18 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 80.14/12.18 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl14105])).
% 80.14/12.18 thf(zip_derived_cl14205, plain, ($false),
% 80.14/12.18 inference('simplify', [status(thm)], [zip_derived_cl14204])).
% 80.14/12.18
% 80.14/12.18 % SZS output end Refutation
% 80.14/12.18
% 80.14/12.18
% 80.14/12.18 % Terminating...
% 80.80/12.27 % Runner terminated.
% 80.80/12.28 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------