%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP106-1 : TPTP v9.2.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3KbrA2mNF9 true
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:35:38 PM UTC 2025
% Result : Unsatisfiable 20.29s 3.51s
% Output : Refutation 20.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP106-1 : TPTP v9.2.0. Bugfixed v2.7.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3KbrA2mNF9 true
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 14:16:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.44/0.63 % Total configuration time : 435
% 0.44/0.63 % Estimated wc time : 1092
% 0.44/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.51/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.51/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 20.29/3.51 % Solved by fo/fo13.sh.
% 20.29/3.51 % done 303 iterations in 2.737s
% 20.29/3.51 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 20.29/3.51 % SZS output start Refutation
% 20.29/3.51 thf(b3_type, type, b3: $i).
% 20.29/3.51 thf(multiply_type, type, multiply: $i > $i > $i).
% 20.29/3.51 thf(b1_type, type, b1: $i).
% 20.29/3.51 thf(inverse_type, type, inverse: $i > $i).
% 20.29/3.51 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 20.29/3.51 thf(a4_type, type, a4: $i).
% 20.29/3.51 thf(a3_type, type, a3: $i).
% 20.29/3.51 thf(a2_type, type, a2: $i).
% 20.29/3.51 thf(a1_type, type, a1: $i).
% 20.29/3.51 thf(b2_type, type, b2: $i).
% 20.29/3.51 thf(b4_type, type, b4: $i).
% 20.29/3.51 thf(c3_type, type, c3: $i).
% 20.29/3.51 thf(prove_these_axioms, conjecture,
% 20.29/3.51 (~( ( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 20.29/3.51 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 20.29/3.51 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 20.29/3.51 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 20.29/3.51 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 20.29/3.51 ( multiply @ ( inverse @ b1 ) @ b1 ) ) ))).
% 20.29/3.51 thf(zf_stmt_0, negated_conjecture,
% 20.29/3.51 (( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 20.29/3.51 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 20.29/3.51 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 20.29/3.51 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 20.29/3.51 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 20.29/3.51 ( multiply @ ( inverse @ b1 ) @ b1 ) )),
% 20.29/3.51 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 20.29/3.51 thf(zip_derived_cl2, plain,
% 20.29/3.51 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 20.29/3.51 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 20.29/3.51 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 20.29/3.51 | ((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) != (a2))
% 20.29/3.51 | ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))),
% 20.29/3.51 inference('cnf', [status(esa)], [zf_stmt_0])).
% 20.29/3.51 thf(single_axiom, axiom,
% 20.29/3.51 (( inverse @
% 20.29/3.51 ( double_divide @
% 20.29/3.51 ( double_divide @ X @ Y ) @
% 20.29/3.51 ( inverse @
% 20.29/3.51 ( double_divide @ X @ ( inverse @ ( double_divide @ Z @ Y ) ) ) ) ) ) =
% 20.29/3.51 ( Z ))).
% 20.29/3.51 thf(zip_derived_cl0, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((inverse @
% 20.29/3.51 (double_divide @ (double_divide @ X1 @ X2) @
% 20.29/3.51 (inverse @
% 20.29/3.51 (double_divide @ X1 @ (inverse @ (double_divide @ X0 @ X2))))))
% 20.29/3.51 = (X0))),
% 20.29/3.51 inference('cnf', [status(esa)], [single_axiom])).
% 20.29/3.51 thf(multiply, axiom,
% 20.29/3.51 (( multiply @ X @ Y ) = ( inverse @ ( double_divide @ Y @ X ) ))).
% 20.29/3.51 thf(zip_derived_cl1, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 20.29/3.51 inference('cnf', [status(esa)], [multiply])).
% 20.29/3.51 thf(zip_derived_cl1, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 20.29/3.51 inference('cnf', [status(esa)], [multiply])).
% 20.29/3.51 thf(zip_derived_cl1, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 20.29/3.51 inference('cnf', [status(esa)], [multiply])).
