TSTP Solution File: GRP129-1.003 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CyWreU57rb true
% Computer : n006.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 01:50:13 EDT 2023
% Result : Unsatisfiable 0.60s 1.06s
% Output : Refutation 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.14/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CyWreU57rb true
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 01:14:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.49/0.67 % Total configuration time : 435
% 0.49/0.67 % Estimated wc time : 1092
% 0.49/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.49/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.49/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.59/0.80 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.60/1.06 % Solved by fo/fo1_av.sh.
% 0.60/1.06 % done 1304 iterations in 0.246s
% 0.60/1.06 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.60/1.06 % SZS output start Refutation
% 0.60/1.06 thf(e_1_type, type, e_1: $i).
% 0.60/1.06 thf(e_3_type, type, e_3: $i).
% 0.60/1.06 thf(group_element_type, type, group_element: $i > $o).
% 0.60/1.06 thf(e_2_type, type, e_2: $i).
% 0.60/1.06 thf(product_type, type, product: $i > $i > $i > $o).
% 0.60/1.06 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.60/1.06 thf(element_2, axiom, (group_element @ e_2)).
% 0.60/1.06 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_2])).
% 0.60/1.06 thf(element_3, axiom, (group_element @ e_3)).
% 0.60/1.06 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_3])).
% 0.60/1.06 thf(product_total_function1, axiom,
% 0.60/1.06 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.60/1.06 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.60/1.06 ( product @ X @ Y @ e_3 ))).
% 0.60/1.06 thf(zip_derived_cl9, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | ~ (group_element @ X1)
% 0.60/1.06 | (product @ X0 @ X1 @ e_1)
% 0.60/1.06 | (product @ X0 @ X1 @ e_2)
% 0.60/1.06 | (product @ X0 @ X1 @ e_3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_total_function1])).
% 0.60/1.06 thf(zip_derived_cl21, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_3 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_3 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_3 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl42, plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_1)
% 0.60/1.06 | (product @ e_3 @ e_2 @ e_2)
% 0.60/1.06 | (product @ e_3 @ e_2 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 0.60/1.06 thf(zip_derived_cl360, plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl42])).
% 0.60/1.06 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_2])).
% 0.60/1.06 thf(zip_derived_cl9, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | ~ (group_element @ X1)
% 0.60/1.06 | (product @ X0 @ X1 @ e_1)
% 0.60/1.06 | (product @ X0 @ X1 @ e_2)
% 0.60/1.06 | (product @ X0 @ X1 @ e_3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_total_function1])).
% 0.60/1.06 thf(zip_derived_cl20, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_2])).
% 0.60/1.06 thf(zip_derived_cl33, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_3)
% 0.60/1.06 | (product @ e_2 @ e_2 @ e_2)
% 0.60/1.06 | (product @ e_2 @ e_2 @ e_1))),
% 0.60/1.06 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl1])).
% 0.60/1.06 thf(zip_derived_cl201, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl33])).
% 0.60/1.06 thf(product_left_cancellation, axiom,
% 0.60/1.06 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.60/1.06 ( equalish @ W @ Z ))).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl205, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl622, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_2 @ e_2 @ e_2)) & ( (product @ e_3 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl360, zip_derived_cl205])).
% 0.60/1.06 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.60/1.06 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.60/1.06 thf('0', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_2 @ e_2)) | ~ ( (product @ e_3 @ e_2 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl622, zip_derived_cl6])).
% 0.60/1.06 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_3])).
% 0.60/1.06 thf(element_1, axiom, (group_element @ e_1)).
% 0.60/1.06 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_1])).
% 0.60/1.06 thf(zip_derived_cl9, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | ~ (group_element @ X1)
% 0.60/1.06 | (product @ X0 @ X1 @ e_1)
% 0.60/1.06 | (product @ X0 @ X1 @ e_2)
% 0.60/1.06 | (product @ X0 @ X1 @ e_3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_total_function1])).
% 0.60/1.06 thf(zip_derived_cl19, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl28, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_1)
% 0.60/1.06 | (product @ e_1 @ e_3 @ e_2)
% 0.60/1.06 | (product @ e_1 @ e_3 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl19])).
