%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP126-1.004 : TPTP v9.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WiBTwT9Qce true
% Computer : n005.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 04:35:43 PM UTC 2025
% Result : Unsatisfiable 3.47s 1.10s
% Output : Refutation 3.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP126-1.004 : TPTP v9.2.0. Released v1.2.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WiBTwT9Qce true
% 0.13/0.34 % Computer : n005.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 : Wed Oct 1 14:20:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.57/0.64 % Total configuration time : 435
% 0.57/0.64 % Estimated wc time : 1092
% 0.57/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 3.47/1.10 % Solved by fo/fo1_av.sh.
% 3.47/1.10 % done 494 iterations in 0.327s
% 3.47/1.10 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.47/1.10 % SZS output start Refutation
% 3.47/1.10 thf(product_type, type, product: $i > $i > $i > $o).
% 3.47/1.10 thf(e_1_type, type, e_1: $i).
% 3.47/1.10 thf(e_3_type, type, e_3: $i).
% 3.47/1.10 thf(group_element_type, type, group_element: $i > $o).
% 3.47/1.10 thf(e_2_type, type, e_2: $i).
% 3.47/1.10 thf(e_4_type, type, e_4: $i).
% 3.47/1.10 thf(equalish_type, type, equalish: $i > $i > $o).
% 3.47/1.10 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 3.47/1.10 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 3.47/1.10 inference('cnf', [status(esa)], [product_idempotence])).
% 3.47/1.10 thf(product_left_cancellation, axiom,
% 3.47/1.10 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 3.47/1.10 ( equalish @ W @ Z ))).
% 3.47/1.10 thf(zip_derived_cl19, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X3 @ X1 @ X2)
% 3.47/1.10 | (equalish @ X0 @ X3))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_left_cancellation])).
% 3.47/1.10 thf(zip_derived_cl41, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 3.47/1.10 thf(product_total_function1, axiom,
% 3.47/1.10 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 3.47/1.10 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 3.47/1.10 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 3.47/1.10 thf(zip_derived_cl16, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (group_element @ X0)
% 3.47/1.10 | ~ (group_element @ X1)
% 3.47/1.10 | (product @ X0 @ X1 @ e_1)
% 3.47/1.10 | (product @ X0 @ X1 @ e_2)
% 3.47/1.10 | (product @ X0 @ X1 @ e_3)
% 3.47/1.10 | (product @ X0 @ X1 @ e_4))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_total_function1])).
% 3.47/1.10 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 3.47/1.10 inference('cnf', [status(esa)], [product_idempotence])).
% 3.47/1.10 thf(product_right_cancellation, axiom,
% 3.47/1.10 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 3.47/1.10 ( equalish @ W @ Z ))).
% 3.47/1.10 thf(zip_derived_cl18, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X0 @ X3 @ X2)
% 3.47/1.10 | (equalish @ X1 @ X3))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.47/1.10 thf(zip_derived_cl31, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 3.47/1.10 thf(zip_derived_cl38, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ e_4 @ X0 @ e_3)
% 3.47/1.10 | (product @ e_4 @ X0 @ e_2)
% 3.47/1.10 | (product @ e_4 @ X0 @ e_1)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | ~ (group_element @ e_4)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl31])).
% 3.47/1.10 thf(element_4, axiom, (group_element @ e_4)).
% 3.47/1.10 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_4])).
% 3.47/1.10 thf(zip_derived_cl39, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ e_4 @ X0 @ e_3)
% 3.47/1.10 | (product @ e_4 @ X0 @ e_2)
% 3.47/1.10 | (product @ e_4 @ X0 @ e_1)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl3])).
% 3.47/1.10 thf(zip_derived_cl290, plain,
% 3.47/1.10 (( (equalish @ e_3 @ e_4)
% 3.47/1.10 | (product @ e_4 @ e_3 @ e_2)
% 3.47/1.10 | (product @ e_4 @ e_3 @ e_1)
% 3.47/1.10 | ~ (group_element @ e_3)
% 3.47/1.10 | (equalish @ e_4 @ e_3))),
% 3.47/1.10 inference('s_sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 3.47/1.10 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 3.47/1.10 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.47/1.10 thf(element_3, axiom, (group_element @ e_3)).