% 20.29/3.51 thf(zip_derived_cl3, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ (multiply @ X2 @ X0) @ X1) @
% 20.29/3.51 (double_divide @ X1 @ X2)) = (X0))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1,
% 20.29/3.51 zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl3, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ (multiply @ X2 @ X0) @ X1) @
% 20.29/3.51 (double_divide @ X1 @ X2)) = (X0))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1,
% 20.29/3.51 zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl4, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ X3) @
% 20.29/3.51 (double_divide @ X3 @ (multiply @ (multiply @ X1 @ X0) @ X2)))
% 20.29/3.51 = (double_divide @ X2 @ X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl3, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ (multiply @ X2 @ X0) @ X1) @
% 20.29/3.51 (double_divide @ X1 @ X2)) = (X0))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1,
% 20.29/3.51 zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl3, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ (multiply @ X2 @ X0) @ X1) @
% 20.29/3.51 (double_divide @ X1 @ X2)) = (X0))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1,
% 20.29/3.51 zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl5, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X0 @
% 20.29/3.51 (double_divide @ (double_divide @ X1 @ X2) @ (multiply @ X2 @ X0)))
% 20.29/3.51 = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl4, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ X3) @
% 20.29/3.51 (double_divide @ X3 @ (multiply @ (multiply @ X1 @ X0) @ X2)))
% 20.29/3.51 = (double_divide @ X2 @ X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl19, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((X0)
% 20.29/3.51 = (double_divide @
% 20.29/3.51 (multiply @ X2 @ (double_divide @ X0 @ (multiply @ X1 @ X2))) @
% 20.29/3.51 X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 20.29/3.51 thf(zip_derived_cl35, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((X1)
% 20.29/3.51 = (double_divide @ (double_divide @ (multiply @ X2 @ X1) @ X0) @
% 20.29/3.51 (multiply @ X0 @ X2)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl19])).
% 20.29/3.51 thf(zip_derived_cl1, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 20.29/3.51 inference('cnf', [status(esa)], [multiply])).
% 20.29/3.51 thf(zip_derived_cl42, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X2 @ X1) @
% 20.29/3.51 (double_divide @ (multiply @ X1 @ X0) @ X2)) = (inverse @ X0))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl5, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X0 @
% 20.29/3.51 (double_divide @ (double_divide @ X1 @ X2) @ (multiply @ X2 @ X0)))
% 20.29/3.51 = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl5, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X0 @
% 20.29/3.51 (double_divide @ (double_divide @ X1 @ X2) @ (multiply @ X2 @ X0)))
% 20.29/3.51 = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl3, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ (multiply @ X2 @ X0) @ X1) @
% 20.29/3.51 (double_divide @ X1 @ X2)) = (X0))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1,
% 20.29/3.51 zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl8, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ X3) @ (double_divide @ X3 @ X1))
% 20.29/3.51 = (double_divide @ (double_divide @ X0 @ X2) @ (multiply @ X2 @ X1)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl5, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X0 @
% 20.29/3.51 (double_divide @ (double_divide @ X1 @ X2) @ (multiply @ X2 @ X0)))
% 20.29/3.51 = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl137, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X0 @
% 20.29/3.51 (multiply @ (multiply @ X2 @ X1) @ (double_divide @ X1 @ X0)))
% 20.29/3.51 = (X2))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 20.29/3.51 thf(zip_derived_cl204, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @
% 20.29/3.51 (multiply @ X2 @ (multiply @ X1 @ (double_divide @ X0 @ X2))) @ X0)
% 20.29/3.51 = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl137])).
% 20.29/3.51 thf(zip_derived_cl928, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X2 @ (inverse @ X0)) @ (multiply @ X1 @ X0))
% 20.29/3.51 = (multiply @ X2 @ X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl204])).
% 20.29/3.51 thf(zip_derived_cl35, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((X1)
% 20.29/3.51 = (double_divide @ (double_divide @ (multiply @ X2 @ X1) @ X0) @
% 20.29/3.51 (multiply @ X0 @ X2)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl19])).
% 20.29/3.51 thf(zip_derived_cl8, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ X3) @ (double_divide @ X3 @ X1))
% 20.29/3.51 = (double_divide @ (double_divide @ X0 @ X2) @ (multiply @ X2 @ X1)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl1, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 20.29/3.51 inference('cnf', [status(esa)], [multiply])).
% 20.29/3.51 thf(zip_derived_cl130, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X3 @ X0) @ (double_divide @ X2 @ X3))
% 20.29/3.51 = (inverse @
% 20.29/3.51 (multiply @ (multiply @ X2 @ X1) @ (double_divide @ X1 @ X0))))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl130, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X3 @ X0) @ (double_divide @ X2 @ X3))
% 20.29/3.51 = (inverse @
% 20.29/3.51 (multiply @ (multiply @ X2 @ X1) @ (double_divide @ X1 @ X0))))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl1059, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X3 @ X2) @ (double_divide @ X1 @ X3))
% 20.29/3.51 = (multiply @ (multiply @ X0 @ X2) @ (double_divide @ X1 @ X0)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl130, zip_derived_cl130])).
