TSTP Solution File: GRP130-1.003 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP130-1.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.P2QowQMMqD true
% Computer : n013.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 01:50:14 EDT 2023
% Result : Unsatisfiable 0.57s 0.91s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP130-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.P2QowQMMqD true
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:59:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.53/0.64 % Total configuration time : 435
% 0.53/0.64 % Estimated wc time : 1092
% 0.53/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.57/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.91 % Solved by fo/fo3_bce.sh.
% 0.57/0.91 % BCE start: 14
% 0.57/0.91 % BCE eliminated: 0
% 0.57/0.91 % PE start: 14
% 0.57/0.91 logic: neq
% 0.57/0.91 % PE eliminated: -9
% 0.57/0.91 % done 322 iterations in 0.180s
% 0.57/0.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.57/0.91 % SZS output start Refutation
% 0.57/0.91 thf(e_1_type, type, e_1: $i).
% 0.57/0.91 thf(e_3_type, type, e_3: $i).
% 0.57/0.91 thf(group_element_type, type, group_element: $i > $o).
% 0.57/0.91 thf(e_2_type, type, e_2: $i).
% 0.57/0.91 thf(product_type, type, product: $i > $i > $i > $o).
% 0.57/0.91 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.57/0.91 thf(product_right_cancellation, axiom,
% 0.57/0.91 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.57/0.91 ( equalish @ W @ Z ))).
% 0.57/0.91 thf(zip_derived_cl11, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X0 @ X3 @ X2)
% 0.57/0.91 | (equalish @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/0.91 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.57/0.91 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.57/0.91 thf(zip_derived_cl20, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl3])).
% 0.57/0.91 thf(product_left_cancellation, axiom,
% 0.57/0.91 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.57/0.91 ( equalish @ W @ Z ))).
% 0.57/0.91 thf(zip_derived_cl12, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X3 @ X1 @ X2)
% 0.57/0.91 | (equalish @ X0 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/0.91 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.57/0.91 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.57/0.91 thf(zip_derived_cl27, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl4])).
% 0.57/0.91 thf(product_total_function1, axiom,
% 0.57/0.91 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.57/0.91 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.57/0.91 ( product @ X @ Y @ e_3 ))).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl27, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl20, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl40, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_2 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_2 @ e_1)
% 0.57/0.91 | ~ (group_element @ e_2)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl20])).
% 0.57/0.91 thf(element_2, axiom, (group_element @ e_2)).
% 0.57/0.91 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_2])).
% 0.57/0.91 thf(zip_derived_cl41, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_2 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_2 @ e_1)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl76, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_2)
% 0.57/0.91 | ~ (product @ e_3 @ e_1 @ e_3)
% 0.57/0.91 | ~ (group_element @ e_3)
% 0.57/0.91 | (product @ e_3 @ e_2 @ e_1))),
% 0.57/0.91 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl41])).
% 0.57/0.91 thf(element_3, axiom, (group_element @ e_3)).
% 0.57/0.91 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.57/0.91 thf(zip_derived_cl79, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_2)
% 0.57/0.91 | ~ (product @ e_3 @ e_1 @ e_3)
% 0.57/0.91 | (product @ e_3 @ e_2 @ e_1))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl12, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X3 @ X1 @ X2)
% 0.57/0.91 | (equalish @ X0 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/0.91 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.57/0.91 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.57/0.91 thf(zip_derived_cl29, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl6])).
% 0.57/0.91 thf(zip_derived_cl88, plain,
% 0.57/0.91 ((~ (product @ e_3 @ e_1 @ e_3)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_2)
% 0.57/0.91 | ~ (product @ e_2 @ e_2 @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl29])).
% 0.57/0.91 thf(qg3, conjecture,
% 0.57/0.91 (~( ( product @ Z2 @ Y @ X ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 0.57/0.91 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 0.57/0.91 thf(zf_stmt_0, negated_conjecture,
% 0.57/0.91 (( product @ Z2 @ Y @ X ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 0.57/0.91 ( ~( product @ X @ Y @ Z1 ) )),
% 0.57/0.91 inference('cnf.neg', [status(esa)], [qg3])).
