TSTP Solution File: GRP124-6.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-6.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.tyLSOtdbvQ true
% Computer : n002.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 01:50:05 EDT 2023
% Result : Unsatisfiable 2.47s 1.07s
% Output : Refutation 2.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP124-6.004 : TPTP v8.1.2. Released v1.2.0.
% 0.10/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.tyLSOtdbvQ true
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 21:51:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 2.47/1.07 % Solved by fo/fo1_av.sh.
% 2.47/1.07 % done 644 iterations in 0.286s
% 2.47/1.07 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.47/1.07 % SZS output start Refutation
% 2.47/1.07 thf(product1_type, type, product1: $i > $i > $i > $o).
% 2.47/1.07 thf(e_1_type, type, e_1: $i).
% 2.47/1.07 thf(product2_type, type, product2: $i > $i > $i > $o).
% 2.47/1.07 thf(e_3_type, type, e_3: $i).
% 2.47/1.07 thf(group_element_type, type, group_element: $i > $o).
% 2.47/1.07 thf(e_2_type, type, e_2: $i).
% 2.47/1.07 thf(e_4_type, type, e_4: $i).
% 2.47/1.07 thf(equalish_type, type, equalish: $i > $i > $o).
% 2.47/1.07 thf(element_2, axiom, (group_element @ e_2)).
% 2.47/1.07 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 2.47/1.07 inference('cnf', [status(esa)], [element_2])).
% 2.47/1.07 thf(product1_total_function1, axiom,
% 2.47/1.07 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 2.47/1.07 ( product1 @ X @ Y @ e_1 ) | ( product1 @ X @ Y @ e_2 ) |
% 2.47/1.07 ( product1 @ X @ Y @ e_3 ) | ( product1 @ X @ Y @ e_4 ))).
% 2.47/1.07 thf(zip_derived_cl16, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i]:
% 2.47/1.07 (~ (group_element @ X0)
% 2.47/1.07 | ~ (group_element @ X1)
% 2.47/1.07 | (product1 @ X0 @ X1 @ e_1)
% 2.47/1.07 | (product1 @ X0 @ X1 @ e_2)
% 2.47/1.07 | (product1 @ X0 @ X1 @ e_3)
% 2.47/1.07 | (product1 @ X0 @ X1 @ e_4))),
% 2.47/1.07 inference('cnf', [status(esa)], [product1_total_function1])).
% 2.47/1.07 thf(zip_derived_cl28, plain,
% 2.47/1.07 (![X0 : $i]:
% 2.47/1.07 (~ (group_element @ X0)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_1)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_2)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_3)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_4))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl16])).
% 2.47/1.07 thf(element_3, axiom, (group_element @ e_3)).
% 2.47/1.07 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 2.47/1.07 inference('cnf', [status(esa)], [element_3])).
% 2.47/1.07 thf(zip_derived_cl101, plain,
% 2.47/1.07 (( (product1 @ e_2 @ e_3 @ e_4)
% 2.47/1.07 | (product1 @ e_2 @ e_3 @ e_3)
% 2.47/1.07 | (product1 @ e_2 @ e_3 @ e_2)
% 2.47/1.07 | (product1 @ e_2 @ e_3 @ e_1))),
% 2.47/1.07 inference('s_sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl2])).
% 2.47/1.07 thf(zip_derived_cl644, plain,
% 2.47/1.07 (( (product1 @ e_2 @ e_3 @ e_1)) <= (( (product1 @ e_2 @ e_3 @ e_1)))),
% 2.47/1.07 inference('split', [status(esa)], [zip_derived_cl101])).
% 2.47/1.07 thf(element_1, axiom, (group_element @ e_1)).
% 2.47/1.07 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 2.47/1.07 inference('cnf', [status(esa)], [element_1])).
% 2.47/1.07 thf(zip_derived_cl16, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i]:
% 2.47/1.07 (~ (group_element @ X0)
% 2.47/1.07 | ~ (group_element @ X1)
% 2.47/1.07 | (product1 @ X0 @ X1 @ e_1)
% 2.47/1.07 | (product1 @ X0 @ X1 @ e_2)
% 2.47/1.07 | (product1 @ X0 @ X1 @ e_3)
% 2.47/1.07 | (product1 @ X0 @ X1 @ e_4))),
% 2.47/1.07 inference('cnf', [status(esa)], [product1_total_function1])).
% 2.47/1.07 thf(zip_derived_cl27, plain,
% 2.47/1.07 (![X0 : $i]:
% 2.47/1.07 (~ (group_element @ X0)
% 2.47/1.07 | (product1 @ e_1 @ X0 @ e_1)
% 2.47/1.07 | (product1 @ e_1 @ X0 @ e_2)
% 2.47/1.07 | (product1 @ e_1 @ X0 @ e_3)
% 2.47/1.07 | (product1 @ e_1 @ X0 @ e_4))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 2.47/1.07 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 2.47/1.07 inference('cnf', [status(esa)], [element_2])).
% 2.47/1.07 thf(zip_derived_cl90, plain,
% 2.47/1.07 (( (product1 @ e_1 @ e_2 @ e_4)
% 2.47/1.07 | (product1 @ e_1 @ e_2 @ e_3)
% 2.47/1.07 | (product1 @ e_1 @ e_2 @ e_2)
% 2.47/1.07 | (product1 @ e_1 @ e_2 @ e_1))),
% 2.47/1.07 inference('s_sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl1])).
