%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP048-10 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.79eCB3M6YT true
% Computer : n029.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 04:35:31 PM UTC 2025
% Result : Unsatisfiable 35.56s 5.66s
% Output : Refutation 35.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP048-10 : TPTP v9.2.0. Released v7.5.0.
% 0.00/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.79eCB3M6YT true
% 0.10/0.30 % Computer : n029.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Wed Oct 1 14:17:38 EDT 2025
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.10/0.31 % Python version: Python 3.6.8
% 0.15/0.31 % Running in FO mode
% 0.15/0.55 % Total configuration time : 435
% 0.15/0.55 % Estimated wc time : 1092
% 0.15/0.55 % Estimated cpu time (7 cpus) : 156.0
% 0.90/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.90/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.90/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.90/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.90/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.90/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.90/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 35.56/5.66 % Solved by fo/fo4.sh.
% 35.56/5.66 % done 1584 iterations in 4.957s
% 35.56/5.66 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 35.56/5.66 % SZS output start Refutation
% 35.56/5.66 thf(a_type, type, a: $i).
% 35.56/5.66 thf(product_type, type, product: $i > $i > $i > $i).
% 35.56/5.66 thf(equalish_type, type, equalish: $i > $i > $i).
% 35.56/5.66 thf(identity_type, type, identity: $i).
% 35.56/5.66 thf(b_type, type, b: $i).
% 35.56/5.66 thf(ifeq_type, type, ifeq: $i > $i > $i > $i > $i).
% 35.56/5.66 thf(true_type, type, true: $i).
% 35.56/5.66 thf(inverse_type, type, inverse: $i > $i).
% 35.56/5.66 thf(multiply_type, type, multiply: $i > $i > $i).
% 35.56/5.66 thf(total_function1, axiom,
% 35.56/5.66 (( product @ X @ Y @ ( multiply @ X @ Y ) ) = ( true ))).
% 35.56/5.66 thf(zip_derived_cl3, plain,
% 35.56/5.66 (![X0 : $i, X1 : $i]:
% 35.56/5.66 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 35.56/5.66 inference('cnf', [status(esa)], [total_function1])).
% 35.56/5.66 thf(left_inverse, axiom,
% 35.56/5.66 (( product @ ( inverse @ X ) @ X @ identity ) = ( true ))).
% 35.56/5.66 thf(zip_derived_cl2, plain,
% 35.56/5.66 (![X0 : $i]: ((product @ (inverse @ X0) @ X0 @ identity) = (true))),
% 35.56/5.66 inference('cnf', [status(esa)], [left_inverse])).
% 35.56/5.66 thf(left_identity, axiom, (( product @ identity @ X @ X ) = ( true ))).
% 35.56/5.66 thf(zip_derived_cl1, plain,
% 35.56/5.66 (![X0 : $i]: ((product @ identity @ X0 @ X0) = (true))),
% 35.56/5.66 inference('cnf', [status(esa)], [left_identity])).
% 35.56/5.66 thf(associativity1, axiom,
% 35.56/5.66 (( ifeq @
% 35.56/5.66 ( product @ U @ Z @ W ) @ true @
% 35.56/5.66 ( ifeq @
% 35.56/5.66 ( product @ Y @ Z @ V ) @ true @
% 35.56/5.66 ( ifeq @
% 35.56/5.66 ( product @ X @ Y @ U ) @ true @ ( product @ X @ V @ W ) @ true ) @
% 35.56/5.66 true ) @
% 35.56/5.66 true ) =
% 35.56/5.66 ( true ))).
% 35.56/5.66 thf(zip_derived_cl5, plain,
% 35.56/5.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 35.56/5.66 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 35.56/5.66 (ifeq @ (product @ X3 @ X1 @ X4) @ true @
% 35.56/5.66 (ifeq @ (product @ X5 @ X3 @ X0) @ true @
% 35.56/5.66 (product @ X5 @ X4 @ X2) @ true) @
% 35.56/5.66 true) @
% 35.56/5.66 true) = (true))),
% 35.56/5.66 inference('cnf', [status(esa)], [associativity1])).