% 3.47/1.10 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_3])).
% 3.47/1.10 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 3.47/1.10 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_3)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.47/1.10 thf(zip_derived_cl291, plain,
% 3.47/1.10 (( (product @ e_4 @ e_3 @ e_2) | (product @ e_4 @ e_3 @ e_1))),
% 3.47/1.10 inference('demod', [status(thm)],
% 3.47/1.10 [zip_derived_cl290, zip_derived_cl12, zip_derived_cl2,
% 3.47/1.10 zip_derived_cl15])).
% 3.47/1.10 thf(zip_derived_cl298, plain,
% 3.47/1.10 (( (product @ e_4 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl291])).
% 3.47/1.10 thf(zip_derived_cl16, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (group_element @ X0)
% 3.47/1.10 | ~ (group_element @ X1)
% 3.47/1.10 | (product @ X0 @ X1 @ e_1)
% 3.47/1.10 | (product @ X0 @ X1 @ e_2)
% 3.47/1.10 | (product @ X0 @ X1 @ e_3)
% 3.47/1.10 | (product @ X0 @ X1 @ e_4))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_total_function1])).
% 3.47/1.10 thf(zip_derived_cl41, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 3.47/1.10 thf(zip_derived_cl48, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_4 @ e_3)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_2)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_1)
% 3.47/1.10 | ~ (group_element @ e_4)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl41])).
% 3.47/1.10 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_4])).
% 3.47/1.10 thf(zip_derived_cl49, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_4 @ e_3)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_2)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_1)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl3])).
% 3.47/1.10 thf(zip_derived_cl298, plain,
% 3.47/1.10 (( (product @ e_4 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl291])).
% 3.47/1.10 thf(qg4, conjecture,
% 3.47/1.10 (~( ( product @ Z1 @ Z2 @ Y ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 3.47/1.10 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 3.47/1.10 thf(zf_stmt_0, negated_conjecture,
% 3.47/1.10 (( product @ Z1 @ Z2 @ Y ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 3.47/1.10 ( ~( product @ X @ Y @ Z1 ) )),
% 3.47/1.10 inference('cnf.neg', [status(esa)], [qg4])).
% 3.47/1.10 thf(zip_derived_cl21, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 ( (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X2 @ X3 @ X1)
% 3.47/1.10 | ~ (product @ X3 @ X2 @ X0))),
% 3.47/1.10 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.47/1.10 thf(zip_derived_cl303, plain,
% 3.47/1.10 ((![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_1 @ e_4) | ~ (product @ e_3 @ e_4 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl21])).
% 3.47/1.10 thf(zip_derived_cl376, plain,
% 3.47/1.10 ((( (equalish @ e_4 @ e_3)
% 3.47/1.10 | ~ (group_element @ e_3)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_1)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_2)
% 3.47/1.10 | (product @ e_3 @ e_1 @ e_4))) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl303])).
% 3.47/1.10 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_3)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.47/1.10 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_3])).
% 3.47/1.10 thf(zip_derived_cl384, plain,
% 3.47/1.10 ((( (product @ e_3 @ e_4 @ e_1)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_2)
% 3.47/1.10 | (product @ e_3 @ e_1 @ e_4))) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('demod', [status(thm)],
% 3.47/1.10 [zip_derived_cl376, zip_derived_cl15, zip_derived_cl2])).
% 3.47/1.10 thf(zip_derived_cl399, plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl384])).
% 3.47/1.10 thf(zip_derived_cl21, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 ( (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X2 @ X3 @ X1)
% 3.47/1.10 | ~ (product @ X3 @ X2 @ X0))),
% 3.47/1.10 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.47/1.10 thf(zip_derived_cl414, plain,
% 3.47/1.10 ((![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_2 @ e_3) | ~ (product @ e_4 @ e_3 @ X0)))
% 3.47/1.10 <= (( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl399, zip_derived_cl21])).