% 20.29/3.51 thf(zip_derived_cl8, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ X3) @ (double_divide @ X3 @ X1))
% 20.29/3.51 = (double_divide @ (double_divide @ X0 @ X2) @ (multiply @ X2 @ X1)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl8, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ X3) @ (double_divide @ X3 @ X1))
% 20.29/3.51 = (double_divide @ (double_divide @ X0 @ X2) @ (multiply @ X2 @ X1)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl3])).
% 20.29/3.51 thf(zip_derived_cl138, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X2 @ X3) @ (double_divide @ X3 @ X0))
% 20.29/3.51 = (multiply @ (multiply @ X2 @ X1) @ (double_divide @ X1 @ X0)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl8])).
% 20.29/3.51 thf(zip_derived_cl1217, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ X1) @ (double_divide @ X1 @ X0))
% 20.29/3.51 = (multiply @ (multiply @ X2 @ X3) @ (double_divide @ X3 @ X2)))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl1059, zip_derived_cl138])).
% 20.29/3.51 thf(zip_derived_cl1445, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 20.29/3.51 ((multiply @
% 20.29/3.51 (multiply @ (multiply @ X4 @ X3) @
% 20.29/3.51 (double_divide @ (multiply @ X3 @ X0) @ X4)) @
% 20.29/3.51 X0) = (multiply @ (multiply @ X1 @ X2) @ (double_divide @ X2 @ X1)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1217])).
% 20.29/3.51 thf(zip_derived_cl42, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X2 @ X1) @
% 20.29/3.51 (double_divide @ (multiply @ X1 @ X0) @ X2)) = (inverse @ X0))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl1504, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X0) @ X0)
% 20.29/3.51 = (multiply @ (multiply @ X1 @ X2) @ (double_divide @ X2 @ X1)))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl1445, zip_derived_cl42])).
% 20.29/3.51 thf(zip_derived_cl137, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X0 @
% 20.29/3.51 (multiply @ (multiply @ X2 @ X1) @ (double_divide @ X1 @ X0)))
% 20.29/3.51 = (X2))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 20.29/3.51 thf(zip_derived_cl1570, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ (multiply @ (inverse @ X0) @ X0)) = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl1504, zip_derived_cl137])).
% 20.29/3.51 thf(zip_derived_cl1059, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X3 @ X2) @ (double_divide @ X1 @ X3))
% 20.29/3.51 = (multiply @ (multiply @ X0 @ X2) @ (double_divide @ X1 @ X0)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl130, zip_derived_cl130])).
% 20.29/3.51 thf(zip_derived_cl1932, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ X0 @ (double_divide @ X2 @ X0))
% 20.29/3.51 = (multiply @ (multiply @ X1 @ (multiply @ (inverse @ X3) @ X3)) @
% 20.29/3.51 (double_divide @ X2 @ X1)))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl1570, zip_derived_cl1059])).
% 20.29/3.51 thf(zip_derived_cl1570, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ (multiply @ (inverse @ X0) @ X0)) = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl1504, zip_derived_cl137])).
% 20.29/3.51 thf(zip_derived_cl1968, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X0 @ (double_divide @ X2 @ X0))
% 20.29/3.51 = (multiply @ X1 @ (double_divide @ X2 @ X1)))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl1932, zip_derived_cl1570])).
% 20.29/3.51 thf(zip_derived_cl204, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @
% 20.29/3.51 (multiply @ X2 @ (multiply @ X1 @ (double_divide @ X0 @ X2))) @ X0)
% 20.29/3.51 = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl137])).
% 20.29/3.51 thf(zip_derived_cl3576, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @
% 20.29/3.51 (multiply @ X2 @ (multiply @ X0 @ (double_divide @ X1 @ X0))) @ X1)
% 20.29/3.51 = (X2))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl1968, zip_derived_cl204])).
% 20.29/3.51 thf(zip_derived_cl4748, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 20.29/3.51 = (multiply @ X1 @ (inverse @ (double_divide @ X2 @ X0))))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl928, zip_derived_cl3576])).
% 20.29/3.51 thf(zip_derived_cl1, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 20.29/3.51 inference('cnf', [status(esa)], [multiply])).