% 0.60/1.06 thf(zip_derived_cl128, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl28])).
% 0.60/1.06 thf(zip_derived_cl19, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_1])).
% 0.60/1.06 thf(zip_derived_cl23, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_3)
% 0.60/1.06 | (product @ e_1 @ e_1 @ e_2)
% 0.60/1.06 | (product @ e_1 @ e_1 @ e_1))),
% 0.60/1.06 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl0])).
% 0.60/1.06 thf(zip_derived_cl45, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(product_right_cancellation, axiom,
% 0.60/1.06 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.60/1.06 ( equalish @ W @ Z ))).
% 0.60/1.06 thf(zip_derived_cl11, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X0 @ X3 @ X2)
% 0.60/1.06 | (equalish @ X1 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.60/1.06 thf(zip_derived_cl55, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl182, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl55])).
% 0.60/1.06 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.60/1.06 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.60/1.06 thf('1', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl4])).
% 0.60/1.06 thf(zip_derived_cl21, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_3 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_3 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_3 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_2])).
% 0.60/1.06 thf(zip_derived_cl39, plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_3)
% 0.60/1.06 | (product @ e_3 @ e_2 @ e_2)
% 0.60/1.06 | (product @ e_3 @ e_2 @ e_1))),
% 0.60/1.06 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl1])).
% 0.60/1.06 thf(zip_derived_cl308, plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_3 @ e_2 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl39])).
% 0.60/1.06 thf(zip_derived_cl45, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl19, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_2])).
% 0.60/1.06 thf(zip_derived_cl24, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_3)
% 0.60/1.06 | (product @ e_1 @ e_2 @ e_2)
% 0.60/1.06 | (product @ e_1 @ e_2 @ e_1))),
% 0.60/1.06 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl1])).
% 0.60/1.06 thf(zip_derived_cl61, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.60/1.06 thf(qg3, conjecture,
% 0.60/1.06 (~( ( product @ Z1 @ Y @ Z2 ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 0.60/1.06 ( ~( product @ Y @ X @ Z1 ) ) ))).
% 0.60/1.06 thf(zf_stmt_0, negated_conjecture,
% 0.60/1.06 (( product @ Z1 @ Y @ Z2 ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 0.60/1.06 ( ~( product @ Y @ X @ Z1 ) )),
% 0.60/1.06 inference('cnf.neg', [status(esa)], [qg3])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl67, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_2 @ X0 @ e_3) | ~ (product @ X0 @ e_1 @ e_2)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl90, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl67])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl94, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_1 @ X0 @ e_3) | ~ (product @ X0 @ e_2 @ e_1)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl846, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) &
% 0.60/1.06 ( (product @ e_1 @ e_2 @ e_3)) &
% 0.60/1.06 ( (product @ e_3 @ e_2 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl308, zip_derived_cl94])).
% 0.60/1.06 thf(zip_derived_cl61, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.60/1.06 thf(zip_derived_cl11, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X0 @ X3 @ X2)
% 0.60/1.06 | (equalish @ X1 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.60/1.06 thf(zip_derived_cl65, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl872, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) &
% 0.60/1.06 ( (product @ e_1 @ e_2 @ e_3)) &
% 0.60/1.06 ( (product @ e_3 @ e_2 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl846, zip_derived_cl65])).
% 0.60/1.06 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.60/1.06 thf('2', plain,
% 0.60/1.06 (~ ( (product @ e_3 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_3)) |
% 0.60/1.06 ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl872, zip_derived_cl6])).
% 0.60/1.06 thf(zip_derived_cl63, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.60/1.06 thf(zip_derived_cl20, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_1])).
% 0.60/1.06 thf(zip_derived_cl32, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3)
% 0.60/1.06 | (product @ e_2 @ e_1 @ e_2)
% 0.60/1.06 | (product @ e_2 @ e_1 @ e_1))),
% 0.60/1.06 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 0.60/1.06 thf(zip_derived_cl185, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl191, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_1 @ X0 @ e_3) | ~ (product @ X0 @ e_2 @ e_1)))
% 0.60/1.06 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl616, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl191])).