% 2.47/1.07 thf(zip_derived_cl110, plain,
% 2.47/1.07 (( (product1 @ e_1 @ e_2 @ e_3)) <= (( (product1 @ e_1 @ e_2 @ e_3)))),
% 2.47/1.07 inference('split', [status(esa)], [zip_derived_cl90])).
% 2.47/1.07 thf(qg2a, conjecture,
% 2.47/1.07 (~( ( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 2.47/1.07 ( ~( product1 @ X @ Y @ Z1 ) ) ))).
% 2.47/1.07 thf(zf_stmt_0, negated_conjecture,
% 2.47/1.07 (( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 2.47/1.07 ( ~( product1 @ X @ Y @ Z1 ) )),
% 2.47/1.07 inference('cnf.neg', [status(esa)], [qg2a])).
% 2.47/1.07 thf(zip_derived_cl26, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.07 ( (product2 @ X0 @ X1 @ X2)
% 2.47/1.07 | ~ (product1 @ X3 @ X2 @ X0)
% 2.47/1.07 | ~ (product1 @ X2 @ X1 @ X3))),
% 2.47/1.07 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.47/1.07 thf(zip_derived_cl141, plain,
% 2.47/1.07 ((![X0 : $i]:
% 2.47/1.07 ( (product2 @ e_3 @ X0 @ e_2) | ~ (product1 @ e_2 @ X0 @ e_1)))
% 2.47/1.07 <= (( (product1 @ e_1 @ e_2 @ e_3)))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl26])).
% 2.47/1.07 thf(product2_idempotence, axiom, (product2 @ X @ X @ X)).
% 2.47/1.07 thf(zip_derived_cl25, plain, (![X0 : $i]: (product2 @ X0 @ X0 @ X0)),
% 2.47/1.07 inference('cnf', [status(esa)], [product2_idempotence])).
% 2.47/1.07 thf(product2_total_function2, axiom,
% 2.47/1.07 (( ~( product2 @ X @ Y @ W ) ) | ( ~( product2 @ X @ Y @ Z ) ) |
% 2.47/1.07 ( equalish @ W @ Z ))).
% 2.47/1.07 thf(zip_derived_cl22, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.07 (~ (product2 @ X0 @ X1 @ X2)
% 2.47/1.07 | ~ (product2 @ X0 @ X1 @ X3)
% 2.47/1.07 | (equalish @ X2 @ X3))),
% 2.47/1.07 inference('cnf', [status(esa)], [product2_total_function2])).
% 2.47/1.07 thf(zip_derived_cl46, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i]:
% 2.47/1.07 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl22])).
% 2.47/1.07 thf(zip_derived_cl153, plain,
% 2.47/1.07 (((~ (product1 @ e_2 @ e_3 @ e_1) | (equalish @ e_3 @ e_2)))
% 2.47/1.07 <= (( (product1 @ e_1 @ e_2 @ e_3)))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl46])).
% 2.47/1.07 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 2.47/1.07 thf(zip_derived_cl11, plain, (~ (equalish @ e_3 @ e_2)),
% 2.47/1.07 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 2.47/1.07 thf(zip_derived_cl155, plain,
% 2.47/1.07 ((~ (product1 @ e_2 @ e_3 @ e_1)) <= (( (product1 @ e_1 @ e_2 @ e_3)))),
% 2.47/1.07 inference('demod', [status(thm)], [zip_derived_cl153, zip_derived_cl11])).
% 2.47/1.07 thf(zip_derived_cl1726, plain,
% 2.47/1.07 (($false)
% 2.47/1.07 <= (( (product1 @ e_1 @ e_2 @ e_3)) & ( (product1 @ e_2 @ e_3 @ e_1)))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl644, zip_derived_cl155])).
% 2.47/1.07 thf(zip_derived_cl112, plain,
% 2.47/1.07 (( (product1 @ e_1 @ e_2 @ e_1)) <= (( (product1 @ e_1 @ e_2 @ e_1)))),
% 2.47/1.07 inference('split', [status(esa)], [zip_derived_cl90])).
% 2.47/1.07 thf(product1_idempotence, axiom, (product1 @ X @ X @ X)).
% 2.47/1.07 thf(zip_derived_cl20, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 2.47/1.07 inference('cnf', [status(esa)], [product1_idempotence])).
% 2.47/1.07 thf(product1_right_cancellation, axiom,
% 2.47/1.07 (( ~( product1 @ X @ W @ Y ) ) | ( ~( product1 @ X @ Z @ Y ) ) |
% 2.47/1.07 ( equalish @ W @ Z ))).
% 2.47/1.07 thf(zip_derived_cl18, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.07 (~ (product1 @ X0 @ X1 @ X2)
% 2.47/1.07 | ~ (product1 @ X0 @ X3 @ X2)
% 2.47/1.07 | (equalish @ X1 @ X3))),
% 2.47/1.07 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 2.47/1.07 thf(zip_derived_cl36, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i]:
% 2.47/1.07 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 2.47/1.07 thf(zip_derived_cl264, plain,
% 2.47/1.07 (( (equalish @ e_1 @ e_2)) <= (( (product1 @ e_1 @ e_2 @ e_1)))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl36])).