% 0.57/0.91 thf(zip_derived_cl13, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ( (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X2 @ X3 @ X0)
% 0.57/0.91 | ~ (product @ X2 @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.91 thf(zip_derived_cl36, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.57/0.91 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl127, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_2) | ~ (product @ e_3 @ e_1 @ e_3))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl88, zip_derived_cl36])).
% 0.57/0.91 thf(zip_derived_cl129, plain,
% 0.57/0.91 (( (product @ e_3 @ e_1 @ e_2)
% 0.57/0.91 | (product @ e_3 @ e_1 @ e_1)
% 0.57/0.91 | ~ (group_element @ e_1)
% 0.57/0.91 | ~ (group_element @ e_3)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl127])).
% 0.57/0.91 thf(element_1, axiom, (group_element @ e_1)).
% 0.57/0.91 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.57/0.91 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.57/0.91 thf(zip_derived_cl130, plain,
% 0.57/0.91 (( (product @ e_3 @ e_1 @ e_2)
% 0.57/0.91 | (product @ e_3 @ e_1 @ e_1)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl129, zip_derived_cl0, zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl13, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ( (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X2 @ X3 @ X0)
% 0.57/0.91 | ~ (product @ X2 @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.91 thf(zip_derived_cl34, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.91 ( (product @ X1 @ X0 @ e_2)
% 0.57/0.91 | (product @ X1 @ X0 @ e_1)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | ~ (product @ X1 @ X2 @ X0)
% 0.57/0.91 | (product @ e_3 @ X2 @ X1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl135, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_2)
% 0.57/0.91 | (product @ e_3 @ e_1 @ e_1)
% 0.57/0.91 | (product @ e_3 @ e_1 @ e_3)
% 0.57/0.91 | ~ (group_element @ e_3)
% 0.57/0.91 | ~ (group_element @ e_2)
% 0.57/0.91 | (product @ e_3 @ e_2 @ e_1)
% 0.57/0.91 | (product @ e_3 @ e_2 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl34])).
% 0.57/0.91 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.57/0.91 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_2])).
% 0.57/0.91 thf(zip_derived_cl143, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_2)
% 0.57/0.91 | (product @ e_3 @ e_1 @ e_1)
% 0.57/0.91 | (product @ e_3 @ e_1 @ e_3)
% 0.57/0.91 | (product @ e_3 @ e_2 @ e_1)
% 0.57/0.91 | (product @ e_3 @ e_2 @ e_2))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl135, zip_derived_cl2, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl127, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_2) | ~ (product @ e_3 @ e_1 @ e_3))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl88, zip_derived_cl36])).
% 0.57/0.91 thf(zip_derived_cl953, plain,
% 0.57/0.91 (( (product @ e_3 @ e_2 @ e_2)
% 0.57/0.91 | (product @ e_3 @ e_2 @ e_1)
% 0.57/0.91 | (product @ e_3 @ e_1 @ e_1)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl143, zip_derived_cl127])).
% 0.57/0.91 thf(zip_derived_cl27, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl954, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_2)
% 0.57/0.91 | (product @ e_3 @ e_1 @ e_1)
% 0.57/0.91 | (product @ e_3 @ e_2 @ e_1))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl953, zip_derived_cl27])).
% 0.57/0.91 thf(zip_derived_cl29, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl6])).
% 0.57/0.91 thf(zip_derived_cl959, plain,
% 0.57/0.91 (( (product @ e_3 @ e_1 @ e_1)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_2)
% 0.57/0.91 | ~ (product @ e_2 @ e_2 @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl954, zip_derived_cl29])).
% 0.57/0.91 thf(zip_derived_cl36, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.57/0.91 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl1122, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_2) | (product @ e_3 @ e_1 @ e_1))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl959, zip_derived_cl36])).
% 0.57/0.91 thf(zip_derived_cl1129, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_1 @ e_1) | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.57/0.91 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl1122])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl11, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X0 @ X3 @ X2)
% 0.57/0.91 | (equalish @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/0.91 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.57/0.91 thf(zip_derived_cl23, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_2 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl6])).
% 0.57/0.91 thf(zip_derived_cl48, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_3 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_3 @ e_1)
% 0.57/0.91 | ~ (group_element @ e_3)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (product @ X0 @ e_2 @ e_3))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl23])).