% 0.60/1.06 thf(zip_derived_cl185, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl190, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_3) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl1414, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_1))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl616, zip_derived_cl190])).
% 0.60/1.06 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.60/1.06 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.60/1.06 thf('3', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1414, zip_derived_cl5])).
% 0.60/1.06 thf(zip_derived_cl44, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl128, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl28])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl133, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_3 @ X0 @ e_2) | ~ (product @ X0 @ e_1 @ e_3)))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl510, plain,
% 0.60/1.06 (( (product @ e_3 @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_1 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl133])).
% 0.60/1.06 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_1])).
% 0.60/1.06 thf(zip_derived_cl20, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl35, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_1)
% 0.60/1.06 | (product @ e_2 @ e_1 @ e_2)
% 0.60/1.06 | (product @ e_2 @ e_1 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl20])).
% 0.60/1.06 thf(zip_derived_cl240, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl244, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_2) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl705, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)) &
% 0.60/1.06 ( (product @ e_1 @ e_3 @ e_2)) &
% 0.60/1.06 ( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl510, zip_derived_cl244])).
% 0.60/1.06 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.60/1.06 thf('4', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_1 @ e_3)) |
% 0.60/1.06 ~ ( (product @ e_2 @ e_1 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl705, zip_derived_cl6])).
% 0.60/1.06 thf(zip_derived_cl19, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_3])).
% 0.60/1.06 thf(zip_derived_cl25, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_3)
% 0.60/1.06 | (product @ e_1 @ e_3 @ e_2)
% 0.60/1.06 | (product @ e_1 @ e_3 @ e_1))),
% 0.60/1.06 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 0.60/1.06 thf(zip_derived_cl80, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.60/1.06 thf(zip_derived_cl44, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl11, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X0 @ X3 @ X2)
% 0.60/1.06 | (equalish @ X1 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.60/1.06 thf(zip_derived_cl48, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl110, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_1 @ e_3 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl48])).
% 0.60/1.06 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.60/1.06 thf('5', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl4])).
% 0.60/1.06 thf(zip_derived_cl63, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.60/1.06 thf(zip_derived_cl11, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X0 @ X3 @ X2)
% 0.60/1.06 | (equalish @ X1 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.60/1.06 thf(zip_derived_cl413, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl82, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.60/1.06 thf(zip_derived_cl1037, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_1)) & ( (product @ e_1 @ e_3 @ e_1)))),
% 0.60/1.06 inference('s_sup+', [status(thm)], [zip_derived_cl413, zip_derived_cl82])).
% 0.60/1.06 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.60/1.06 thf('6', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_3 @ e_1))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1037, zip_derived_cl6])).
% 0.60/1.06 thf(zip_derived_cl240, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.60/1.06 thf(zip_derived_cl45, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl56, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_2) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl249, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl56])).
% 0.60/1.06 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('7', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl249, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl201, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl33])).
% 0.60/1.06 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_2])).
% 0.60/1.06 thf(zip_derived_cl19, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_1 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl27, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_1)
% 0.60/1.06 | (product @ e_1 @ e_2 @ e_2)
% 0.60/1.06 | (product @ e_1 @ e_2 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl19])).
% 0.60/1.06 thf(zip_derived_cl116, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl27])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl120, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl479, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl120])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('8', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl479, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl185, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl80, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl86, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_3 @ X0 @ e_3) | ~ (product @ X0 @ e_1 @ e_3)))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl214, plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl86])).
% 0.60/1.06 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_3])).
% 0.60/1.06 thf(zip_derived_cl20, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl37, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_1)
% 0.60/1.06 | (product @ e_2 @ e_3 @ e_2)
% 0.60/1.06 | (product @ e_2 @ e_3 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl20])).
% 0.60/1.06 thf(zip_derived_cl280, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl37])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl285, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_3 @ X0 @ e_2) | ~ (product @ X0 @ e_2 @ e_3)))
% 0.60/1.06 <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl770, plain,
% 0.60/1.06 (( (product @ e_3 @ e_3 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 0.60/1.06 ( (product @ e_2 @ e_1 @ e_3)) &
% 0.60/1.06 ( (product @ e_2 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl285])).