% 2.47/1.07 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 2.47/1.07 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 2.47/1.07 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 2.47/1.07 thf('0', plain, (~ ( (product1 @ e_1 @ e_2 @ e_1))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl264, zip_derived_cl4])).
% 2.47/1.07 thf(zip_derived_cl111, plain,
% 2.47/1.07 (( (product1 @ e_1 @ e_2 @ e_2)) <= (( (product1 @ e_1 @ e_2 @ e_2)))),
% 2.47/1.07 inference('split', [status(esa)], [zip_derived_cl90])).
% 2.47/1.07 thf(zip_derived_cl20, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 2.47/1.07 inference('cnf', [status(esa)], [product1_idempotence])).
% 2.47/1.07 thf(product1_left_cancellation, axiom,
% 2.47/1.07 (( ~( product1 @ W @ Y @ X ) ) | ( ~( product1 @ Z @ Y @ X ) ) |
% 2.47/1.07 ( equalish @ W @ Z ))).
% 2.47/1.07 thf(zip_derived_cl19, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.07 (~ (product1 @ X0 @ X1 @ X2)
% 2.47/1.07 | ~ (product1 @ X3 @ X1 @ X2)
% 2.47/1.07 | (equalish @ X0 @ X3))),
% 2.47/1.07 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 2.47/1.07 thf(zip_derived_cl41, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i]:
% 2.47/1.07 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 2.47/1.07 thf(zip_derived_cl199, plain,
% 2.47/1.07 (( (equalish @ e_2 @ e_1)) <= (( (product1 @ e_1 @ e_2 @ e_2)))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl41])).
% 2.47/1.07 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 2.47/1.07 thf(zip_derived_cl7, plain, (~ (equalish @ e_2 @ e_1)),
% 2.47/1.07 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 2.47/1.07 thf('1', plain, (~ ( (product1 @ e_1 @ e_2 @ e_2))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl7])).
% 2.47/1.07 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 2.47/1.07 inference('cnf', [status(esa)], [element_3])).
% 2.47/1.07 thf(zip_derived_cl28, plain,
% 2.47/1.07 (![X0 : $i]:
% 2.47/1.07 (~ (group_element @ X0)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_1)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_2)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_3)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_4))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl16])).
% 2.47/1.07 thf(zip_derived_cl105, plain,
% 2.47/1.07 (( (product1 @ e_2 @ e_3 @ e_1)
% 2.47/1.07 | (product1 @ e_2 @ e_3 @ e_2)
% 2.47/1.07 | (product1 @ e_2 @ e_3 @ e_3)
% 2.47/1.07 | (product1 @ e_2 @ e_3 @ e_4))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl28])).
% 2.47/1.07 thf(zip_derived_cl708, plain,
% 2.47/1.07 (( (product1 @ e_2 @ e_3 @ e_3)) <= (( (product1 @ e_2 @ e_3 @ e_3)))),
% 2.47/1.07 inference('split', [status(esa)], [zip_derived_cl105])).
% 2.47/1.07 thf(zip_derived_cl41, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i]:
% 2.47/1.07 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 2.47/1.07 thf(zip_derived_cl715, plain,
% 2.47/1.07 (( (equalish @ e_3 @ e_2)) <= (( (product1 @ e_2 @ e_3 @ e_3)))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl708, zip_derived_cl41])).
% 2.47/1.07 thf(zip_derived_cl11, plain, (~ (equalish @ e_3 @ e_2)),
% 2.47/1.07 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 2.47/1.07 thf('2', plain, (~ ( (product1 @ e_2 @ e_3 @ e_3))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl715, zip_derived_cl11])).
% 2.47/1.07 thf(zip_derived_cl643, plain,
% 2.47/1.07 (( (product1 @ e_2 @ e_3 @ e_2)) <= (( (product1 @ e_2 @ e_3 @ e_2)))),
% 2.47/1.07 inference('split', [status(esa)], [zip_derived_cl101])).
% 2.47/1.07 thf(zip_derived_cl36, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i]:
% 2.47/1.07 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 2.47/1.07 thf(zip_derived_cl1701, plain,
% 2.47/1.07 (( (equalish @ e_2 @ e_3)) <= (( (product1 @ e_2 @ e_3 @ e_2)))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl643, zip_derived_cl36])).
% 2.47/1.07 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 2.47/1.07 thf(zip_derived_cl8, plain, (~ (equalish @ e_2 @ e_3)),
% 2.47/1.07 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 2.47/1.07 thf('3', plain, (~ ( (product1 @ e_2 @ e_3 @ e_2))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl1701, zip_derived_cl8])).
% 2.47/1.07 thf(zip_derived_cl644, plain,
% 2.47/1.07 (( (product1 @ e_2 @ e_3 @ e_1)) <= (( (product1 @ e_2 @ e_3 @ e_1)))),
% 2.47/1.07 inference('split', [status(esa)], [zip_derived_cl101])).
% 2.47/1.07 thf(zip_derived_cl28, plain,
% 2.47/1.07 (![X0 : $i]:
% 2.47/1.07 (~ (group_element @ X0)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_1)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_2)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_3)
% 2.47/1.07 | (product1 @ e_2 @ X0 @ e_4))),
% 2.47/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl16])).
