%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP040-4 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.qCIaFWB3lz 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 Oct 2 04:35:30 PM UTC 2025
% Result : Unsatisfiable 1.04s 0.85s
% Output : Refutation 1.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : GRP040-4 : TPTP v9.2.0. Released v1.0.0.
% 0.05/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.qCIaFWB3lz true
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Oct 1 14:09:38 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.11/0.34 % Running portfolio for 300 s
% 0.11/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34 % Number of cores: 8
% 0.11/0.34 % Python version: Python 3.6.8
% 0.11/0.34 % Running in FO mode
% 0.16/0.54 % Total configuration time : 435
% 0.16/0.54 % Estimated wc time : 1092
% 0.16/0.54 % Estimated cpu time (7 cpus) : 156.0
% 0.75/0.68 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.75/0.69 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.75/0.69 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.75/0.69 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.75/0.69 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.04/0.71 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.04/0.72 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.04/0.85 % Solved by fo/fo13.sh.
% 1.04/0.85 % done 233 iterations in 0.092s
% 1.04/0.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.04/0.85 % SZS output start Refutation
% 1.04/0.85 thf(inverse_type, type, inverse: $i > $i).
% 1.04/0.85 thf(d_type, type, d: $i).
% 1.04/0.85 thf(product_type, type, product: $i > $i > $i > $o).
% 1.04/0.85 thf(element_in_O2_type, type, element_in_O2: $i > $i > $i).
% 1.04/0.85 thf(b_type, type, b: $i).
% 1.04/0.85 thf(a_type, type, a: $i).
% 1.04/0.85 thf(identity_type, type, identity: $i).
% 1.04/0.85 thf(subgroup_member_type, type, subgroup_member: $i > $o).
% 1.04/0.85 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.04/0.85 thf(c_type, type, c: $i).
% 1.04/0.85 thf(total_function1, axiom, (product @ X @ Y @ ( multiply @ X @ Y ))).
% 1.04/0.85 thf(zip_derived_cl4, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 1.04/0.85 inference('cnf', [status(esa)], [total_function1])).
% 1.04/0.85 thf(left_identity, axiom, (product @ identity @ X @ X)).
% 1.04/0.85 thf(zip_derived_cl0, plain, (![X0 : $i]: (product @ identity @ X0 @ X0)),
% 1.04/0.85 inference('cnf', [status(esa)], [left_identity])).
% 1.04/0.85 thf(zip_derived_cl4, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 1.04/0.85 inference('cnf', [status(esa)], [total_function1])).
% 1.04/0.85 thf(prove_inverse_is_self_cancelling, conjecture,
% 1.04/0.85 (( inverse @ ( inverse @ A ) ) != ( A ))).
% 1.04/0.85 thf(zf_stmt_0, negated_conjecture, (( inverse @ ( inverse @ A ) ) = ( A )),
% 1.04/0.85 inference('cnf.neg', [status(esa)], [prove_inverse_is_self_cancelling])).
% 1.04/0.85 thf(zip_derived_cl20, plain,
% 1.04/0.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 1.04/0.85 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.04/0.85 thf(left_inverse, axiom, (product @ ( inverse @ X ) @ X @ identity)).
% 1.04/0.85 thf(zip_derived_cl2, plain,
% 1.04/0.85 (![X0 : $i]: (product @ (inverse @ X0) @ X0 @ identity)),
% 1.04/0.85 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/0.85 thf(total_function2, axiom,
% 1.04/0.85 (( ~( product @ X @ Y @ Z ) ) | ( ~( product @ X @ Y @ W ) ) |
% 1.04/0.85 ( ( Z ) = ( W ) ))).
% 1.04/0.85 thf(zip_derived_cl5, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/0.85 (~ (product @ X0 @ X1 @ X2)
% 1.04/0.85 | ~ (product @ X0 @ X1 @ X3)
% 1.04/0.85 | ((X2) = (X3)))),
% 1.04/0.85 inference('cnf', [status(esa)], [total_function2])).
% 1.04/0.85 thf(zip_derived_cl29, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 (~ (product @ (inverse @ X0) @ X0 @ X1) | ((identity) = (X1)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl5])).
% 1.04/0.85 thf(zip_derived_cl156, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 (~ (product @ X0 @ (inverse @ X0) @ X1) | ((identity) = (X1)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl29])).
% 1.04/0.85 thf(zip_derived_cl157, plain,
% 1.04/0.85 (![X0 : $i]: ((identity) = (multiply @ X0 @ (inverse @ X0)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl156])).
% 1.04/0.85 thf(zip_derived_cl4, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 1.04/0.85 inference('cnf', [status(esa)], [total_function1])).
% 1.04/0.85 thf(associativity1, axiom,
% 1.04/0.85 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ Y @ Z @ V ) ) |
% 1.04/0.85 ( ~( product @ U @ Z @ W ) ) | ( product @ X @ V @ W ))).