% 3.47/1.10 thf(zip_derived_cl771, plain,
% 3.47/1.10 (( (product @ e_1 @ e_2 @ e_3))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl414])).
% 3.47/1.10 thf(zip_derived_cl19, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X3 @ X1 @ X2)
% 3.47/1.10 | (equalish @ X0 @ X3))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_left_cancellation])).
% 3.47/1.10 thf(zip_derived_cl785, plain,
% 3.47/1.10 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl771, zip_derived_cl19])).
% 3.47/1.10 thf(zip_derived_cl39, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ e_4 @ X0 @ e_3)
% 3.47/1.10 | (product @ e_4 @ X0 @ e_2)
% 3.47/1.10 | (product @ e_4 @ X0 @ e_1)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl3])).
% 3.47/1.10 thf(zip_derived_cl998, plain,
% 3.47/1.10 ((( (equalish @ e_1 @ e_4)
% 3.47/1.10 | (product @ e_4 @ e_2 @ e_2)
% 3.47/1.10 | (product @ e_4 @ e_2 @ e_1)
% 3.47/1.10 | ~ (group_element @ e_2)
% 3.47/1.10 | (equalish @ e_4 @ e_2)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup+', [status(thm)], [zip_derived_cl785, zip_derived_cl39])).
% 3.47/1.10 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 3.47/1.10 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.47/1.10 thf(element_2, axiom, (group_element @ e_2)).
% 3.47/1.10 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_2])).
% 3.47/1.10 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 3.47/1.10 thf(zip_derived_cl14, plain, (~ (equalish @ e_4 @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.47/1.10 thf(zip_derived_cl1008, plain,
% 3.47/1.10 ((( (product @ e_4 @ e_2 @ e_2) | (product @ e_4 @ e_2 @ e_1)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('demod', [status(thm)],
% 3.47/1.10 [zip_derived_cl998, zip_derived_cl6, zip_derived_cl1,
% 3.47/1.10 zip_derived_cl14])).
% 3.47/1.10 thf(zip_derived_cl2489, plain,
% 3.47/1.10 (( (product @ e_4 @ e_2 @ e_2)) <= (( (product @ e_4 @ e_2 @ e_2)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl1008])).
% 3.47/1.10 thf(zip_derived_cl41, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 3.47/1.10 thf(zip_derived_cl2496, plain,
% 3.47/1.10 (( (equalish @ e_2 @ e_4)) <= (( (product @ e_4 @ e_2 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2489, zip_derived_cl41])).
% 3.47/1.10 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 3.47/1.10 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.47/1.10 thf('0', plain, (~ ( (product @ e_4 @ e_2 @ e_2))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2496, zip_derived_cl9])).
% 3.47/1.10 thf(zip_derived_cl39, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ e_4 @ X0 @ e_3)
% 3.47/1.10 | (product @ e_4 @ X0 @ e_2)
% 3.47/1.10 | (product @ e_4 @ X0 @ e_1)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl3])).
% 3.47/1.10 thf(zip_derived_cl785, plain,
% 3.47/1.10 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl771, zip_derived_cl19])).
% 3.47/1.10 thf(zip_derived_cl1002, plain,
% 3.47/1.10 ((( (equalish @ e_4 @ e_2)
% 3.47/1.10 | ~ (group_element @ e_2)
% 3.47/1.10 | (product @ e_4 @ e_2 @ e_1)
% 3.47/1.10 | (product @ e_4 @ e_2 @ e_2)
% 3.47/1.10 | (equalish @ e_1 @ e_4)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl785])).
% 3.47/1.10 thf(zip_derived_cl14, plain, (~ (equalish @ e_4 @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.47/1.10 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_2])).
% 3.47/1.10 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.47/1.10 thf(zip_derived_cl1005, plain,
% 3.47/1.10 ((( (product @ e_4 @ e_2 @ e_1) | (product @ e_4 @ e_2 @ e_2)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('demod', [status(thm)],
% 3.47/1.10 [zip_derived_cl1002, zip_derived_cl14, zip_derived_cl1,
% 3.47/1.10 zip_derived_cl6])).