% 20.29/3.51 thf(zip_derived_cl4768, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 20.29/3.51 = (multiply @ X1 @ (multiply @ X0 @ X2)))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl4748, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl4768, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 20.29/3.51 = (multiply @ X1 @ (multiply @ X0 @ X2)))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl4748, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl4771, plain,
% 20.29/3.51 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 20.29/3.51 | ((multiply @ a3 @ (multiply @ b3 @ c3))
% 20.29/3.51 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 20.29/3.51 | ((multiply @ (inverse @ b2) @ (multiply @ b2 @ a2)) != (a2))
% 20.29/3.51 | ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl2, zip_derived_cl4768, zip_derived_cl4768])).
% 20.29/3.51 thf(zip_derived_cl4772, plain,
% 20.29/3.51 ((((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1))
% 20.29/3.51 | ((multiply @ (inverse @ b2) @ (multiply @ b2 @ a2)) != (a2))
% 20.29/3.51 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 20.29/3.51 inference('simplify', [status(thm)], [zip_derived_cl4771])).
% 20.29/3.51 thf(zip_derived_cl1504, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X0) @ X0)
% 20.29/3.51 = (multiply @ (multiply @ X1 @ X2) @ (double_divide @ X2 @ X1)))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl1445, zip_derived_cl42])).
% 20.29/3.51 thf(zip_derived_cl1504, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X0) @ X0)
% 20.29/3.51 = (multiply @ (multiply @ X1 @ X2) @ (double_divide @ X2 @ X1)))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl1445, zip_derived_cl42])).
% 20.29/3.51 thf(zip_derived_cl1579, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl1504, zip_derived_cl1504])).
% 20.29/3.51 thf(zip_derived_cl4773, plain,
% 20.29/3.51 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 20.29/3.51 | ((multiply @ (inverse @ b2) @ (multiply @ b2 @ a2)) != (a2)))),
% 20.29/3.51 inference('simplify_reflect+', [status(thm)],
% 20.29/3.51 [zip_derived_cl4772, zip_derived_cl1579])).
% 20.29/3.51 thf(zip_derived_cl4768, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 20.29/3.51 = (multiply @ X1 @ (multiply @ X0 @ X2)))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl4748, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl1968, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X0 @ (double_divide @ X2 @ X0))
% 20.29/3.51 = (multiply @ X1 @ (double_divide @ X2 @ X1)))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl1932, zip_derived_cl1570])).
% 20.29/3.51 thf(zip_derived_cl4823, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 20.29/3.51 ((multiply @ X1 @
% 20.29/3.51 (multiply @ X0 @ (double_divide @ X2 @ (multiply @ X1 @ X0))))
% 20.29/3.51 = (multiply @ X3 @ (double_divide @ X2 @ X3)))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl4768, zip_derived_cl1968])).
% 20.29/3.51 thf(zip_derived_cl19, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((X0)
% 20.29/3.51 = (double_divide @
% 20.29/3.51 (multiply @ X2 @ (double_divide @ X0 @ (multiply @ X1 @ X2))) @
% 20.29/3.51 X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl4])).
% 20.29/3.51 thf(zip_derived_cl1, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 20.29/3.51 inference('cnf', [status(esa)], [multiply])).
% 20.29/3.51 thf(zip_derived_cl31, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ X1 @
% 20.29/3.51 (multiply @ X2 @ (double_divide @ X0 @ (multiply @ X1 @ X2))))
% 20.29/3.51 = (inverse @ X0))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl4909, plain,
% 20.29/3.51 (![X2 : $i, X3 : $i]:
% 20.29/3.51 ((inverse @ X2) = (multiply @ X3 @ (double_divide @ X2 @ X3)))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl4823, zip_derived_cl31])).
% 20.29/3.51 thf(zip_derived_cl204, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @
% 20.29/3.51 (multiply @ X2 @ (multiply @ X1 @ (double_divide @ X0 @ X2))) @ X0)
% 20.29/3.51 = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl137])).
% 20.29/3.51 thf(zip_derived_cl5059, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl4909, zip_derived_cl204])).
% 20.29/3.51 thf(zip_derived_cl5059, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl4909, zip_derived_cl204])).
% 20.29/3.51 thf(zip_derived_cl5100, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X0 @ X1) = (multiply @ X0 @ (inverse @ (inverse @ X1))))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl5059, zip_derived_cl5059])).
% 20.29/3.51 thf(zip_derived_cl35, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((X1)
% 20.29/3.51 = (double_divide @ (double_divide @ (multiply @ X2 @ X1) @ X0) @
% 20.29/3.51 (multiply @ X0 @ X2)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl19])).
% 20.29/3.51 thf(zip_derived_cl5150, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((inverse @ (inverse @ X0))
% 20.29/3.51 = (double_divide @ (double_divide @ (multiply @ X1 @ X0) @ X2) @
% 20.29/3.51 (multiply @ X2 @ X1)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl5100, zip_derived_cl35])).