% 0.60/1.06 thf(zip_derived_cl280, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl37])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl284, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl786, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 0.60/1.06 ( (product @ e_2 @ e_1 @ e_3)) &
% 0.60/1.06 ( (product @ e_2 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl770, zip_derived_cl284])).
% 0.60/1.06 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.60/1.06 thf('9', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_3)) |
% 0.60/1.06 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl786, zip_derived_cl6])).
% 0.60/1.06 thf(zip_derived_cl20, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_3])).
% 0.60/1.06 thf(zip_derived_cl34, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_3)
% 0.60/1.06 | (product @ e_2 @ e_3 @ e_2)
% 0.60/1.06 | (product @ e_2 @ e_3 @ e_1))),
% 0.60/1.06 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 0.60/1.06 thf(zip_derived_cl222, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl34])).
% 0.60/1.06 thf(zip_derived_cl80, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl85, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl448, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_3 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl222, zip_derived_cl85])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('10', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_3 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl448, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl80, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.60/1.06 thf(zip_derived_cl65, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl271, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_1 @ e_3 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl65])).
% 0.60/1.06 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.60/1.06 thf('11', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_3 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl271, zip_derived_cl6])).
% 0.60/1.06 thf('12', plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_1)) | ( (product @ e_2 @ e_3 @ e_2)) |
% 0.60/1.06 ( (product @ e_2 @ e_3 @ e_3))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl34])).
% 0.60/1.06 thf(zip_derived_cl185, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl133, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_3 @ X0 @ e_2) | ~ (product @ X0 @ e_1 @ e_3)))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl512, plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl133])).
% 0.60/1.06 thf(zip_derived_cl205, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl1159, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_2)) &
% 0.60/1.06 ( (product @ e_2 @ e_2 @ e_2)) &
% 0.60/1.06 ( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl512, zip_derived_cl205])).
% 0.60/1.06 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.60/1.06 thf('13', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2)) |
% 0.60/1.06 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1159, zip_derived_cl6])).
% 0.60/1.06 thf(zip_derived_cl222, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl34])).
% 0.60/1.06 thf(zip_derived_cl185, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl11, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X0 @ X3 @ X2)
% 0.60/1.06 | (equalish @ X1 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.60/1.06 thf(zip_derived_cl189, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl563, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_3))
% 0.60/1.06 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_2 @ e_3 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl222, zip_derived_cl189])).
% 0.60/1.06 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.60/1.06 thf('14', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_3 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl563, zip_derived_cl4])).
% 0.60/1.06 thf(zip_derived_cl280, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl37])).
% 0.60/1.06 thf(zip_derived_cl128, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl28])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl132, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl506, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_2 @ e_3 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl132])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('15', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_2 @ e_3 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl506, zip_derived_cl3])).
% 0.60/1.06 thf('16', plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_1)) | ( (product @ e_1 @ e_3 @ e_3)) |
% 0.60/1.06 ( (product @ e_1 @ e_3 @ e_2))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.60/1.06 thf(zip_derived_cl82, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.60/1.06 thf(zip_derived_cl46, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl11, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X0 @ X3 @ X2)
% 0.60/1.06 | (equalish @ X1 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.60/1.06 thf(zip_derived_cl72, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl459, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_1 @ e_3 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl72])).
% 0.60/1.06 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.60/1.06 thf('17', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_3 @ e_1))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl459, zip_derived_cl4])).
% 0.60/1.06 thf(zip_derived_cl224, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl34])).
% 0.60/1.06 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_2])).
% 0.60/1.06 thf(zip_derived_cl9, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | ~ (group_element @ X1)
% 0.60/1.06 | (product @ X0 @ X1 @ e_1)
% 0.60/1.06 | (product @ X0 @ X1 @ e_2)
% 0.60/1.06 | (product @ X0 @ X1 @ e_3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_total_function1])).