% 1.04/0.85 thf(zip_derived_cl6, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.04/0.85 (~ (product @ X0 @ X1 @ X2)
% 1.04/0.85 | ~ (product @ X1 @ X3 @ X4)
% 1.04/0.85 | ~ (product @ X2 @ X3 @ X5)
% 1.04/0.85 | (product @ X0 @ X4 @ X5))),
% 1.04/0.85 inference('cnf', [status(esa)], [associativity1])).
% 1.04/0.85 thf(zip_derived_cl112, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.04/0.85 (~ (product @ X0 @ X3 @ X2)
% 1.04/0.85 | ~ (product @ (multiply @ X1 @ X0) @ X3 @ X4)
% 1.04/0.85 | (product @ X1 @ X2 @ X4))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl6])).
% 1.04/0.85 thf(zip_derived_cl296, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/0.85 (~ (product @ (inverse @ X2) @ X1 @ X3)
% 1.04/0.85 | ~ (product @ identity @ X1 @ X0)
% 1.04/0.85 | (product @ X2 @ X3 @ X0))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl157, zip_derived_cl112])).
% 1.04/0.85 thf(zip_derived_cl306, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/0.85 (~ (product @ (inverse @ X2) @ X0 @ X1) | (product @ X2 @ X1 @ X0))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl296])).
% 1.04/0.85 thf(zip_derived_cl310, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0)),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl306])).
% 1.04/0.85 thf(a_times_c_is_d, axiom, (product @ a @ c @ d)).
% 1.04/0.85 thf(zip_derived_cl19, plain, ( (product @ a @ c @ d)),
% 1.04/0.85 inference('cnf', [status(esa)], [a_times_c_is_d])).
% 1.04/0.85 thf(product_right_cancellation, axiom,
% 1.04/0.85 (( ~( product @ A @ B @ C ) ) | ( ~( product @ A @ D @ C ) ) |
% 1.04/0.85 ( ( D ) = ( B ) ))).
% 1.04/0.85 thf(zip_derived_cl11, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/0.85 (~ (product @ X0 @ X1 @ X2)
% 1.04/0.85 | ~ (product @ X0 @ X3 @ X2)
% 1.04/0.85 | ((X3) = (X1)))),
% 1.04/0.85 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.04/0.85 thf(zip_derived_cl50, plain,
% 1.04/0.85 (![X0 : $i]: (~ (product @ a @ X0 @ d) | ((X0) = (c)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl11])).
% 1.04/0.85 thf(zip_derived_cl334, plain, (((multiply @ (inverse @ a) @ d) = (c))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl310, zip_derived_cl50])).
% 1.04/0.85 thf(closure_of_inverse, axiom,
% 1.04/0.85 (( ~( subgroup_member @ A ) ) | ( subgroup_member @ ( inverse @ A ) ))).
% 1.04/0.85 thf(zip_derived_cl10, plain,
% 1.04/0.85 (![X0 : $i]:
% 1.04/0.85 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 1.04/0.85 inference('cnf', [status(esa)], [closure_of_inverse])).
% 1.04/0.85 thf(zip_derived_cl310, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 (product @ X1 @ (multiply @ (inverse @ X1) @ X0) @ X0)),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl306])).
% 1.04/0.85 thf(zip_derived_cl4, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 1.04/0.85 inference('cnf', [status(esa)], [total_function1])).
% 1.04/0.85 thf(zip_derived_cl11, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/0.85 (~ (product @ X0 @ X1 @ X2)
% 1.04/0.85 | ~ (product @ X0 @ X3 @ X2)
% 1.04/0.85 | ((X3) = (X1)))),
% 1.04/0.85 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.04/0.85 thf(zip_derived_cl64, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/0.85 (~ (product @ X1 @ X2 @ (multiply @ X1 @ X0)) | ((X2) = (X0)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl11])).
% 1.04/0.85 thf(zip_derived_cl328, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)) = (X0))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl310, zip_derived_cl64])).
% 1.04/0.85 thf(zip_derived_cl4, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 1.04/0.85 inference('cnf', [status(esa)], [total_function1])).
% 1.04/0.85 thf(zip_derived_cl10, plain,
% 1.04/0.85 (![X0 : $i]:
% 1.04/0.85 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 1.04/0.85 inference('cnf', [status(esa)], [closure_of_inverse])).
% 1.04/0.85 thf(zip_derived_cl20, plain,
% 1.04/0.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 1.04/0.85 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.04/0.85 thf(closure_of_product_and_inverse, axiom,
% 1.04/0.85 (( ~( subgroup_member @ A ) ) | ( ~( subgroup_member @ B ) ) |
% 1.04/0.85 ( ~( product @ A @ ( inverse @ B ) @ C ) ) | ( subgroup_member @ C ))).
% 1.04/0.85 thf(zip_derived_cl8, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/0.85 (~ (subgroup_member @ X0)
% 1.04/0.85 | ~ (subgroup_member @ X1)
% 1.04/0.85 | ~ (product @ X0 @ (inverse @ X1) @ X2)
% 1.04/0.85 | (subgroup_member @ X2))),
% 1.04/0.85 inference('cnf', [status(esa)], [closure_of_product_and_inverse])).