% 0.57/0.91 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.57/0.91 thf(zip_derived_cl49, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_3 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_3 @ e_1)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (product @ X0 @ e_2 @ e_3))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl20, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl12, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X3 @ X1 @ X2)
% 0.57/0.91 | (equalish @ X0 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/0.91 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.57/0.91 thf(zip_derived_cl26, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl55, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ e_2 @ X0 @ e_2)
% 0.57/0.91 | (product @ e_2 @ X0 @ e_1)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ e_2)
% 0.57/0.91 | ~ (product @ e_1 @ X0 @ e_3))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl26])).
% 0.57/0.91 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_2])).
% 0.57/0.91 thf(zip_derived_cl56, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ e_2 @ X0 @ e_2)
% 0.57/0.91 | (product @ e_2 @ X0 @ e_1)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (product @ e_1 @ X0 @ e_3))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl353, plain,
% 0.57/0.91 ((~ (product @ e_2 @ e_1 @ e_2)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_3)
% 0.57/0.91 | ~ (group_element @ e_2)
% 0.57/0.91 | (product @ e_2 @ e_2 @ e_1))),
% 0.57/0.91 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl56])).
% 0.57/0.91 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_2])).
% 0.57/0.91 thf(zip_derived_cl359, plain,
% 0.57/0.91 ((~ (product @ e_2 @ e_1 @ e_2)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_3)
% 0.57/0.91 | (product @ e_2 @ e_2 @ e_1))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl353, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_2])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl36, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.57/0.91 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl51, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_3 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_3 @ e_1)
% 0.57/0.91 | ~ (group_element @ e_3)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | (product @ e_3 @ e_3 @ X0))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl36])).
% 0.57/0.91 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.57/0.91 thf(zip_derived_cl53, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_3 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_3 @ e_1)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | (product @ e_3 @ e_3 @ X0))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl123, plain,
% 0.57/0.91 (( (product @ e_3 @ e_3 @ e_2)
% 0.57/0.91 | (product @ e_2 @ e_3 @ e_1)
% 0.57/0.91 | (product @ e_2 @ e_3 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl53])).
% 0.57/0.91 thf(zip_derived_cl27, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl204, plain,
% 0.57/0.91 (( (product @ e_2 @ e_3 @ e_2)
% 0.57/0.91 | (product @ e_2 @ e_3 @ e_1)
% 0.57/0.91 | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl27])).
% 0.57/0.91 thf(zip_derived_cl26, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl380, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | (product @ e_2 @ e_3 @ e_1))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl204, zip_derived_cl26])).
% 0.57/0.91 thf(zip_derived_cl23, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_2 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl6])).
% 0.57/0.91 thf(zip_derived_cl384, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | ~ (product @ e_2 @ e_2 @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl380, zip_derived_cl23])).
% 0.57/0.91 thf(zip_derived_cl699, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_3)
% 0.57/0.91 | ~ (product @ e_2 @ e_1 @ e_2)
% 0.57/0.91 | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl359, zip_derived_cl384])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl26, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl12, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl11, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X0 @ X3 @ X2)
% 0.57/0.91 | (equalish @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/0.91 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.57/0.91 thf(zip_derived_cl21, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl44, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_3 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_3 @ e_1)
% 0.57/0.91 | ~ (group_element @ e_3)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl21])).
% 0.57/0.91 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.57/0.91 thf(zip_derived_cl45, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_3 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_3 @ e_1)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl44, zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl183, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2)
% 0.57/0.91 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.57/0.91 | ~ (group_element @ e_2)
% 0.57/0.91 | (product @ e_2 @ e_3 @ e_1))),
% 0.57/0.91 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl45])).
% 0.57/0.91 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_2])).