% 35.56/5.66 thf(zip_derived_cl40, plain,
% 35.56/5.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.66 ((ifeq @ true @ true @
% 35.56/5.66 (ifeq @ (product @ X3 @ X0 @ X1) @ true @
% 35.56/5.67 (ifeq @ (product @ X2 @ X3 @ identity) @ true @
% 35.56/5.67 (product @ X2 @ X1 @ X0) @ true) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 35.56/5.67 thf(zip_derived_cl2026, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 35.56/5.67 ((ifeq @ true @ true @
% 35.56/5.67 (ifeq @ (product @ X2 @ X0 @ X1) @ true @
% 35.56/5.67 (ifeq @ true @ true @ (product @ (inverse @ X2) @ X1 @ X0) @ true) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl40])).
% 35.56/5.67 thf(ifeq_axiom, axiom, (( ifeq @ A @ A @ B @ C ) = ( B ))).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl2052, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X2 @ X0 @ X1) @ true @
% 35.56/5.67 (product @ (inverse @ X2) @ X1 @ X0) @ true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)],
% 35.56/5.67 [zip_derived_cl2026, zip_derived_cl0, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl2199, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ true @ true @
% 35.56/5.67 (product @ (inverse @ X1) @ (multiply @ X1 @ X0) @ X0) @ true)
% 35.56/5.67 = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2052])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl2777, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((true) = (product @ (inverse @ X1) @ (multiply @ X1 @ X0) @ X0))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl2199, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl2052, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X2 @ X0 @ X1) @ true @
% 35.56/5.67 (product @ (inverse @ X2) @ X1 @ X0) @ true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)],
% 35.56/5.67 [zip_derived_cl2026, zip_derived_cl0, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl2809, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ true @ true @
% 35.56/5.67 (product @ (inverse @ (inverse @ X1)) @ X0 @ (multiply @ X1 @ X0)) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl2777, zip_derived_cl2052])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl34613, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((true)
% 35.56/5.67 = (product @ (inverse @ (inverse @ X1)) @ X0 @ (multiply @ X1 @ X0)))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl2809, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl2, plain,
% 35.56/5.67 (![X0 : $i]: ((product @ (inverse @ X0) @ X0 @ identity) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [left_inverse])).
% 35.56/5.67 thf(total_function2, axiom,
% 35.56/5.67 (( ifeq @
% 35.56/5.67 ( product @ X @ Y @ W ) @ true @
% 35.56/5.67 ( ifeq @ ( product @ X @ Y @ Z ) @ true @ ( equalish @ Z @ W ) @ true ) @
% 35.56/5.67 true ) =
% 35.56/5.67 ( true ))).
% 35.56/5.67 thf(zip_derived_cl4, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 35.56/5.67 (ifeq @ (product @ X0 @ X1 @ X3) @ true @ (equalish @ X3 @ X2) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [total_function2])).
% 35.56/5.67 thf(zip_derived_cl16, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ true @ true @
% 35.56/5.67 (ifeq @ (product @ (inverse @ X1) @ X1 @ X0) @ true @
% 35.56/5.67 (equalish @ X0 @ identity) @ true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl713, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((true)
% 35.56/5.67 = (ifeq @ (product @ (inverse @ X1) @ X1 @ X0) @ true @
% 35.56/5.67 (equalish @ X0 @ identity) @ true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl34719, plain,
% 35.56/5.67 (![X0 : $i]:
% 35.56/5.67 ((true)
% 35.56/5.67 = (ifeq @ true @ true @
% 35.56/5.67 (equalish @ (multiply @ X0 @ (inverse @ X0)) @ identity) @ true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl34613, zip_derived_cl713])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl35828, plain,
% 35.56/5.67 (![X0 : $i]:
% 35.56/5.67 ((true) = (equalish @ (multiply @ X0 @ (inverse @ X0)) @ identity))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl34719, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl3, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [total_function1])).