% 20.29/3.51 thf(zip_derived_cl35, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((X1)
% 20.29/3.51 = (double_divide @ (double_divide @ (multiply @ X2 @ X1) @ X0) @
% 20.29/3.51 (multiply @ X0 @ X2)))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl19])).
% 20.29/3.51 thf(zip_derived_cl5194, plain,
% 20.29/3.51 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl5150, zip_derived_cl35])).
% 20.29/3.51 thf(zip_derived_cl1579, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl1504, zip_derived_cl1504])).
% 20.29/3.51 thf(zip_derived_cl5204, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X1) @ X1) = (multiply @ X0 @ (inverse @ X0)))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl5194, zip_derived_cl1579])).
% 20.29/3.51 thf(zip_derived_cl5059, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl4909, zip_derived_cl204])).
% 20.29/3.51 thf(zip_derived_cl5274, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1)
% 20.29/3.51 = (inverse @ (inverse @ X1)))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl5204, zip_derived_cl5059])).
% 20.29/3.51 thf(zip_derived_cl5194, plain,
% 20.29/3.51 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl5150, zip_derived_cl35])).
% 20.29/3.51 thf(zip_derived_cl5336, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl5274, zip_derived_cl5194])).
% 20.29/3.51 thf(zip_derived_cl928, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X2 @ (inverse @ X0)) @ (multiply @ X1 @ X0))
% 20.29/3.51 = (multiply @ X2 @ X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl204])).
% 20.29/3.51 thf(zip_derived_cl5717, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl5336, zip_derived_cl928])).
% 20.29/3.51 thf(zip_derived_cl5746, plain,
% 20.29/3.51 ((((multiply @ a4 @ b4) != (multiply @ a4 @ b4))
% 20.29/3.51 | ((multiply @ (inverse @ b2) @ (multiply @ b2 @ a2)) != (a2)))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl4773, zip_derived_cl5717])).
% 20.29/3.51 thf(zip_derived_cl5747, plain,
% 20.29/3.51 (((multiply @ (inverse @ b2) @ (multiply @ b2 @ a2)) != (a2))),
% 20.29/3.51 inference('simplify', [status(thm)], [zip_derived_cl5746])).
% 20.29/3.51 thf(zip_derived_cl5194, plain,
% 20.29/3.51 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl5150, zip_derived_cl35])).
% 20.29/3.51 thf(zip_derived_cl5204, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X1) @ X1) = (multiply @ X0 @ (inverse @ X0)))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl5194, zip_derived_cl1579])).
% 20.29/3.51 thf(zip_derived_cl5059, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl4909, zip_derived_cl204])).
% 20.29/3.51 thf(zip_derived_cl5246, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl5204, zip_derived_cl5059])).
% 20.29/3.51 thf(zip_derived_cl5204, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X1) @ X1) = (multiply @ X0 @ (inverse @ X0)))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl5194, zip_derived_cl1579])).
% 20.29/3.51 thf(zip_derived_cl4768, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i, X2 : $i]:
% 20.29/3.51 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 20.29/3.51 = (multiply @ X1 @ (multiply @ X0 @ X2)))),
% 20.29/3.51 inference('demod', [status(thm)], [zip_derived_cl4748, zip_derived_cl1])).
% 20.29/3.51 thf(zip_derived_cl5333, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl5246, zip_derived_cl5204, zip_derived_cl4768])).
% 20.29/3.51 thf(zip_derived_cl5680, plain,
% 20.29/3.51 (![X0 : $i, X1 : $i]:
% 20.29/3.51 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 20.29/3.51 inference('s_sup+', [status(thm)],
% 20.29/3.51 [zip_derived_cl5194, zip_derived_cl5333])).
% 20.29/3.51 thf(zip_derived_cl6164, plain, (((a2) != (a2))),
% 20.29/3.51 inference('demod', [status(thm)],
% 20.29/3.51 [zip_derived_cl5747, zip_derived_cl5680])).
% 20.29/3.51 thf(zip_derived_cl6165, plain, ($false),
% 20.29/3.51 inference('simplify', [status(thm)], [zip_derived_cl6164])).
% 20.29/3.51
% 20.29/3.51 % SZS output end Refutation
% 20.29/3.51
% 20.29/3.51
% 20.29/3.51 % Terminating...
% 20.57/3.59 % Runner terminated.
% 20.57/3.61 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------