TSTP Solution File: GRP126-3.004 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP126-3.004 : 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.jb5vRJiJF8 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 01:50:09 EDT 2023
% Result : Unsatisfiable 0.57s 1.02s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP126-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jb5vRJiJF8 true
% 0.13/0.35 % Computer : n006.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
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Aug 28 21:24:36 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.21/0.63 % Total configuration time : 435
% 0.21/0.63 % Estimated wc time : 1092
% 0.21/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.57/1.02 % Solved by fo/fo1_av.sh.
% 0.57/1.02 % done 801 iterations in 0.234s
% 0.57/1.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.57/1.02 % SZS output start Refutation
% 0.57/1.02 thf(e_4_type, type, e_4: $i).
% 0.57/1.02 thf(e_3_type, type, e_3: $i).
% 0.57/1.02 thf(e_2_type, type, e_2: $i).
% 0.57/1.02 thf(e_1_type, type, e_1: $i).
% 0.57/1.02 thf(product_type, type, product: $i > $i > $i > $o).
% 0.57/1.02 thf(group_element_type, type, group_element: $i > $o).
% 0.57/1.02 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.57/1.02 thf(element_1, axiom, (group_element @ e_1)).
% 0.57/1.02 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_1])).
% 0.57/1.02 thf(product_total_function1, axiom,
% 0.57/1.02 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.57/1.02 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.57/1.02 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 0.57/1.02 thf(zip_derived_cl37, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | ~ (group_element @ X1)
% 0.57/1.02 | (product @ X0 @ X1 @ e_1)
% 0.57/1.02 | (product @ X0 @ X1 @ e_2)
% 0.57/1.02 | (product @ X0 @ X1 @ e_3)
% 0.57/1.02 | (product @ X0 @ X1 @ e_4))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/1.02 thf(zip_derived_cl96, plain,
% 0.57/1.02 (![X0 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.02 thf(element_4, axiom, (group_element @ e_4)).
% 0.57/1.02 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_4])).
% 0.57/1.02 thf(zip_derived_cl229, plain,
% 0.57/1.02 (( (product @ e_1 @ e_4 @ e_4)
% 0.57/1.02 | (product @ e_1 @ e_4 @ e_3)
% 0.57/1.02 | (product @ e_1 @ e_4 @ e_2)
% 0.57/1.02 | (product @ e_1 @ e_4 @ e_1))),
% 0.57/1.02 inference('s_sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl24])).
% 0.57/1.02 thf(zip_derived_cl792, plain,
% 0.57/1.02 (( (product @ e_1 @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl229])).
% 0.57/1.02 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 0.57/1.02 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.57/1.02 inference('cnf', [status(esa)], [product_idempotence])).
% 0.57/1.02 thf(product_right_cancellation, axiom,
% 0.57/1.02 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.57/1.02 ( equalish @ W @ Z ))).
% 0.57/1.02 thf(zip_derived_cl39, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X0 @ X3 @ X2)
% 0.57/1.02 | (equalish @ X1 @ X3))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/1.02 thf(zip_derived_cl66, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.02 thf(zip_derived_cl1359, plain,
% 0.57/1.02 (( (equalish @ e_1 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl792, zip_derived_cl66])).
% 0.57/1.02 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 0.57/1.02 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.57/1.02 thf('0', plain, (~ ( (product @ e_1 @ e_4 @ e_1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1359, zip_derived_cl27])).
% 0.57/1.02 thf(zip_derived_cl789, plain,
% 0.57/1.02 (( (product @ e_1 @ e_4 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl229])).
% 0.57/1.02 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.57/1.02 inference('cnf', [status(esa)], [product_idempotence])).
% 0.57/1.02 thf(product_left_cancellation, axiom,
% 0.57/1.02 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.57/1.02 ( equalish @ W @ Z ))).
% 0.57/1.02 thf(zip_derived_cl40, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X3 @ X1 @ X2)
% 0.57/1.02 | (equalish @ X0 @ X3))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/1.02 thf(zip_derived_cl70, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.02 thf(zip_derived_cl797, plain,
% 0.57/1.02 (( (equalish @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl789, zip_derived_cl70])).
% 0.57/1.02 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 0.57/1.02 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.57/1.02 thf('1', plain, (~ ( (product @ e_1 @ e_4 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl797, zip_derived_cl34])).
% 0.57/1.02 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_4])).
% 0.57/1.02 thf(zip_derived_cl96, plain,
% 0.57/1.02 (![X0 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.02 thf(zip_derived_cl233, plain,
% 0.57/1.02 (( (product @ e_1 @ e_4 @ e_1)
% 0.57/1.02 | (product @ e_1 @ e_4 @ e_2)
% 0.57/1.02 | (product @ e_1 @ e_4 @ e_3)
% 0.57/1.02 | (product @ e_1 @ e_4 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl96])).