% 35.56/5.67 thf(product_substitution3, axiom,
% 35.56/5.67 (( ifeq @
% 35.56/5.67 ( equalish @ X @ Y ) @ true @
% 35.56/5.67 ( ifeq @ ( product @ W @ Z @ X ) @ true @ ( product @ W @ Z @ Y ) @ true ) @
% 35.56/5.67 true ) =
% 35.56/5.67 ( true ))).
% 35.56/5.67 thf(zip_derived_cl7, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.67 ((ifeq @ (equalish @ X0 @ X1) @ true @
% 35.56/5.67 (ifeq @ (product @ X2 @ X3 @ X0) @ true @
% 35.56/5.67 (product @ X2 @ X3 @ X1) @ true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [product_substitution3])).
% 35.56/5.67 thf(zip_derived_cl79, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 35.56/5.67 ((ifeq @ (equalish @ (multiply @ X2 @ X1) @ X0) @ true @
% 35.56/5.67 (ifeq @ true @ true @ (product @ X2 @ X1 @ X0) @ true) @ true)
% 35.56/5.67 = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl7])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl86, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 35.56/5.67 ((ifeq @ (equalish @ (multiply @ X2 @ X1) @ X0) @ true @
% 35.56/5.67 (product @ X2 @ X1 @ X0) @ true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl35845, plain,
% 35.56/5.67 (![X0 : $i]:
% 35.56/5.67 ((ifeq @ true @ true @ (product @ X0 @ (inverse @ X0) @ identity) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl35828, zip_derived_cl86])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl36271, plain,
% 35.56/5.67 (![X0 : $i]: ((true) = (product @ X0 @ (inverse @ X0) @ identity))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl35845, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl1, plain,
% 35.56/5.67 (![X0 : $i]: ((product @ identity @ X0 @ X0) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [left_identity])).
% 35.56/5.67 thf(a_equals_b, axiom, (( equalish @ a @ b ) = ( true ))).
% 35.56/5.67 thf(zip_derived_cl8, plain, (((equalish @ a @ b) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [a_equals_b])).
% 35.56/5.67 thf(zip_derived_cl1, plain,
% 35.56/5.67 (![X0 : $i]: ((product @ identity @ X0 @ X0) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [left_identity])).
% 35.56/5.67 thf(zip_derived_cl7, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.67 ((ifeq @ (equalish @ X0 @ X1) @ true @
% 35.56/5.67 (ifeq @ (product @ X2 @ X3 @ X0) @ true @
% 35.56/5.67 (product @ X2 @ X3 @ X1) @ true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [product_substitution3])).
% 35.56/5.67 thf(zip_derived_cl80, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ (equalish @ X1 @ X0) @ true @
% 35.56/5.67 (ifeq @ true @ true @ (product @ identity @ X1 @ X0) @ true) @ true)
% 35.56/5.67 = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl87, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ (equalish @ X1 @ X0) @ true @
% 35.56/5.67 (product @ identity @ X1 @ X0) @ true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl120, plain,
% 35.56/5.67 (((ifeq @ true @ true @ (product @ identity @ a @ b) @ true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl87])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl125, plain, (((true) = (product @ identity @ a @ b))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl120, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl4, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 35.56/5.67 (ifeq @ (product @ X0 @ X1 @ X3) @ true @ (equalish @ X3 @ X2) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [total_function2])).
% 35.56/5.67 thf(zip_derived_cl131, plain,
% 35.56/5.67 (![X0 : $i]:
% 35.56/5.67 ((ifeq @ (product @ identity @ a @ X0) @ true @
% 35.56/5.67 (ifeq @ true @ true @ (equalish @ b @ X0) @ true) @ true) = (
% 35.56/5.67 true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl4])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl143, plain,
% 35.56/5.67 (![X0 : $i]:
% 35.56/5.67 ((ifeq @ (product @ identity @ a @ X0) @ true @ (equalish @ b @ X0) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl203, plain,
% 35.56/5.67 (((ifeq @ true @ true @ (equalish @ b @ a) @ true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl143])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl208, plain, (((true) = (equalish @ b @ a))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl203, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl87, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ (equalish @ X1 @ X0) @ true @
% 35.56/5.67 (product @ identity @ X1 @ X0) @ true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl213, plain,
% 35.56/5.67 (((ifeq @ true @ true @ (product @ identity @ b @ a) @ true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl208, zip_derived_cl87])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl218, plain, (((true) = (product @ identity @ b @ a))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl213, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl1, plain,
% 35.56/5.67 (![X0 : $i]: ((product @ identity @ X0 @ X0) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [left_identity])).