% 3.47/1.10 thf(zip_derived_cl2424, plain,
% 3.47/1.10 (( (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_1)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl1005])).
% 3.47/1.10 thf(zip_derived_cl298, plain,
% 3.47/1.10 (( (product @ e_4 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl291])).
% 3.47/1.10 thf(zip_derived_cl18, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X0 @ X3 @ X2)
% 3.47/1.10 | (equalish @ X1 @ X3))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.47/1.10 thf(zip_derived_cl301, plain,
% 3.47/1.10 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl18])).
% 3.47/1.10 thf(zip_derived_cl2435, plain,
% 3.47/1.10 (( (equalish @ e_3 @ e_2))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_4 @ e_2 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)],
% 3.47/1.10 [zip_derived_cl2424, zip_derived_cl301])).
% 3.47/1.10 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 3.47/1.10 thf(zip_derived_cl11, plain, (~ (equalish @ e_3 @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.47/1.10 thf('1', plain,
% 3.47/1.10 (~ ( (product @ e_4 @ e_2 @ e_1)) | ~ ( (product @ e_4 @ e_3 @ e_1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2435, zip_derived_cl11])).
% 3.47/1.10 thf(zip_derived_cl16, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (group_element @ X0)
% 3.47/1.10 | ~ (group_element @ X1)
% 3.47/1.10 | (product @ X0 @ X1 @ e_1)
% 3.47/1.10 | (product @ X0 @ X1 @ e_2)
% 3.47/1.10 | (product @ X0 @ X1 @ e_3)
% 3.47/1.10 | (product @ X0 @ X1 @ e_4))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_total_function1])).
% 3.47/1.10 thf(zip_derived_cl303, plain,
% 3.47/1.10 ((![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_1 @ e_4) | ~ (product @ e_3 @ e_4 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl21])).
% 3.47/1.10 thf(zip_derived_cl328, plain,
% 3.47/1.10 ((( (product @ e_3 @ e_4 @ e_3)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_2)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_1)
% 3.47/1.10 | ~ (group_element @ e_4)
% 3.47/1.10 | ~ (group_element @ e_3)
% 3.47/1.10 | (product @ e_4 @ e_1 @ e_4))) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl303])).
% 3.47/1.10 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_4])).
% 3.47/1.10 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_3])).
% 3.47/1.10 thf(zip_derived_cl329, plain,
% 3.47/1.10 ((( (product @ e_3 @ e_4 @ e_3)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_2)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_1)
% 3.47/1.10 | (product @ e_4 @ e_1 @ e_4))) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('demod', [status(thm)],
% 3.47/1.10 [zip_derived_cl328, zip_derived_cl3, zip_derived_cl2])).
% 3.47/1.10 thf(zip_derived_cl2804, plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl329])).
% 3.47/1.10 thf(zip_derived_cl31, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 3.47/1.10 thf(zip_derived_cl2837, plain,
% 3.47/1.10 (( (equalish @ e_3 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2804, zip_derived_cl31])).
% 3.47/1.10 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.47/1.10 thf('2', plain, (~ ( (product @ e_3 @ e_4 @ e_3))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2837, zip_derived_cl12])).
% 3.47/1.10 thf(zip_derived_cl2802, plain,
% 3.47/1.10 (( (product @ e_4 @ e_1 @ e_4)) <= (( (product @ e_4 @ e_1 @ e_4)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl329])).
% 3.47/1.10 thf(zip_derived_cl31, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 3.47/1.10 thf(zip_derived_cl2811, plain,
% 3.47/1.10 (( (equalish @ e_4 @ e_1)) <= (( (product @ e_4 @ e_1 @ e_4)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2802, zip_derived_cl31])).
% 3.47/1.10 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 3.47/1.10 thf(zip_derived_cl13, plain, (~ (equalish @ e_4 @ e_1)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 3.47/1.10 thf('3', plain, (~ ( (product @ e_4 @ e_1 @ e_4))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2811, zip_derived_cl13])).
% 3.47/1.10 thf(zip_derived_cl400, plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl384])).