% 0.57/0.91 thf(zip_derived_cl186, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2)
% 0.57/0.91 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.57/0.91 | (product @ e_2 @ e_3 @ e_1))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl13, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ( (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X2 @ X3 @ X0)
% 0.57/0.91 | ~ (product @ X2 @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.91 thf(zip_derived_cl240, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_2 @ e_1 @ e_3)
% 0.57/0.91 | ~ (product @ e_1 @ e_3 @ e_2)
% 0.57/0.91 | ~ (product @ e_2 @ X0 @ e_3)
% 0.57/0.91 | (product @ e_1 @ X0 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl186, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl278, plain,
% 0.57/0.91 (( (product @ e_1 @ e_1 @ e_2)
% 0.57/0.91 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.57/0.91 | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.57/0.91 inference('eq_fact', [status(thm)], [zip_derived_cl240])).
% 0.57/0.91 thf(zip_derived_cl21, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl280, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | ~ (product @ e_2 @ e_1 @ e_3))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl278, zip_derived_cl21])).
% 0.57/0.91 thf(zip_derived_cl282, plain,
% 0.57/0.91 (( (product @ e_2 @ e_1 @ e_2)
% 0.57/0.91 | (product @ e_2 @ e_1 @ e_1)
% 0.57/0.91 | ~ (group_element @ e_1)
% 0.57/0.91 | ~ (group_element @ e_2)
% 0.57/0.91 | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl280])).
% 0.57/0.91 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.57/0.91 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_2])).
% 0.57/0.91 thf(zip_derived_cl283, plain,
% 0.57/0.91 (( (product @ e_2 @ e_1 @ e_2)
% 0.57/0.91 | (product @ e_2 @ e_1 @ e_1)
% 0.57/0.91 | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl282, zip_derived_cl0, zip_derived_cl1])).
% 0.57/0.91 thf(zip_derived_cl380, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | (product @ e_2 @ e_3 @ e_1))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl204, zip_derived_cl26])).
% 0.57/0.91 thf(zip_derived_cl21, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl383, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | ~ (product @ e_2 @ e_1 @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl380, zip_derived_cl21])).
% 0.57/0.91 thf(zip_derived_cl671, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | (product @ e_2 @ e_1 @ e_2))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl283, zip_derived_cl383])).
% 0.57/0.91 thf(zip_derived_cl718, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl699, zip_derived_cl671])).
% 0.57/0.91 thf(zip_derived_cl722, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_3)
% 0.57/0.91 | ~ (group_element @ e_1)
% 0.57/0.91 | (product @ e_1 @ e_3 @ e_1)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl718])).
% 0.57/0.91 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.57/0.91 thf(zip_derived_cl724, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_2 @ e_3)
% 0.57/0.91 | (product @ e_1 @ e_3 @ e_1)
% 0.57/0.91 | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl722, zip_derived_cl0])).
% 0.57/0.91 thf(zip_derived_cl725, plain,
% 0.57/0.91 (( (product @ e_1 @ e_3 @ e_1) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.57/0.91 inference('simplify', [status(thm)], [zip_derived_cl724])).
% 0.57/0.91 thf(zip_derived_cl13, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ( (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X2 @ X3 @ X0)
% 0.57/0.91 | ~ (product @ X2 @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.91 thf(zip_derived_cl730, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_1 @ e_2 @ e_3)
% 0.57/0.91 | ~ (product @ e_1 @ X0 @ e_3)
% 0.57/0.91 | (product @ e_1 @ X0 @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl725, zip_derived_cl13])).
% 0.57/0.91 thf(product_total_function2, axiom,
% 0.57/0.91 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 0.57/0.91 ( equalish @ W @ Z ))).
% 0.57/0.91 thf(zip_derived_cl10, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X0 @ X1 @ X3)
% 0.57/0.91 | (equalish @ X2 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function2])).
% 0.57/0.91 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.57/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.57/0.91 thf(zip_derived_cl15, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ X0 @ e_3) | ~ (product @ X1 @ X0 @ e_1))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl10, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl744, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_1 @ X0 @ e_3) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl730, zip_derived_cl15])).
% 0.57/0.91 thf(zip_derived_cl745, plain, (~ (product @ e_1 @ e_2 @ e_3)),
% 0.57/0.91 inference('condensation', [status(thm)], [zip_derived_cl744])).
% 0.57/0.91 thf(zip_derived_cl747, plain,
% 0.57/0.91 (( (product @ e_1 @ e_2 @ e_2)
% 0.57/0.91 | (product @ e_1 @ e_2 @ e_1)
% 0.57/0.91 | ~ (group_element @ e_2)
% 0.57/0.91 | ~ (group_element @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl745])).