% 35.56/5.67 thf(associativity2, axiom,
% 35.56/5.67 (( ifeq @
% 35.56/5.67 ( product @ Y @ Z @ V ) @ true @
% 35.56/5.67 ( ifeq @
% 35.56/5.67 ( product @ X @ V @ W ) @ true @
% 35.56/5.67 ( ifeq @
% 35.56/5.67 ( product @ X @ Y @ U ) @ true @ ( product @ U @ Z @ W ) @ true ) @
% 35.56/5.67 true ) @
% 35.56/5.67 true ) =
% 35.56/5.67 ( true ))).
% 35.56/5.67 thf(zip_derived_cl6, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 35.56/5.67 (ifeq @ (product @ X3 @ X2 @ X4) @ true @
% 35.56/5.67 (ifeq @ (product @ X3 @ X0 @ X5) @ true @
% 35.56/5.67 (product @ X5 @ X1 @ X4) @ true) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [associativity2])).
% 35.56/5.67 thf(zip_derived_cl96, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X3 @ X1 @ X0) @ true @
% 35.56/5.67 (ifeq @ true @ true @
% 35.56/5.67 (ifeq @ (product @ identity @ X3 @ X2) @ true @
% 35.56/5.67 (product @ X2 @ X1 @ X0) @ true) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl6])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl105, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X3 @ X1 @ X0) @ true @
% 35.56/5.67 (ifeq @ (product @ identity @ X3 @ X2) @ true @
% 35.56/5.67 (product @ X2 @ X1 @ X0) @ true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)], [zip_derived_cl96, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl20966, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ (product @ b @ X1 @ X0) @ true @
% 35.56/5.67 (ifeq @ true @ true @ (product @ a @ X1 @ X0) @ true) @ true)
% 35.56/5.67 = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl105])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl21173, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ (product @ b @ X1 @ X0) @ true @ (product @ a @ X1 @ X0) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)], [zip_derived_cl20966, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl36398, plain,
% 35.56/5.67 (((ifeq @ true @ true @ (product @ a @ (inverse @ b) @ identity) @ true)
% 35.56/5.67 = (true))),
% 35.56/5.67 inference('sup+', [status(thm)],
% 35.56/5.67 [zip_derived_cl36271, zip_derived_cl21173])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl38859, plain,
% 35.56/5.67 (((true) = (product @ a @ (inverse @ b) @ identity))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl36398, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl2052, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X2 @ X0 @ X1) @ true @
% 35.56/5.67 (product @ (inverse @ X2) @ X1 @ X0) @ true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)],
% 35.56/5.67 [zip_derived_cl2026, zip_derived_cl0, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl38928, plain,
% 35.56/5.67 (((ifeq @ true @ true @
% 35.56/5.67 (product @ (inverse @ a) @ identity @ (inverse @ b)) @ true) = (
% 35.56/5.67 true))),
% 35.56/5.67 inference('sup+', [status(thm)],
% 35.56/5.67 [zip_derived_cl38859, zip_derived_cl2052])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl43471, plain,
% 35.56/5.67 (((true) = (product @ (inverse @ a) @ identity @ (inverse @ b)))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl38928, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl36271, plain,
% 35.56/5.67 (![X0 : $i]: ((true) = (product @ X0 @ (inverse @ X0) @ identity))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl35845, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl2, plain,
% 35.56/5.67 (![X0 : $i]: ((product @ (inverse @ X0) @ X0 @ identity) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [left_inverse])).