% 3.47/1.10 thf(zip_derived_cl303, plain,
% 3.47/1.10 ((![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_1 @ e_4) | ~ (product @ e_3 @ e_4 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl21])).
% 3.47/1.10 thf(zip_derived_cl435, plain,
% 3.47/1.10 (( (product @ e_1 @ e_1 @ e_4))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl400, zip_derived_cl303])).
% 3.47/1.10 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 3.47/1.10 inference('cnf', [status(esa)], [product_idempotence])).
% 3.47/1.10 thf(product_total_function2, axiom,
% 3.47/1.10 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 3.47/1.10 ( equalish @ W @ Z ))).
% 3.47/1.10 thf(zip_derived_cl17, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X0 @ X1 @ X3)
% 3.47/1.10 | (equalish @ X2 @ X3))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_total_function2])).
% 3.47/1.10 thf(zip_derived_cl22, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl17])).
% 3.47/1.10 thf(zip_derived_cl474, plain,
% 3.47/1.10 (( (equalish @ e_1 @ e_4))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl435, zip_derived_cl22])).
% 3.47/1.10 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.47/1.10 thf('4', plain,
% 3.47/1.10 (~ ( (product @ e_3 @ e_4 @ e_1)) | ~ ( (product @ e_4 @ e_3 @ e_1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl474, zip_derived_cl6])).
% 3.47/1.10 thf(zip_derived_cl299, plain,
% 3.47/1.10 (( (product @ e_4 @ e_3 @ e_2)) <= (( (product @ e_4 @ e_3 @ e_2)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl291])).
% 3.47/1.10 thf(zip_derived_cl400, plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl384])).
% 3.47/1.10 thf(zip_derived_cl21, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 ( (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X2 @ X3 @ X1)
% 3.47/1.10 | ~ (product @ X3 @ X2 @ X0))),
% 3.47/1.10 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.47/1.10 thf(zip_derived_cl432, plain,
% 3.47/1.10 ((![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_1 @ e_3) | ~ (product @ e_4 @ e_3 @ X0)))
% 3.47/1.10 <= (( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl400, zip_derived_cl21])).
% 3.47/1.10 thf(zip_derived_cl778, plain,
% 3.47/1.10 (( (product @ e_2 @ e_1 @ e_3))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl299, zip_derived_cl432])).
% 3.47/1.10 thf(zip_derived_cl18, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X0 @ X3 @ X2)
% 3.47/1.10 | (equalish @ X1 @ X3))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.47/1.10 thf(zip_derived_cl826, plain,
% 3.47/1.10 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl778, zip_derived_cl18])).
% 3.47/1.10 thf(zip_derived_cl49, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_4 @ e_3)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_2)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_1)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl3])).
% 3.47/1.10 thf(zip_derived_cl1110, plain,
% 3.47/1.10 ((( (equalish @ e_1 @ e_4)
% 3.47/1.10 | (product @ e_2 @ e_4 @ e_2)
% 3.47/1.10 | (product @ e_2 @ e_4 @ e_1)
% 3.47/1.10 | ~ (group_element @ e_2)
% 3.47/1.10 | (equalish @ e_4 @ e_2)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup+', [status(thm)], [zip_derived_cl826, zip_derived_cl49])).
% 3.47/1.10 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.47/1.10 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_2])).
% 3.47/1.10 thf(zip_derived_cl14, plain, (~ (equalish @ e_4 @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.47/1.10 thf(zip_derived_cl1121, plain,
% 3.47/1.10 ((( (product @ e_2 @ e_4 @ e_2) | (product @ e_2 @ e_4 @ e_1)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('demod', [status(thm)],
% 3.47/1.10 [zip_derived_cl1110, zip_derived_cl6, zip_derived_cl1,
% 3.47/1.10 zip_derived_cl14])).
% 3.47/1.10 thf(zip_derived_cl2995, plain,
% 3.47/1.10 (( (product @ e_2 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl1121])).
% 3.47/1.10 thf(zip_derived_cl31, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 3.47/1.10 thf(zip_derived_cl3002, plain,
% 3.47/1.10 (( (equalish @ e_2 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2995, zip_derived_cl31])).