% 2.47/1.07 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 2.47/1.07 inference('cnf', [status(esa)], [element_1])).
% 2.47/1.07 thf(zip_derived_cl99, plain,
% 2.47/1.07 (( (product1 @ e_2 @ e_1 @ e_4)
% 2.47/1.07 | (product1 @ e_2 @ e_1 @ e_3)
% 2.47/1.07 | (product1 @ e_2 @ e_1 @ e_2)
% 2.47/1.07 | (product1 @ e_2 @ e_1 @ e_1))),
% 2.47/1.07 inference('s_sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl0])).
% 2.47/1.07 thf(zip_derived_cl609, plain,
% 2.47/1.07 (( (product1 @ e_2 @ e_1 @ e_4)) <= (( (product1 @ e_2 @ e_1 @ e_4)))),
% 2.47/1.07 inference('split', [status(esa)], [zip_derived_cl99])).
% 2.47/1.07 thf(zip_derived_cl26, plain,
% 2.47/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.07 ( (product2 @ X0 @ X1 @ X2)
% 2.47/1.07 | ~ (product1 @ X3 @ X2 @ X0)
% 2.47/1.07 | ~ (product1 @ X2 @ X1 @ X3))),
% 2.47/1.07 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.47/1.07 thf(zip_derived_cl616, plain,
% 2.47/1.07 ((![X0 : $i]:
% 2.47/1.07 ( (product2 @ e_4 @ X0 @ e_1) | ~ (product1 @ e_1 @ X0 @ e_2)))
% 2.47/1.07 <= (( (product1 @ e_2 @ e_1 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl609, zip_derived_cl26])).
% 2.47/1.08 thf(zip_derived_cl109, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_2 @ e_4)) <= (( (product1 @ e_1 @ e_2 @ e_4)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl90])).
% 2.47/1.08 thf(zip_derived_cl26, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.08 ( (product2 @ X0 @ X1 @ X2)
% 2.47/1.08 | ~ (product1 @ X3 @ X2 @ X0)
% 2.47/1.08 | ~ (product1 @ X2 @ X1 @ X3))),
% 2.47/1.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.47/1.08 thf(zip_derived_cl116, plain,
% 2.47/1.08 ((![X0 : $i]:
% 2.47/1.08 ( (product2 @ e_4 @ X0 @ e_2) | ~ (product1 @ e_2 @ X0 @ e_1)))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl26])).
% 2.47/1.08 thf(zip_derived_cl22, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.08 (~ (product2 @ X0 @ X1 @ X2)
% 2.47/1.08 | ~ (product2 @ X0 @ X1 @ X3)
% 2.47/1.08 | (equalish @ X2 @ X3))),
% 2.47/1.08 inference('cnf', [status(esa)], [product2_total_function2])).
% 2.47/1.08 thf(zip_derived_cl121, plain,
% 2.47/1.08 ((![X0 : $i, X1 : $i]:
% 2.47/1.08 (~ (product1 @ e_2 @ X0 @ e_1)
% 2.47/1.08 | ~ (product2 @ e_4 @ X0 @ X1)
% 2.47/1.08 | (equalish @ e_2 @ X1)))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl22])).
% 2.47/1.08 thf(zip_derived_cl628, plain,
% 2.47/1.08 ((![X0 : $i]:
% 2.47/1.08 (~ (product1 @ e_1 @ X0 @ e_2)
% 2.47/1.08 | ~ (product1 @ e_2 @ X0 @ e_1)
% 2.47/1.08 | (equalish @ e_2 @ e_1)))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_4)) & ( (product1 @ e_2 @ e_1 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl616, zip_derived_cl121])).
% 2.47/1.08 thf(zip_derived_cl7, plain, (~ (equalish @ e_2 @ e_1)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 2.47/1.08 thf(zip_derived_cl636, plain,
% 2.47/1.08 ((![X0 : $i]:
% 2.47/1.08 (~ (product1 @ e_1 @ X0 @ e_2) | ~ (product1 @ e_2 @ X0 @ e_1)))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_4)) & ( (product1 @ e_2 @ e_1 @ e_4)))),
% 2.47/1.08 inference('demod', [status(thm)], [zip_derived_cl628, zip_derived_cl7])).
% 2.47/1.08 thf(zip_derived_cl1721, plain,
% 2.47/1.08 ((~ (product1 @ e_1 @ e_3 @ e_2))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_4)) &
% 2.47/1.08 ( (product1 @ e_2 @ e_1 @ e_4)) &
% 2.47/1.08 ( (product1 @ e_2 @ e_3 @ e_1)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl644, zip_derived_cl636])).
% 2.47/1.08 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 2.47/1.08 inference('cnf', [status(esa)], [element_3])).
% 2.47/1.08 thf(zip_derived_cl27, plain,
% 2.47/1.08 (![X0 : $i]:
% 2.47/1.08 (~ (group_element @ X0)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_1)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_2)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_3)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 2.47/1.08 thf(zip_derived_cl95, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_1)
% 2.47/1.08 | (product1 @ e_1 @ e_3 @ e_2)
% 2.47/1.08 | (product1 @ e_1 @ e_3 @ e_3)
% 2.47/1.08 | (product1 @ e_1 @ e_3 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl27])).