% 0.57/1.02 thf(zip_derived_cl855, plain,
% 0.57/1.02 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl233])).
% 0.57/1.02 thf(element_2, axiom, (group_element @ e_2)).
% 0.57/1.02 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_2])).
% 0.57/1.02 thf(zip_derived_cl96, plain,
% 0.57/1.02 (![X0 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.02 thf(zip_derived_cl231, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_1)
% 0.57/1.02 | (product @ e_1 @ e_2 @ e_2)
% 0.57/1.02 | (product @ e_1 @ e_2 @ e_3)
% 0.57/1.02 | (product @ e_1 @ e_2 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl96])).
% 0.57/1.02 thf(zip_derived_cl812, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl231])).
% 0.57/1.02 thf(zip_derived_cl39, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X0 @ X3 @ X2)
% 0.57/1.02 | (equalish @ X1 @ X3))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/1.02 thf(zip_derived_cl816, plain,
% 0.57/1.02 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl812, zip_derived_cl39])).
% 0.57/1.02 thf(zip_derived_cl909, plain,
% 0.57/1.02 (( (equalish @ e_2 @ e_4))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl855, zip_derived_cl816])).
% 0.57/1.02 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 0.57/1.02 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.57/1.02 thf('2', plain,
% 0.57/1.02 (~ ( (product @ e_1 @ e_4 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl909, zip_derived_cl30])).
% 0.57/1.02 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_2])).
% 0.57/1.02 thf(zip_derived_cl37, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | ~ (group_element @ X1)
% 0.57/1.02 | (product @ X0 @ X1 @ e_1)
% 0.57/1.02 | (product @ X0 @ X1 @ e_2)
% 0.57/1.02 | (product @ X0 @ X1 @ e_3)
% 0.57/1.02 | (product @ X0 @ X1 @ e_4))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/1.02 thf(zip_derived_cl97, plain,
% 0.57/1.02 (![X0 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | (product @ e_2 @ X0 @ e_1)
% 0.57/1.02 | (product @ e_2 @ X0 @ e_2)
% 0.57/1.02 | (product @ e_2 @ X0 @ e_3)
% 0.57/1.02 | (product @ e_2 @ X0 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.57/1.02 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_1])).
% 0.57/1.02 thf(zip_derived_cl242, plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_4)
% 0.57/1.02 | (product @ e_2 @ e_1 @ e_3)
% 0.57/1.02 | (product @ e_2 @ e_1 @ e_2)
% 0.57/1.02 | (product @ e_2 @ e_1 @ e_1))),
% 0.57/1.02 inference('s_sup+', [status(thm)], [zip_derived_cl97, zip_derived_cl21])).
% 0.57/1.02 thf(zip_derived_cl873, plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl242])).
% 0.57/1.02 thf(zip_derived_cl70, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.02 thf(zip_derived_cl1425, plain,
% 0.57/1.02 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl873, zip_derived_cl70])).
% 0.57/1.02 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.57/1.02 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.57/1.02 thf('3', plain, (~ ( (product @ e_2 @ e_1 @ e_1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1425, zip_derived_cl25])).
% 0.57/1.02 thf(zip_derived_cl872, plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl242])).
% 0.57/1.02 thf(zip_derived_cl66, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.02 thf(zip_derived_cl1409, plain,
% 0.57/1.02 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl872, zip_derived_cl66])).
% 0.57/1.02 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.57/1.02 thf(zip_derived_cl28, plain, (~ (equalish @ e_2 @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.57/1.02 thf('4', plain, (~ ( (product @ e_2 @ e_1 @ e_2))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1409, zip_derived_cl28])).
% 0.57/1.02 thf(element_3, axiom, (group_element @ e_3)).
% 0.57/1.02 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_3])).
% 0.57/1.02 thf(zip_derived_cl96, plain,
% 0.57/1.02 (![X0 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.02 thf(zip_derived_cl232, plain,
% 0.57/1.02 (( (product @ e_1 @ e_3 @ e_1)
% 0.57/1.02 | (product @ e_1 @ e_3 @ e_2)
% 0.57/1.02 | (product @ e_1 @ e_3 @ e_3)
% 0.57/1.02 | (product @ e_1 @ e_3 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl96])).
% 0.57/1.02 thf(zip_derived_cl827, plain,
% 0.57/1.02 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl232])).
% 0.57/1.02 thf(zip_derived_cl70, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.02 thf(zip_derived_cl834, plain,
% 0.57/1.02 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl827, zip_derived_cl70])).