% 3.47/1.10 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.47/1.10 thf('5', plain, (~ ( (product @ e_2 @ e_4 @ e_2))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl3002, zip_derived_cl9])).
% 3.47/1.10 thf(zip_derived_cl49, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_4 @ e_3)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_2)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_1)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl3])).
% 3.47/1.10 thf(zip_derived_cl826, plain,
% 3.47/1.10 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl778, zip_derived_cl18])).
% 3.47/1.10 thf(zip_derived_cl1114, plain,
% 3.47/1.10 ((( (equalish @ e_4 @ e_2)
% 3.47/1.10 | ~ (group_element @ e_2)
% 3.47/1.10 | (product @ e_2 @ e_4 @ e_1)
% 3.47/1.10 | (product @ e_2 @ e_4 @ e_2)
% 3.47/1.10 | (equalish @ e_1 @ e_4)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl826])).
% 3.47/1.10 thf(zip_derived_cl14, plain, (~ (equalish @ e_4 @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.47/1.10 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_2])).
% 3.47/1.10 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.47/1.10 thf(zip_derived_cl1118, plain,
% 3.47/1.10 ((( (product @ e_2 @ e_4 @ e_1) | (product @ e_2 @ e_4 @ e_2)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('demod', [status(thm)],
% 3.47/1.10 [zip_derived_cl1114, zip_derived_cl14, zip_derived_cl1,
% 3.47/1.10 zip_derived_cl6])).
% 3.47/1.10 thf(zip_derived_cl2859, plain,
% 3.47/1.10 (( (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl1118])).
% 3.47/1.10 thf(zip_derived_cl400, plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl384])).
% 3.47/1.10 thf(zip_derived_cl19, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X3 @ X1 @ X2)
% 3.47/1.10 | (equalish @ X0 @ X3))),
% 3.47/1.10 inference('cnf', [status(esa)], [product_left_cancellation])).
% 3.47/1.10 thf(zip_derived_cl431, plain,
% 3.47/1.10 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_1) | (equalish @ e_3 @ X0)))
% 3.47/1.10 <= (( (product @ e_3 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl400, zip_derived_cl19])).
% 3.47/1.10 thf(zip_derived_cl2871, plain,
% 3.47/1.10 (( (equalish @ e_3 @ e_2))
% 3.47/1.10 <= (( (product @ e_3 @ e_4 @ e_1)) & ( (product @ e_2 @ e_4 @ e_1)))),
% 3.47/1.10 inference('s_sup-', [status(thm)],
% 3.47/1.10 [zip_derived_cl2859, zip_derived_cl431])).
% 3.47/1.10 thf(zip_derived_cl11, plain, (~ (equalish @ e_3 @ e_2)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.47/1.10 thf('6', plain,
% 3.47/1.10 (~ ( (product @ e_2 @ e_4 @ e_1)) | ~ ( (product @ e_3 @ e_4 @ e_1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl2871, zip_derived_cl11])).
% 3.47/1.10 thf(zip_derived_cl49, plain,
% 3.47/1.10 (![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_4 @ e_3)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_2)
% 3.47/1.10 | (product @ X0 @ e_4 @ e_1)
% 3.47/1.10 | ~ (group_element @ X0)
% 3.47/1.10 | (equalish @ e_4 @ X0))),
% 3.47/1.10 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl3])).
% 3.47/1.10 thf(zip_derived_cl31, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 3.47/1.10 thf(zip_derived_cl374, plain,
% 3.47/1.10 (( (equalish @ e_4 @ e_3)
% 3.47/1.10 | ~ (group_element @ e_3)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_1)
% 3.47/1.10 | (product @ e_3 @ e_4 @ e_2)
% 3.47/1.10 | (equalish @ e_3 @ e_4))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl31])).
% 3.47/1.10 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_3)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.47/1.10 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 3.47/1.10 inference('cnf', [status(esa)], [element_3])).
% 3.47/1.10 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.47/1.10 thf(zip_derived_cl382, plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_3 @ e_4 @ e_2))),
% 3.47/1.10 inference('demod', [status(thm)],
% 3.47/1.10 [zip_derived_cl374, zip_derived_cl15, zip_derived_cl2,
% 3.47/1.10 zip_derived_cl12])).