% 2.47/1.08 thf(zip_derived_cl560, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_2)) <= (( (product1 @ e_1 @ e_3 @ e_2)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl95])).
% 2.47/1.08 thf('4', plain,
% 2.47/1.08 (~ ( (product1 @ e_2 @ e_1 @ e_4)) | ~ ( (product1 @ e_2 @ e_3 @ e_1)) |
% 2.47/1.08 ~ ( (product1 @ e_1 @ e_3 @ e_2)) | ~ ( (product1 @ e_1 @ e_2 @ e_4))),
% 2.47/1.08 inference('s_sup+', [status(thm)],
% 2.47/1.08 [zip_derived_cl1721, zip_derived_cl560])).
% 2.47/1.08 thf(zip_derived_cl641, plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_3 @ e_4)) <= (( (product1 @ e_2 @ e_3 @ e_4)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl101])).
% 2.47/1.08 thf(zip_derived_cl609, plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_1 @ e_4)) <= (( (product1 @ e_2 @ e_1 @ e_4)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl99])).
% 2.47/1.08 thf(zip_derived_cl18, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.08 (~ (product1 @ X0 @ X1 @ X2)
% 2.47/1.08 | ~ (product1 @ X0 @ X3 @ X2)
% 2.47/1.08 | (equalish @ X1 @ X3))),
% 2.47/1.08 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 2.47/1.08 thf(zip_derived_cl614, plain,
% 2.47/1.08 ((![X0 : $i]: (~ (product1 @ e_2 @ X0 @ e_4) | (equalish @ e_1 @ X0)))
% 2.47/1.08 <= (( (product1 @ e_2 @ e_1 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl609, zip_derived_cl18])).
% 2.47/1.08 thf(zip_derived_cl734, plain,
% 2.47/1.08 (( (equalish @ e_1 @ e_3))
% 2.47/1.08 <= (( (product1 @ e_2 @ e_1 @ e_4)) & ( (product1 @ e_2 @ e_3 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl641, zip_derived_cl614])).
% 2.47/1.08 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 2.47/1.08 thf(zip_derived_cl5, plain, (~ (equalish @ e_1 @ e_3)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 2.47/1.08 thf('5', plain,
% 2.47/1.08 (~ ( (product1 @ e_2 @ e_3 @ e_4)) | ~ ( (product1 @ e_2 @ e_1 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl734, zip_derived_cl5])).
% 2.47/1.08 thf('6', plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_1 @ e_3)) | ( (product1 @ e_2 @ e_1 @ e_4)) |
% 2.47/1.08 ( (product1 @ e_2 @ e_1 @ e_2)) | ( (product1 @ e_2 @ e_1 @ e_1))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl99])).
% 2.47/1.08 thf(zip_derived_cl611, plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_1 @ e_2)) <= (( (product1 @ e_2 @ e_1 @ e_2)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl99])).
% 2.47/1.08 thf(zip_derived_cl36, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i]:
% 2.47/1.08 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 2.47/1.08 thf(zip_derived_cl1636, plain,
% 2.47/1.08 (( (equalish @ e_2 @ e_1)) <= (( (product1 @ e_2 @ e_1 @ e_2)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl611, zip_derived_cl36])).
% 2.47/1.08 thf(zip_derived_cl7, plain, (~ (equalish @ e_2 @ e_1)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 2.47/1.08 thf('7', plain, (~ ( (product1 @ e_2 @ e_1 @ e_2))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1636, zip_derived_cl7])).
% 2.47/1.08 thf(zip_derived_cl612, plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_1 @ e_1)) <= (( (product1 @ e_2 @ e_1 @ e_1)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl99])).
% 2.47/1.08 thf(zip_derived_cl41, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i]:
% 2.47/1.08 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 2.47/1.08 thf(zip_derived_cl1653, plain,
% 2.47/1.08 (( (equalish @ e_1 @ e_2)) <= (( (product1 @ e_2 @ e_1 @ e_1)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl612, zip_derived_cl41])).
% 2.47/1.08 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 2.47/1.08 thf('8', plain, (~ ( (product1 @ e_2 @ e_1 @ e_1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1653, zip_derived_cl4])).
% 2.47/1.08 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 2.47/1.08 inference('cnf', [status(esa)], [element_1])).
% 2.47/1.08 thf(zip_derived_cl28, plain,
% 2.47/1.08 (![X0 : $i]:
% 2.47/1.08 (~ (group_element @ X0)
% 2.47/1.08 | (product1 @ e_2 @ X0 @ e_1)
% 2.47/1.08 | (product1 @ e_2 @ X0 @ e_2)
% 2.47/1.08 | (product1 @ e_2 @ X0 @ e_3)
% 2.47/1.08 | (product1 @ e_2 @ X0 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl16])).
% 2.47/1.08 thf(zip_derived_cl103, plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_1 @ e_1)
% 2.47/1.08 | (product1 @ e_2 @ e_1 @ e_2)
% 2.47/1.08 | (product1 @ e_2 @ e_1 @ e_3)
% 2.47/1.08 | (product1 @ e_2 @ e_1 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 2.47/1.08 thf(zip_derived_cl683, plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_1 @ e_3)) <= (( (product1 @ e_2 @ e_1 @ e_3)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl103])).