% 0.57/1.02 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.57/1.02 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.57/1.02 thf('5', plain, (~ ( (product @ e_1 @ e_3 @ e_3))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl834, zip_derived_cl31])).
% 0.57/1.02 thf(zip_derived_cl96, plain,
% 0.57/1.02 (![X0 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.02 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_3])).
% 0.57/1.02 thf(zip_derived_cl228, plain,
% 0.57/1.02 (( (product @ e_1 @ e_3 @ e_4)
% 0.57/1.02 | (product @ e_1 @ e_3 @ e_3)
% 0.57/1.02 | (product @ e_1 @ e_3 @ e_2)
% 0.57/1.02 | (product @ e_1 @ e_3 @ e_1))),
% 0.57/1.02 inference('s_sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl23])).
% 0.57/1.02 thf(zip_derived_cl774, plain,
% 0.57/1.02 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.57/1.02 thf(zip_derived_cl66, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.02 thf(zip_derived_cl1322, plain,
% 0.57/1.02 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl774, zip_derived_cl66])).
% 0.57/1.02 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.57/1.02 thf(zip_derived_cl26, plain, (~ (equalish @ e_1 @ e_3)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.57/1.02 thf('6', plain, (~ ( (product @ e_1 @ e_3 @ e_1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1322, zip_derived_cl26])).
% 0.57/1.02 thf(zip_derived_cl96, plain,
% 0.57/1.02 (![X0 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.02 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.02 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_2])).
% 0.57/1.02 thf(zip_derived_cl227, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_4)
% 0.57/1.02 | (product @ e_1 @ e_2 @ e_3)
% 0.57/1.02 | (product @ e_1 @ e_2 @ e_2)
% 0.57/1.02 | (product @ e_1 @ e_2 @ e_1))),
% 0.57/1.02 inference('s_sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl22])).
% 0.57/1.02 thf(zip_derived_cl749, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl227])).
% 0.57/1.02 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [element_1])).
% 0.57/1.02 thf(zip_derived_cl97, plain,
% 0.57/1.02 (![X0 : $i]:
% 0.57/1.02 (~ (group_element @ X0)
% 0.57/1.02 | (product @ e_2 @ X0 @ e_1)
% 0.57/1.02 | (product @ e_2 @ X0 @ e_2)
% 0.57/1.02 | (product @ e_2 @ X0 @ e_3)
% 0.57/1.02 | (product @ e_2 @ X0 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.57/1.02 thf(zip_derived_cl246, plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_1)
% 0.57/1.02 | (product @ e_2 @ e_1 @ e_2)
% 0.57/1.02 | (product @ e_2 @ e_1 @ e_3)
% 0.57/1.02 | (product @ e_2 @ e_1 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl97])).
% 0.57/1.02 thf(zip_derived_cl934, plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl246])).
% 0.57/1.02 thf(qg4, conjecture,
% 0.57/1.02 (~( ( product @ Z1 @ Z2 @ Y ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 0.57/1.02 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 0.57/1.02 thf(zf_stmt_0, negated_conjecture,
% 0.57/1.02 (( product @ Z1 @ Z2 @ Y ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 0.57/1.02 ( ~( product @ X @ Y @ Z1 ) )),
% 0.57/1.02 inference('cnf.neg', [status(esa)], [qg4])).
% 0.57/1.02 thf(zip_derived_cl42, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 ( (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X2 @ X3 @ X1)
% 0.57/1.02 | ~ (product @ X3 @ X2 @ X0))),
% 0.57/1.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.02 thf(zip_derived_cl940, plain,
% 0.57/1.02 ((![X0 : $i]:
% 0.57/1.02 ( (product @ X0 @ e_3 @ e_2) | ~ (product @ e_1 @ e_2 @ X0)))
% 0.57/1.02 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl42])).
% 0.57/1.02 thf(zip_derived_cl1272, plain,
% 0.57/1.02 (( (product @ e_4 @ e_3 @ e_2))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl749, zip_derived_cl940])).
% 0.57/1.02 thf(zip_derived_cl40, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X3 @ X1 @ X2)
% 0.57/1.02 | (equalish @ X0 @ X3))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/1.02 thf(zip_derived_cl1275, plain,
% 0.57/1.02 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_4 @ X0)))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1272, zip_derived_cl40])).
% 0.57/1.02 thf(zip_derived_cl773, plain,
% 0.57/1.02 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.57/1.02 thf(zip_derived_cl1328, plain,
% 0.57/1.02 (( (equalish @ e_4 @ e_1))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_4)) &
% 0.57/1.02 ( (product @ e_1 @ e_3 @ e_2)) &
% 0.57/1.02 ( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.02 inference('s_sup+', [status(thm)],
% 0.57/1.02 [zip_derived_cl1275, zip_derived_cl773])).