% 3.47/1.10 thf('7', plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_1)) | ( (product @ e_3 @ e_4 @ e_2))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl382])).
% 3.47/1.10 thf(zip_derived_cl399, plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl384])).
% 3.47/1.10 thf(zip_derived_cl299, plain,
% 3.47/1.10 (( (product @ e_4 @ e_3 @ e_2)) <= (( (product @ e_4 @ e_3 @ e_2)))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl291])).
% 3.47/1.10 thf(zip_derived_cl21, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.47/1.10 ( (product @ X0 @ X1 @ X2)
% 3.47/1.10 | ~ (product @ X2 @ X3 @ X1)
% 3.47/1.10 | ~ (product @ X3 @ X2 @ X0))),
% 3.47/1.10 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.47/1.10 thf(zip_derived_cl333, plain,
% 3.47/1.10 ((![X0 : $i]:
% 3.47/1.10 ( (product @ X0 @ e_2 @ e_4) | ~ (product @ e_3 @ e_4 @ X0)))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl299, zip_derived_cl21])).
% 3.47/1.10 thf(zip_derived_cl417, plain,
% 3.47/1.10 (( (product @ e_2 @ e_2 @ e_4))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl399, zip_derived_cl333])).
% 3.47/1.10 thf(zip_derived_cl22, plain,
% 3.47/1.10 (![X0 : $i, X1 : $i]:
% 3.47/1.10 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl17])).
% 3.47/1.10 thf(zip_derived_cl459, plain,
% 3.47/1.10 (( (equalish @ e_2 @ e_4))
% 3.47/1.10 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl417, zip_derived_cl22])).
% 3.47/1.10 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_4)),
% 3.47/1.10 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.47/1.10 thf('8', plain,
% 3.47/1.10 (~ ( (product @ e_3 @ e_4 @ e_2)) | ~ ( (product @ e_4 @ e_3 @ e_2))),
% 3.47/1.10 inference('s_sup-', [status(thm)], [zip_derived_cl459, zip_derived_cl9])).
% 3.47/1.10 thf('9', plain,
% 3.47/1.10 (( (product @ e_2 @ e_4 @ e_1)) | ~ ( (product @ e_3 @ e_4 @ e_1)) |
% 3.47/1.10 ( (product @ e_2 @ e_4 @ e_2)) | ~ ( (product @ e_4 @ e_3 @ e_2))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl1118])).
% 3.47/1.10 thf('10', plain,
% 3.47/1.10 (( (product @ e_4 @ e_3 @ e_1)) | ( (product @ e_4 @ e_3 @ e_2))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl291])).
% 3.47/1.10 thf('11', plain,
% 3.47/1.10 (( (product @ e_3 @ e_4 @ e_2)) | ~ ( (product @ e_4 @ e_3 @ e_1)) |
% 3.47/1.10 ( (product @ e_3 @ e_4 @ e_1)) | ( (product @ e_4 @ e_1 @ e_4)) |
% 3.47/1.10 ( (product @ e_3 @ e_4 @ e_3))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl329])).
% 3.47/1.10 thf('12', plain,
% 3.47/1.10 (~ ( (product @ e_3 @ e_4 @ e_2)) | ~ ( (product @ e_4 @ e_3 @ e_1)) |
% 3.47/1.10 ( (product @ e_4 @ e_2 @ e_1)) | ( (product @ e_4 @ e_2 @ e_2))),
% 3.47/1.10 inference('split', [status(esa)], [zip_derived_cl1005])).
% 3.47/1.10 thf(zip_derived_cl3024, plain, ($false),
% 3.47/1.10 inference('sat_resolution*', [status(thm)],
% 3.47/1.10 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 3.47/1.10 '12'])).
% 3.47/1.10
% 3.47/1.10 % SZS output end Refutation
% 3.47/1.10
% 3.47/1.10
% 3.47/1.10 % Terminating...
% 3.78/1.15 % Runner terminated.
% 3.78/1.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------