% 0.60/1.06 thf(zip_derived_cl22, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 ( (product @ X0 @ X0 @ e_3)
% 0.60/1.06 | (product @ X0 @ X0 @ e_2)
% 0.60/1.06 | (product @ X0 @ X0 @ e_1)
% 0.60/1.06 | ~ (group_element @ X0))),
% 0.60/1.06 inference('eq_fact', [status(thm)], [zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl30, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_3)
% 0.60/1.06 | (product @ e_2 @ e_2 @ e_2)
% 0.60/1.06 | (product @ e_2 @ e_2 @ e_1))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 0.60/1.06 thf(zip_derived_cl156, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.60/1.06 thf(zip_derived_cl11, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X0 @ X3 @ X2)
% 0.60/1.06 | (equalish @ X1 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.60/1.06 thf(zip_derived_cl160, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 0.60/1.06 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl676, plain,
% 0.60/1.06 (( (equalish @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_2 @ e_3 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl224, zip_derived_cl160])).
% 0.60/1.06 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.60/1.06 thf('18', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_2 @ e_3 @ e_1))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl676, zip_derived_cl6])).
% 0.60/1.06 thf(zip_derived_cl240, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.60/1.06 thf(zip_derived_cl67, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_2 @ X0 @ e_3) | ~ (product @ X0 @ e_1 @ e_2)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl250, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl67])).
% 0.60/1.06 thf(zip_derived_cl61, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl66, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl378, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl66])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('19', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl378, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [element_2])).
% 0.60/1.06 thf(zip_derived_cl20, plain,
% 0.60/1.06 (![X0 : $i]:
% 0.60/1.06 (~ (group_element @ X0)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_1)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_2)
% 0.60/1.06 | (product @ e_2 @ X0 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.60/1.06 thf(zip_derived_cl36, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_1)
% 0.60/1.06 | (product @ e_2 @ e_2 @ e_2)
% 0.60/1.06 | (product @ e_2 @ e_2 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl20])).
% 0.60/1.06 thf(zip_derived_cl257, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl36])).
% 0.60/1.06 thf(zip_derived_cl189, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl562, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_2 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl257, zip_derived_cl189])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('20', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl562, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl257, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl36])).
% 0.60/1.06 thf(zip_derived_cl66, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl318, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl257, zip_derived_cl66])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('21', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl318, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl240, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.60/1.06 thf(zip_derived_cl116, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl27])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl121, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_2 @ X0 @ e_2) | ~ (product @ X0 @ e_1 @ e_2)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl488, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl121])).
% 0.60/1.06 thf(zip_derived_cl120, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl528, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl488, zip_derived_cl120])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('22', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl528, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl187, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl46, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl73, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl604, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl73])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('23', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_1 @ e_1)) | ~ ( (product @ e_2 @ e_1 @ e_1))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl604, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl63, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.60/1.06 thf(zip_derived_cl72, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl420, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_1 @ e_2 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl72])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('24', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_1))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl187, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl44, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl50, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_1 @ X0 @ e_3) | ~ (product @ X0 @ e_1 @ e_1)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl602, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl50])).
% 0.60/1.06 thf(zip_derived_cl48, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl1374, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl602, zip_derived_cl48])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('25', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_1 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_1))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1374, zip_derived_cl3])).
% 0.60/1.06 thf(zip_derived_cl187, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl45, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl57, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_1 @ X0 @ e_2) | ~ (product @ X0 @ e_1 @ e_1)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl603, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl57])).
% 0.60/1.06 thf(zip_derived_cl55, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl1395, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl55])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('26', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1395, zip_derived_cl3])).
% 0.60/1.06 thf('27', plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3)) | ( (product @ e_2 @ e_1 @ e_1)) |
% 0.60/1.06 ( (product @ e_2 @ e_1 @ e_2))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl185, plain,
% 0.60/1.06 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.60/1.06 thf(zip_derived_cl44, plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl49, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl195, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl49])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('28', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_1 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl195, zip_derived_cl3])).
% 0.60/1.06 thf('29', plain,
% 0.60/1.06 (( (product @ e_1 @ e_1 @ e_2)) | ( (product @ e_1 @ e_1 @ e_3)) |
% 0.60/1.06 ( (product @ e_1 @ e_1 @ e_1))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl23])).
% 0.60/1.06 thf(zip_derived_cl116, plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl27])).
% 0.60/1.06 thf(zip_derived_cl55, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl11])).