% 2.47/1.08 thf(zip_derived_cl26, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.08 ( (product2 @ X0 @ X1 @ X2)
% 2.47/1.08 | ~ (product1 @ X3 @ X2 @ X0)
% 2.47/1.08 | ~ (product1 @ X2 @ X1 @ X3))),
% 2.47/1.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.47/1.08 thf(zip_derived_cl689, plain,
% 2.47/1.08 ((![X0 : $i]:
% 2.47/1.08 ( (product2 @ e_3 @ X0 @ e_1) | ~ (product1 @ e_1 @ X0 @ e_2)))
% 2.47/1.08 <= (( (product1 @ e_2 @ e_1 @ e_3)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl683, zip_derived_cl26])).
% 2.47/1.08 thf(zip_derived_cl46, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i]:
% 2.47/1.08 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl22])).
% 2.47/1.08 thf(zip_derived_cl695, plain,
% 2.47/1.08 (((~ (product1 @ e_1 @ e_3 @ e_2) | (equalish @ e_3 @ e_1)))
% 2.47/1.08 <= (( (product1 @ e_2 @ e_1 @ e_3)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl689, zip_derived_cl46])).
% 2.47/1.08 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 2.47/1.08 thf(zip_derived_cl10, plain, (~ (equalish @ e_3 @ e_1)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 2.47/1.08 thf(zip_derived_cl700, plain,
% 2.47/1.08 ((~ (product1 @ e_1 @ e_3 @ e_2)) <= (( (product1 @ e_2 @ e_1 @ e_3)))),
% 2.47/1.08 inference('demod', [status(thm)], [zip_derived_cl695, zip_derived_cl10])).
% 2.47/1.08 thf(zip_derived_cl560, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_2)) <= (( (product1 @ e_1 @ e_3 @ e_2)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl95])).
% 2.47/1.08 thf('9', plain,
% 2.47/1.08 (~ ( (product1 @ e_1 @ e_3 @ e_2)) | ~ ( (product1 @ e_2 @ e_1 @ e_3))),
% 2.47/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl700, zip_derived_cl560])).
% 2.47/1.08 thf(zip_derived_cl27, plain,
% 2.47/1.08 (![X0 : $i]:
% 2.47/1.08 (~ (group_element @ X0)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_1)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_2)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_3)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 2.47/1.08 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 2.47/1.08 inference('cnf', [status(esa)], [element_3])).
% 2.47/1.08 thf(zip_derived_cl91, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_4)
% 2.47/1.08 | (product1 @ e_1 @ e_3 @ e_3)
% 2.47/1.08 | (product1 @ e_1 @ e_3 @ e_2)
% 2.47/1.08 | (product1 @ e_1 @ e_3 @ e_1))),
% 2.47/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl2])).
% 2.47/1.08 thf('10', plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_4)) | ( (product1 @ e_1 @ e_3 @ e_2)) |
% 2.47/1.08 ( (product1 @ e_1 @ e_3 @ e_3)) | ( (product1 @ e_1 @ e_3 @ e_1))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl91])).
% 2.47/1.08 thf(zip_derived_cl480, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_3)) <= (( (product1 @ e_1 @ e_3 @ e_3)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl91])).
% 2.47/1.08 thf(zip_derived_cl41, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i]:
% 2.47/1.08 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 2.47/1.08 thf(zip_derived_cl552, plain,
% 2.47/1.08 (( (equalish @ e_3 @ e_1)) <= (( (product1 @ e_1 @ e_3 @ e_3)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl480, zip_derived_cl41])).
% 2.47/1.08 thf(zip_derived_cl10, plain, (~ (equalish @ e_3 @ e_1)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 2.47/1.08 thf('11', plain, (~ ( (product1 @ e_1 @ e_3 @ e_3))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl552, zip_derived_cl10])).
% 2.47/1.08 thf(zip_derived_cl482, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_1)) <= (( (product1 @ e_1 @ e_3 @ e_1)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl91])).
% 2.47/1.08 thf(zip_derived_cl36, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i]:
% 2.47/1.08 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 2.47/1.08 thf(zip_derived_cl1150, plain,
% 2.47/1.08 (( (equalish @ e_1 @ e_3)) <= (( (product1 @ e_1 @ e_3 @ e_1)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl482, zip_derived_cl36])).
% 2.47/1.08 thf(zip_derived_cl5, plain, (~ (equalish @ e_1 @ e_3)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 2.47/1.08 thf('12', plain, (~ ( (product1 @ e_1 @ e_3 @ e_1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1150, zip_derived_cl5])).
% 2.47/1.08 thf(zip_derived_cl479, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_4)) <= (( (product1 @ e_1 @ e_3 @ e_4)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl91])).
% 2.47/1.08 thf(zip_derived_cl109, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_2 @ e_4)) <= (( (product1 @ e_1 @ e_2 @ e_4)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl90])).