% 0.57/1.02 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.57/1.02 thf('7', plain,
% 0.57/1.02 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_4)) |
% 0.57/1.02 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1328, zip_derived_cl34])).
% 0.57/1.02 thf(zip_derived_cl771, plain,
% 0.57/1.02 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.57/1.02 thf(zip_derived_cl749, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl227])).
% 0.57/1.02 thf(zip_derived_cl39, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X0 @ X3 @ X2)
% 0.57/1.02 | (equalish @ X1 @ X3))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/1.02 thf(zip_derived_cl754, plain,
% 0.57/1.02 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_4) | (equalish @ e_2 @ X0)))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl749, zip_derived_cl39])).
% 0.57/1.02 thf(zip_derived_cl779, plain,
% 0.57/1.02 (( (equalish @ e_2 @ e_3))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_1 @ e_3 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl771, zip_derived_cl754])).
% 0.57/1.02 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.57/1.02 thf(zip_derived_cl29, plain, (~ (equalish @ e_2 @ e_3)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.57/1.02 thf('8', plain,
% 0.57/1.02 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl779, zip_derived_cl29])).
% 0.57/1.02 thf(zip_derived_cl751, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl227])).
% 0.57/1.02 thf(zip_derived_cl70, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.02 thf(zip_derived_cl988, plain,
% 0.57/1.02 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl751, zip_derived_cl70])).
% 0.57/1.02 thf(zip_derived_cl28, plain, (~ (equalish @ e_2 @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.57/1.02 thf('9', plain, (~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl988, zip_derived_cl28])).
% 0.57/1.02 thf(zip_derived_cl752, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl227])).
% 0.57/1.02 thf(zip_derived_cl66, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.02 thf(zip_derived_cl1283, plain,
% 0.57/1.02 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl752, zip_derived_cl66])).
% 0.57/1.02 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.57/1.02 thf('10', plain, (~ ( (product @ e_1 @ e_2 @ e_1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1283, zip_derived_cl25])).
% 0.57/1.02 thf(zip_derived_cl934, plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl246])).
% 0.57/1.02 thf(zip_derived_cl812, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl231])).
% 0.57/1.02 thf(zip_derived_cl42, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 ( (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X2 @ X3 @ X1)
% 0.57/1.02 | ~ (product @ X3 @ X2 @ X0))),
% 0.57/1.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.02 thf(zip_derived_cl818, plain,
% 0.57/1.02 ((![X0 : $i]:
% 0.57/1.02 ( (product @ X0 @ e_3 @ e_1) | ~ (product @ e_2 @ e_1 @ X0)))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl812, zip_derived_cl42])).
% 0.57/1.02 thf(zip_derived_cl944, plain,
% 0.57/1.02 (( (product @ e_3 @ e_3 @ e_1))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl818])).
% 0.57/1.02 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.57/1.02 inference('cnf', [status(esa)], [product_idempotence])).
% 0.57/1.02 thf(product_total_function2, axiom,
% 0.57/1.02 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 0.57/1.02 ( equalish @ W @ Z ))).
% 0.57/1.02 thf(zip_derived_cl38, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X0 @ X1 @ X3)
% 0.57/1.02 | (equalish @ X2 @ X3))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_total_function2])).
% 0.57/1.02 thf(zip_derived_cl58, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl38])).
% 0.57/1.02 thf(zip_derived_cl972, plain,
% 0.57/1.02 (( (equalish @ e_3 @ e_1))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl944, zip_derived_cl58])).
% 0.57/1.02 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.57/1.02 thf('11', plain,
% 0.57/1.02 (~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl972, zip_derived_cl31])).
% 0.57/1.02 thf('12', plain,
% 0.57/1.02 (( (product @ e_1 @ e_3 @ e_2)) | ( (product @ e_1 @ e_3 @ e_4)) |
% 0.57/1.02 ( (product @ e_1 @ e_3 @ e_3)) | ( (product @ e_1 @ e_3 @ e_1))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.57/1.02 thf('13', plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_4)) | ( (product @ e_2 @ e_1 @ e_3)) |
% 0.57/1.02 ( (product @ e_2 @ e_1 @ e_2)) | ( (product @ e_2 @ e_1 @ e_1))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl242])).
% 0.57/1.02 thf(zip_derived_cl870, plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl242])).
% 0.57/1.02 thf(zip_derived_cl749, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl227])).