% 0.57/0.91 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_2])).
% 0.57/0.91 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.57/0.91 thf(zip_derived_cl748, plain,
% 0.57/0.91 (( (product @ e_1 @ e_2 @ e_2) | (product @ e_1 @ e_2 @ e_1))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl747, zip_derived_cl1, zip_derived_cl0])).
% 0.57/0.91 thf(zip_derived_cl20, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl11, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl808, plain,
% 0.57/0.91 (( (product @ e_1 @ e_2 @ e_1) | ~ (product @ e_1 @ e_1 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl748, zip_derived_cl20])).
% 0.57/0.91 thf(zip_derived_cl13, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ( (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X2 @ X3 @ X0)
% 0.57/0.91 | ~ (product @ X2 @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.91 thf(zip_derived_cl883, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_1 @ e_1 @ e_2)
% 0.57/0.91 | ~ (product @ e_1 @ X0 @ e_2)
% 0.57/0.91 | (product @ e_1 @ X0 @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl808, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl10, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X0 @ X1 @ X3)
% 0.57/0.91 | (equalish @ X2 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function2])).
% 0.57/0.91 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.57/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.57/0.91 thf(zip_derived_cl14, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ X0 @ e_2) | ~ (product @ X1 @ X0 @ e_1))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl10, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl945, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_1 @ X0 @ e_2) | ~ (product @ e_1 @ e_1 @ e_2))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl883, zip_derived_cl14])).
% 0.57/0.91 thf(zip_derived_cl946, plain, (~ (product @ e_1 @ e_1 @ e_2)),
% 0.57/0.91 inference('condensation', [status(thm)], [zip_derived_cl945])).
% 0.57/0.91 thf(zip_derived_cl9, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (group_element @ X0)
% 0.57/0.91 | ~ (group_element @ X1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_1)
% 0.57/0.91 | (product @ X0 @ X1 @ e_2)
% 0.57/0.91 | (product @ X0 @ X1 @ e_3))),
% 0.57/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/0.91 thf(zip_derived_cl45, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 ( (product @ X0 @ e_3 @ e_2)
% 0.57/0.91 | (product @ X0 @ e_3 @ e_1)
% 0.57/0.91 | ~ (group_element @ X0)
% 0.57/0.91 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl44, zip_derived_cl2])).
% 0.57/0.91 thf(zip_derived_cl380, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | (product @ e_2 @ e_3 @ e_1))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl204, zip_derived_cl26])).
% 0.57/0.91 thf(zip_derived_cl671, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | (product @ e_2 @ e_1 @ e_2))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl283, zip_derived_cl383])).
% 0.57/0.91 thf(zip_derived_cl13, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ( (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X2 @ X3 @ X0)
% 0.57/0.91 | ~ (product @ X2 @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.91 thf(zip_derived_cl672, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_1 @ e_3 @ e_2)
% 0.57/0.91 | ~ (product @ e_2 @ X0 @ e_1)
% 0.57/0.91 | (product @ e_2 @ X0 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl671, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl14, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ X0 @ e_2) | ~ (product @ X1 @ X0 @ e_1))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl10, zip_derived_cl3])).
% 0.57/0.91 thf(zip_derived_cl750, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_2 @ X0 @ e_1) | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl672, zip_derived_cl14])).
% 0.57/0.91 thf(zip_derived_cl752, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_3 @ e_2) | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl380, zip_derived_cl750])).
% 0.57/0.91 thf(zip_derived_cl753, plain, (~ (product @ e_1 @ e_3 @ e_2)),
% 0.57/0.91 inference('simplify', [status(thm)], [zip_derived_cl752])).
% 0.57/0.91 thf(zip_derived_cl761, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_1 @ e_3)
% 0.57/0.91 | ~ (group_element @ e_1)
% 0.57/0.91 | (product @ e_1 @ e_3 @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl753])).
% 0.57/0.91 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.57/0.91 thf(zip_derived_cl763, plain,
% 0.57/0.91 ((~ (product @ e_1 @ e_1 @ e_3) | (product @ e_1 @ e_3 @ e_1))),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl761, zip_derived_cl0])).