% 2.47/1.08 thf(zip_derived_cl18, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.08 (~ (product1 @ X0 @ X1 @ X2)
% 2.47/1.08 | ~ (product1 @ X0 @ X3 @ X2)
% 2.47/1.08 | (equalish @ X1 @ X3))),
% 2.47/1.08 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 2.47/1.08 thf(zip_derived_cl114, plain,
% 2.47/1.08 ((![X0 : $i]: (~ (product1 @ e_1 @ X0 @ e_4) | (equalish @ e_2 @ X0)))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl18])).
% 2.47/1.08 thf(zip_derived_cl487, plain,
% 2.47/1.08 (( (equalish @ e_2 @ e_3))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_4)) & ( (product1 @ e_1 @ e_3 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl479, zip_derived_cl114])).
% 2.47/1.08 thf(zip_derived_cl8, plain, (~ (equalish @ e_2 @ e_3)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 2.47/1.08 thf('13', plain,
% 2.47/1.08 (~ ( (product1 @ e_1 @ e_2 @ e_4)) | ~ ( (product1 @ e_1 @ e_3 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl487, zip_derived_cl8])).
% 2.47/1.08 thf('14', plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_3 @ e_1)) | ( (product1 @ e_2 @ e_3 @ e_4)) |
% 2.47/1.08 ( (product1 @ e_2 @ e_3 @ e_3)) | ( (product1 @ e_2 @ e_3 @ e_2))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl101])).
% 2.47/1.08 thf('15', plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_2 @ e_3)) | ( (product1 @ e_1 @ e_2 @ e_4)) |
% 2.47/1.08 ( (product1 @ e_1 @ e_2 @ e_2)) | ( (product1 @ e_1 @ e_2 @ e_1))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl90])).
% 2.47/1.08 thf('16', plain, (( (product1 @ e_1 @ e_2 @ e_3))),
% 2.47/1.08 inference('sat_resolution*', [status(thm)],
% 2.47/1.08 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 2.47/1.08 '12', '13', '14', '15'])).
% 2.47/1.08 thf(zip_derived_cl27, plain,
% 2.47/1.08 (![X0 : $i]:
% 2.47/1.08 (~ (group_element @ X0)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_1)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_2)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_3)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 2.47/1.08 thf(element_4, axiom, (group_element @ e_4)).
% 2.47/1.08 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 2.47/1.08 inference('cnf', [status(esa)], [element_4])).
% 2.47/1.08 thf(zip_derived_cl92, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_4 @ e_4)
% 2.47/1.08 | (product1 @ e_1 @ e_4 @ e_3)
% 2.47/1.08 | (product1 @ e_1 @ e_4 @ e_2)
% 2.47/1.08 | (product1 @ e_1 @ e_4 @ e_1))),
% 2.47/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl3])).
% 2.47/1.08 thf(zip_derived_cl513, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_4 @ e_1)) <= (( (product1 @ e_1 @ e_4 @ e_1)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl92])).
% 2.47/1.08 thf(zip_derived_cl36, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i]:
% 2.47/1.08 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 2.47/1.08 thf(zip_derived_cl1512, plain,
% 2.47/1.08 (( (equalish @ e_1 @ e_4)) <= (( (product1 @ e_1 @ e_4 @ e_1)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl36])).
% 2.47/1.08 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 2.47/1.08 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_4)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 2.47/1.08 thf('17', plain, (~ ( (product1 @ e_1 @ e_4 @ e_1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1512, zip_derived_cl6])).
% 2.47/1.08 thf(zip_derived_cl510, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_4 @ e_4)) <= (( (product1 @ e_1 @ e_4 @ e_4)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl92])).
% 2.47/1.08 thf(zip_derived_cl41, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i]:
% 2.47/1.08 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 2.47/1.08 thf(zip_derived_cl518, plain,
% 2.47/1.08 (( (equalish @ e_4 @ e_1)) <= (( (product1 @ e_1 @ e_4 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl510, zip_derived_cl41])).
% 2.47/1.08 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 2.47/1.08 thf(zip_derived_cl13, plain, (~ (equalish @ e_4 @ e_1)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 2.47/1.08 thf('18', plain, (~ ( (product1 @ e_1 @ e_4 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl518, zip_derived_cl13])).
% 2.47/1.08 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 2.47/1.08 inference('cnf', [status(esa)], [element_4])).
% 2.47/1.08 thf(zip_derived_cl27, plain,
% 2.47/1.08 (![X0 : $i]:
% 2.47/1.08 (~ (group_element @ X0)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_1)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_2)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_3)
% 2.47/1.08 | (product1 @ e_1 @ X0 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 2.47/1.08 thf(zip_derived_cl96, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_4 @ e_1)
% 2.47/1.08 | (product1 @ e_1 @ e_4 @ e_2)
% 2.47/1.08 | (product1 @ e_1 @ e_4 @ e_3)
% 2.47/1.08 | (product1 @ e_1 @ e_4 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl27])).
% 2.47/1.08 thf(zip_derived_cl583, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_4 @ e_3)) <= (( (product1 @ e_1 @ e_4 @ e_3)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl96])).
% 2.47/1.08 thf(zip_derived_cl110, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_2 @ e_3)) <= (( (product1 @ e_1 @ e_2 @ e_3)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl90])).