% 0.57/1.02 thf(zip_derived_cl42, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 ( (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X2 @ X3 @ X1)
% 0.57/1.02 | ~ (product @ X3 @ X2 @ X0))),
% 0.57/1.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.02 thf(zip_derived_cl756, plain,
% 0.57/1.02 ((![X0 : $i]:
% 0.57/1.02 ( (product @ X0 @ e_4 @ e_1) | ~ (product @ e_2 @ e_1 @ X0)))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl749, zip_derived_cl42])).
% 0.57/1.02 thf(zip_derived_cl880, plain,
% 0.57/1.02 (( (product @ e_4 @ e_4 @ e_1))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl870, zip_derived_cl756])).
% 0.57/1.02 thf(zip_derived_cl58, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl38])).
% 0.57/1.02 thf(zip_derived_cl895, plain,
% 0.57/1.02 (( (equalish @ e_4 @ e_1))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl880, zip_derived_cl58])).
% 0.57/1.02 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.57/1.02 thf('14', plain,
% 0.57/1.02 (~ ( (product @ e_1 @ e_2 @ e_4)) | ~ ( (product @ e_2 @ e_1 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl895, zip_derived_cl34])).
% 0.57/1.02 thf('15', plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_3)) | ( (product @ e_1 @ e_2 @ e_4)) |
% 0.57/1.02 ( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_1))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl227])).
% 0.57/1.02 thf(zip_derived_cl791, plain,
% 0.57/1.02 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl229])).
% 0.57/1.02 thf(zip_derived_cl812, plain,
% 0.57/1.02 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl231])).
% 0.57/1.02 thf(zip_derived_cl870, plain,
% 0.57/1.02 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl242])).
% 0.57/1.02 thf(zip_derived_cl42, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 ( (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X2 @ X3 @ X1)
% 0.57/1.02 | ~ (product @ X3 @ X2 @ X0))),
% 0.57/1.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.02 thf(zip_derived_cl877, plain,
% 0.57/1.02 ((![X0 : $i]:
% 0.57/1.02 ( (product @ X0 @ e_4 @ e_2) | ~ (product @ e_1 @ e_2 @ X0)))
% 0.57/1.02 <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl870, zip_derived_cl42])).
% 0.57/1.02 thf(zip_derived_cl1132, plain,
% 0.57/1.02 (( (product @ e_3 @ e_4 @ e_2))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl812, zip_derived_cl877])).
% 0.57/1.02 thf(zip_derived_cl40, plain,
% 0.57/1.02 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.02 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.02 | ~ (product @ X3 @ X1 @ X2)
% 0.57/1.02 | (equalish @ X0 @ X3))),
% 0.57/1.02 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/1.02 thf(zip_derived_cl1136, plain,
% 0.57/1.02 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_2) | (equalish @ e_3 @ X0)))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1132, zip_derived_cl40])).
% 0.57/1.02 thf(zip_derived_cl1345, plain,
% 0.57/1.02 (( (equalish @ e_3 @ e_1))
% 0.57/1.02 <= (( (product @ e_1 @ e_2 @ e_3)) &
% 0.57/1.02 ( (product @ e_1 @ e_4 @ e_2)) &
% 0.57/1.02 ( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.02 inference('s_sup-', [status(thm)],
% 0.57/1.02 [zip_derived_cl791, zip_derived_cl1136])).
% 0.57/1.02 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.57/1.02 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.57/1.02 thf('16', plain,
% 0.57/1.02 (~ ( (product @ e_1 @ e_4 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_3)) |
% 0.57/1.02 ~ ( (product @ e_2 @ e_1 @ e_4))),
% 0.57/1.02 inference('s_sup-', [status(thm)], [zip_derived_cl1345, zip_derived_cl31])).
% 0.57/1.02 thf('17', plain,
% 0.57/1.02 (( (product @ e_1 @ e_4 @ e_2)) | ( (product @ e_1 @ e_4 @ e_3)) |
% 0.57/1.02 ( (product @ e_1 @ e_4 @ e_4)) | ( (product @ e_1 @ e_4 @ e_1))),
% 0.57/1.02 inference('split', [status(esa)], [zip_derived_cl229])).
% 0.57/1.02 thf(zip_derived_cl1453, plain, ($false),
% 0.57/1.02 inference('sat_resolution*', [status(thm)],
% 0.57/1.02 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 0.57/1.02 '12', '13', '14', '15', '16', '17'])).
% 0.57/1.02
% 0.57/1.02 % SZS output end Refutation
% 0.57/1.02
% 0.57/1.02
% 0.57/1.02 % Terminating...
% 1.72/1.05 % Runner terminated.
% 1.76/1.07 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------