% 35.56/5.67 thf(zip_derived_cl40, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.67 ((ifeq @ true @ true @
% 35.56/5.67 (ifeq @ (product @ X3 @ X0 @ X1) @ true @
% 35.56/5.67 (ifeq @ (product @ X2 @ X3 @ identity) @ true @
% 35.56/5.67 (product @ X2 @ X1 @ X0) @ true) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 35.56/5.67 thf(zip_derived_cl2045, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ true @ true @
% 35.56/5.67 (ifeq @ true @ true @
% 35.56/5.67 (ifeq @ (product @ X1 @ (inverse @ X0) @ identity) @ true @
% 35.56/5.67 (product @ X1 @ identity @ X0) @ true) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl40])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl2071, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X1 @ (inverse @ X0) @ identity) @ true @
% 35.56/5.67 (product @ X1 @ identity @ X0) @ true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)],
% 35.56/5.67 [zip_derived_cl2045, zip_derived_cl0, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl36359, plain,
% 35.56/5.67 (![X0 : $i]:
% 35.56/5.67 ((ifeq @ true @ true @ (product @ X0 @ identity @ X0) @ true) = (true))),
% 35.56/5.67 inference('sup+', [status(thm)],
% 35.56/5.67 [zip_derived_cl36271, zip_derived_cl2071])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl39118, plain,
% 35.56/5.67 (![X0 : $i]: ((true) = (product @ X0 @ identity @ X0))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl36359, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl4, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 35.56/5.67 (ifeq @ (product @ X0 @ X1 @ X3) @ true @ (equalish @ X3 @ X2) @
% 35.56/5.67 true) @
% 35.56/5.67 true) = (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [total_function2])).
% 35.56/5.67 thf(zip_derived_cl39130, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X1 @ identity @ X0) @ true @
% 35.56/5.67 (ifeq @ true @ true @ (equalish @ X1 @ X0) @ true) @ true) = (
% 35.56/5.67 true))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl39118, zip_derived_cl4])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl39306, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i]:
% 35.56/5.67 ((ifeq @ (product @ X1 @ identity @ X0) @ true @
% 35.56/5.67 (equalish @ X1 @ X0) @ true) = (true))),
% 35.56/5.67 inference('demod', [status(thm)], [zip_derived_cl39130, zip_derived_cl0])).
% 35.56/5.67 thf(zip_derived_cl44511, plain,
% 35.56/5.67 (((ifeq @ true @ true @ (equalish @ (inverse @ a) @ (inverse @ b)) @ true)
% 35.56/5.67 = (true))),
% 35.56/5.67 inference('sup+', [status(thm)],
% 35.56/5.67 [zip_derived_cl43471, zip_derived_cl39306])).
% 35.56/5.67 thf(zip_derived_cl0, plain,
% 35.56/5.67 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 35.56/5.67 inference('cnf', [status(esa)], [ifeq_axiom])).
% 35.56/5.67 thf(zip_derived_cl45136, plain,
% 35.56/5.67 (((true) = (equalish @ (inverse @ a) @ (inverse @ b)))),
% 35.56/5.67 inference('sup+', [status(thm)], [zip_derived_cl44511, zip_derived_cl0])).
% 35.56/5.67 thf(prove_inverse_substitution, conjecture,
% 35.56/5.67 (( equalish @ ( inverse @ a ) @ ( inverse @ b ) ) = ( true ))).
% 35.56/5.67 thf(zf_stmt_0, negated_conjecture,
% 35.56/5.67 (( equalish @ ( inverse @ a ) @ ( inverse @ b ) ) != ( true )),
% 35.56/5.67 inference('cnf.neg', [status(esa)], [prove_inverse_substitution])).
% 35.56/5.67 thf(zip_derived_cl9, plain,
% 35.56/5.67 (((equalish @ (inverse @ a) @ (inverse @ b)) != (true))),
% 35.56/5.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 35.56/5.67 thf(zip_derived_cl45137, plain, ($false),
% 35.56/5.67 inference('simplify_reflect-', [status(thm)],
% 35.56/5.67 [zip_derived_cl45136, zip_derived_cl9])).
% 35.56/5.67
% 35.56/5.67 % SZS output end Refutation
% 35.56/5.67
% 35.56/5.67
% 35.56/5.67 % Terminating...
% 36.34/5.78 % Runner terminated.
% 36.34/5.79 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------