% 2.47/1.08 thf(zip_derived_cl18, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.08 (~ (product1 @ X0 @ X1 @ X2)
% 2.47/1.08 | ~ (product1 @ X0 @ X3 @ X2)
% 2.47/1.08 | (equalish @ X1 @ X3))),
% 2.47/1.08 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 2.47/1.08 thf(zip_derived_cl139, plain,
% 2.47/1.08 ((![X0 : $i]: (~ (product1 @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_3)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl18])).
% 2.47/1.08 thf(zip_derived_cl590, plain,
% 2.47/1.08 (( (equalish @ e_2 @ e_4))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_2 @ e_3)) & ( (product1 @ e_1 @ e_4 @ e_3)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl583, zip_derived_cl139])).
% 2.47/1.08 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 2.47/1.08 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_4)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 2.47/1.08 thf('19', plain,
% 2.47/1.08 (~ ( (product1 @ e_1 @ e_4 @ e_3)) | ~ ( (product1 @ e_1 @ e_2 @ e_3))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl590, zip_derived_cl9])).
% 2.47/1.08 thf('20', plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_4 @ e_2)) | ( (product1 @ e_1 @ e_4 @ e_3)) |
% 2.47/1.08 ( (product1 @ e_1 @ e_4 @ e_4)) | ( (product1 @ e_1 @ e_4 @ e_1))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl92])).
% 2.47/1.08 thf(zip_derived_cl512, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_4 @ e_2)) <= (( (product1 @ e_1 @ e_4 @ e_2)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl92])).
% 2.47/1.08 thf(zip_derived_cl560, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_2)) <= (( (product1 @ e_1 @ e_3 @ e_2)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl95])).
% 2.47/1.08 thf(zip_derived_cl18, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.08 (~ (product1 @ X0 @ X1 @ X2)
% 2.47/1.08 | ~ (product1 @ X0 @ X3 @ X2)
% 2.47/1.08 | (equalish @ X1 @ X3))),
% 2.47/1.08 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 2.47/1.08 thf(zip_derived_cl563, plain,
% 2.47/1.08 ((![X0 : $i]: (~ (product1 @ e_1 @ X0 @ e_2) | (equalish @ e_3 @ X0)))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_3 @ e_2)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl560, zip_derived_cl18])).
% 2.47/1.08 thf(zip_derived_cl1383, plain,
% 2.47/1.08 (( (equalish @ e_3 @ e_4))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_3 @ e_2)) & ( (product1 @ e_1 @ e_4 @ e_2)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl512, zip_derived_cl563])).
% 2.47/1.08 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 2.47/1.08 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_4)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 2.47/1.08 thf('21', plain,
% 2.47/1.08 (~ ( (product1 @ e_1 @ e_3 @ e_2)) | ~ ( (product1 @ e_1 @ e_4 @ e_2))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1383, zip_derived_cl12])).
% 2.47/1.08 thf(zip_derived_cl641, plain,
% 2.47/1.08 (( (product1 @ e_2 @ e_3 @ e_4)) <= (( (product1 @ e_2 @ e_3 @ e_4)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl101])).
% 2.47/1.08 thf(zip_derived_cl479, plain,
% 2.47/1.08 (( (product1 @ e_1 @ e_3 @ e_4)) <= (( (product1 @ e_1 @ e_3 @ e_4)))),
% 2.47/1.08 inference('split', [status(esa)], [zip_derived_cl91])).
% 2.47/1.08 thf(zip_derived_cl19, plain,
% 2.47/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.47/1.08 (~ (product1 @ X0 @ X1 @ X2)
% 2.47/1.08 | ~ (product1 @ X3 @ X1 @ X2)
% 2.47/1.08 | (equalish @ X0 @ X3))),
% 2.47/1.08 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 2.47/1.08 thf(zip_derived_cl485, plain,
% 2.47/1.08 ((![X0 : $i]: (~ (product1 @ X0 @ e_3 @ e_4) | (equalish @ e_1 @ X0)))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_3 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl479, zip_derived_cl19])).
% 2.47/1.08 thf(zip_derived_cl649, plain,
% 2.47/1.08 (( (equalish @ e_1 @ e_2))
% 2.47/1.08 <= (( (product1 @ e_1 @ e_3 @ e_4)) & ( (product1 @ e_2 @ e_3 @ e_4)))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl641, zip_derived_cl485])).
% 2.47/1.08 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 2.47/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 2.47/1.08 thf('22', plain,
% 2.47/1.08 (~ ( (product1 @ e_2 @ e_3 @ e_4)) | ~ ( (product1 @ e_1 @ e_3 @ e_4))),
% 2.47/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl649, zip_derived_cl4])).
% 2.47/1.08 thf('23', plain, (( (product1 @ e_2 @ e_3 @ e_1))),
% 2.47/1.08 inference('sat_resolution*', [status(thm)],
% 2.47/1.08 ['17', '18', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
% 2.47/1.08 '11', '12', '13', '15', '19', '20', '21', '10', '22', '14'])).
% 2.47/1.08 thf(zip_derived_cl1736, plain, ($false),
% 2.47/1.08 inference('simpl_trail', [status(thm)], [zip_derived_cl1726, '16', '23'])).
% 2.47/1.08
% 2.47/1.08 % SZS output end Refutation
% 2.47/1.08
% 2.47/1.08
% 2.47/1.08 % Terminating...
% 3.00/1.16 % Runner terminated.
% 3.00/1.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------