% 0.60/1.06 thf(zip_derived_cl181, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl55])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('30', plain,
% 0.60/1.06 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl181, zip_derived_cl3])).
% 0.60/1.06 thf('31', plain,
% 0.60/1.06 (( (product @ e_1 @ e_2 @ e_3)) | ( (product @ e_1 @ e_2 @ e_2)) |
% 0.60/1.06 ( (product @ e_1 @ e_2 @ e_1))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.60/1.06 thf(zip_derived_cl306, plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_3)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl39])).
% 0.60/1.06 thf(zip_derived_cl66, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl319, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_3))
% 0.60/1.06 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_3 @ e_2 @ e_3)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl306, zip_derived_cl66])).
% 0.60/1.06 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.60/1.06 thf('32', plain,
% 0.60/1.06 (~ ( (product @ e_3 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl319, zip_derived_cl4])).
% 0.60/1.06 thf('33', plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_2)) | ( (product @ e_3 @ e_2 @ e_3)) |
% 0.60/1.06 ( (product @ e_3 @ e_2 @ e_1))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl39])).
% 0.60/1.06 thf(zip_derived_cl360, plain,
% 0.60/1.06 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl42])).
% 0.60/1.06 thf(zip_derived_cl156, plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.60/1.06 thf(zip_derived_cl13, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 ( (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X0 @ X2)
% 0.60/1.06 | ~ (product @ X1 @ X3 @ X0))),
% 0.60/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.60/1.06 thf(zip_derived_cl162, plain,
% 0.60/1.06 ((![X0 : $i]:
% 0.60/1.06 ( (product @ e_2 @ X0 @ e_1) | ~ (product @ X0 @ e_2 @ e_2)))
% 0.60/1.06 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl13])).
% 0.60/1.06 thf(zip_derived_cl544, plain,
% 0.60/1.06 (( (product @ e_2 @ e_3 @ e_1))
% 0.60/1.06 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_3 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl360, zip_derived_cl162])).
% 0.60/1.06 thf(zip_derived_cl82, plain,
% 0.60/1.06 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.60/1.06 thf(zip_derived_cl12, plain,
% 0.60/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.60/1.06 (~ (product @ X0 @ X1 @ X2)
% 0.60/1.06 | ~ (product @ X3 @ X1 @ X2)
% 0.60/1.06 | (equalish @ X0 @ X3))),
% 0.60/1.06 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.60/1.06 thf(zip_derived_cl454, plain,
% 0.60/1.06 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_1) | (equalish @ e_1 @ X0)))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl12])).
% 0.60/1.06 thf(zip_derived_cl1268, plain,
% 0.60/1.06 (( (equalish @ e_1 @ e_2))
% 0.60/1.06 <= (( (product @ e_1 @ e_3 @ e_1)) &
% 0.60/1.06 ( (product @ e_2 @ e_2 @ e_1)) &
% 0.60/1.06 ( (product @ e_3 @ e_2 @ e_2)))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl544, zip_derived_cl454])).
% 0.60/1.06 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.60/1.06 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.60/1.06 thf('34', plain,
% 0.60/1.06 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_3 @ e_2 @ e_2)) |
% 0.60/1.06 ~ ( (product @ e_1 @ e_3 @ e_1))),
% 0.60/1.06 inference('s_sup-', [status(thm)], [zip_derived_cl1268, zip_derived_cl3])).
% 0.60/1.06 thf('35', plain,
% 0.60/1.06 (( (product @ e_2 @ e_2 @ e_1)) | ( (product @ e_2 @ e_2 @ e_2)) |
% 0.60/1.06 ( (product @ e_2 @ e_2 @ e_3))),
% 0.60/1.06 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.60/1.06 thf(zip_derived_cl2019, plain, ($false),
% 0.60/1.06 inference('sat_resolution*', [status(thm)],
% 0.60/1.06 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 0.60/1.06 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 0.60/1.06 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 0.60/1.06 '32', '33', '34', '35'])).
% 0.60/1.06
% 0.60/1.06 % SZS output end Refutation
% 0.60/1.06
% 0.60/1.06
% 0.60/1.06 % Terminating...
% 1.74/1.17 % Runner terminated.
% 1.74/1.18 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------