% 0.57/0.91 thf(zip_derived_cl13, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.91 ( (product @ X0 @ X1 @ X2)
% 0.57/0.91 | ~ (product @ X2 @ X3 @ X0)
% 0.57/0.91 | ~ (product @ X2 @ X1 @ X3))),
% 0.57/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.91 thf(zip_derived_cl819, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_1 @ e_1 @ e_3)
% 0.57/0.91 | ~ (product @ e_1 @ X0 @ e_3)
% 0.57/0.91 | (product @ e_1 @ X0 @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl763, zip_derived_cl13])).
% 0.57/0.91 thf(zip_derived_cl15, plain,
% 0.57/0.91 (![X0 : $i, X1 : $i]:
% 0.57/0.91 (~ (product @ X1 @ X0 @ e_3) | ~ (product @ X1 @ X0 @ e_1))),
% 0.57/0.91 inference('dp-resolution', [status(thm)],
% 0.57/0.91 [zip_derived_cl10, zip_derived_cl4])).
% 0.57/0.91 thf(zip_derived_cl893, plain,
% 0.57/0.91 (![X0 : $i]:
% 0.57/0.91 (~ (product @ e_1 @ X0 @ e_3) | ~ (product @ e_1 @ e_1 @ e_3))),
% 0.57/0.91 inference('clc', [status(thm)], [zip_derived_cl819, zip_derived_cl15])).
% 0.57/0.91 thf(zip_derived_cl894, plain, (~ (product @ e_1 @ e_1 @ e_3)),
% 0.57/0.91 inference('condensation', [status(thm)], [zip_derived_cl893])).
% 0.57/0.91 thf(zip_derived_cl897, plain,
% 0.57/0.91 (( (product @ e_1 @ e_1 @ e_2)
% 0.57/0.91 | (product @ e_1 @ e_1 @ e_1)
% 0.57/0.91 | ~ (group_element @ e_1)
% 0.57/0.91 | ~ (group_element @ e_1))),
% 0.57/0.91 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl894])).
% 0.57/0.91 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.57/0.91 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.57/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.57/0.91 thf(zip_derived_cl898, plain,
% 0.57/0.91 (( (product @ e_1 @ e_1 @ e_2) | (product @ e_1 @ e_1 @ e_1))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl897, zip_derived_cl0, zip_derived_cl0])).
% 0.57/0.91 thf(zip_derived_cl947, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 0.57/0.91 inference('sup+', [status(thm)], [zip_derived_cl946, zip_derived_cl898])).
% 0.57/0.91 thf(zip_derived_cl1132, plain, (~ (product @ e_1 @ e_2 @ e_2)),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl1129, zip_derived_cl947])).
% 0.57/0.91 thf(zip_derived_cl748, plain,
% 0.57/0.91 (( (product @ e_1 @ e_2 @ e_2) | (product @ e_1 @ e_2 @ e_1))),
% 0.57/0.91 inference('demod', [status(thm)],
% 0.57/0.91 [zip_derived_cl747, zip_derived_cl1, zip_derived_cl0])).
% 0.57/0.91 thf(zip_derived_cl1137, plain, ( (product @ e_1 @ e_2 @ e_1)),
% 0.57/0.91 inference('sup+', [status(thm)], [zip_derived_cl1132, zip_derived_cl748])).
% 0.57/0.91 thf(zip_derived_cl1148, plain, (~ (product @ e_1 @ e_1 @ e_1)),
% 0.57/0.91 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl1137])).
% 0.57/0.91 thf(zip_derived_cl947, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 0.57/0.91 inference('sup+', [status(thm)], [zip_derived_cl946, zip_derived_cl898])).
% 0.57/0.91 thf(zip_derived_cl1149, plain, ($false),
% 0.57/0.91 inference('demod', [status(thm)], [zip_derived_cl1148, zip_derived_cl947])).
% 0.57/0.91
% 0.57/0.91 % SZS output end Refutation
% 0.57/0.91
% 0.57/0.91
% 0.57/0.91 % Terminating...
% 0.96/0.96 % Runner terminated.
% 0.96/0.98 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------