% 1.04/0.85 thf(zip_derived_cl76, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/0.85 (~ (subgroup_member @ X2)
% 1.04/0.85 | ~ (subgroup_member @ (inverse @ X0))
% 1.04/0.85 | ~ (product @ X2 @ X0 @ X1)
% 1.04/0.85 | (subgroup_member @ X1))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl8])).
% 1.04/0.85 thf(zip_derived_cl83, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/0.85 (~ (subgroup_member @ X0)
% 1.04/0.85 | ~ (subgroup_member @ X1)
% 1.04/0.85 | ~ (product @ X1 @ X0 @ X2)
% 1.04/0.85 | (subgroup_member @ X2))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl76])).
% 1.04/0.85 thf(zip_derived_cl94, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 (~ (subgroup_member @ X0)
% 1.04/0.85 | ~ (subgroup_member @ X1)
% 1.04/0.85 | (subgroup_member @ (multiply @ X1 @ X0)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl83])).
% 1.04/0.85 thf(zip_derived_cl628, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 (~ (subgroup_member @ (multiply @ X1 @ X0))
% 1.04/0.85 | ~ (subgroup_member @ (inverse @ X1))
% 1.04/0.85 | (subgroup_member @ X0))),
% 1.04/0.85 inference('s_sup+', [status(thm)], [zip_derived_cl328, zip_derived_cl94])).
% 1.04/0.85 thf(zip_derived_cl677, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 (~ (subgroup_member @ X0)
% 1.04/0.85 | ~ (subgroup_member @ (multiply @ X0 @ X1))
% 1.04/0.85 | (subgroup_member @ X1))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl628])).
% 1.04/0.85 thf(zip_derived_cl690, plain,
% 1.04/0.85 ((~ (subgroup_member @ (inverse @ a))
% 1.04/0.85 | ~ (subgroup_member @ c)
% 1.04/0.85 | (subgroup_member @ d))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl334, zip_derived_cl677])).
% 1.04/0.85 thf(property_of_O2, axiom,
% 1.04/0.85 (( product @ A @ ( element_in_O2 @ A @ B ) @ B ) |
% 1.04/0.85 ( subgroup_member @ B ) | ( subgroup_member @ A ))).
% 1.04/0.85 thf(zip_derived_cl14, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 ( (product @ X0 @ (element_in_O2 @ X0 @ X1) @ X1)
% 1.04/0.85 | (subgroup_member @ X1)
% 1.04/0.85 | (subgroup_member @ X0))),
% 1.04/0.85 inference('cnf', [status(esa)], [property_of_O2])).
% 1.04/0.85 thf(zip_derived_cl50, plain,
% 1.04/0.85 (![X0 : $i]: (~ (product @ a @ X0 @ d) | ((X0) = (c)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl11])).
% 1.04/0.85 thf(zip_derived_cl140, plain,
% 1.04/0.85 (( (subgroup_member @ a)
% 1.04/0.85 | (subgroup_member @ d)
% 1.04/0.85 | ((element_in_O2 @ a @ d) = (c)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl50])).
% 1.04/0.85 thf(a_in_subgroup, axiom, (~( subgroup_member @ a ))).
% 1.04/0.85 thf(zip_derived_cl15, plain, (~ (subgroup_member @ a)),
% 1.04/0.85 inference('cnf', [status(esa)], [a_in_subgroup])).
% 1.04/0.85 thf(d_in_subgroup, axiom, (~( subgroup_member @ d ))).
% 1.04/0.85 thf(zip_derived_cl17, plain, (~ (subgroup_member @ d)),
% 1.04/0.85 inference('cnf', [status(esa)], [d_in_subgroup])).
% 1.04/0.85 thf(zip_derived_cl144, plain, (((element_in_O2 @ a @ d) = (c))),
% 1.04/0.85 inference('demod', [status(thm)],
% 1.04/0.85 [zip_derived_cl140, zip_derived_cl15, zip_derived_cl17])).
% 1.04/0.85 thf(an_element_in_O2, axiom,
% 1.04/0.85 (( subgroup_member @ ( element_in_O2 @ A @ B ) ) |
% 1.04/0.85 ( subgroup_member @ B ) | ( subgroup_member @ A ))).
% 1.04/0.85 thf(zip_derived_cl13, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 ( (subgroup_member @ (element_in_O2 @ X0 @ X1))
% 1.04/0.85 | (subgroup_member @ X1)
% 1.04/0.85 | (subgroup_member @ X0))),
% 1.04/0.85 inference('cnf', [status(esa)], [an_element_in_O2])).
% 1.04/0.85 thf(zip_derived_cl145, plain,
% 1.04/0.85 (( (subgroup_member @ c)
% 1.04/0.85 | (subgroup_member @ d)
% 1.04/0.85 | (subgroup_member @ a))),
% 1.04/0.85 inference('s_sup+', [status(thm)], [zip_derived_cl144, zip_derived_cl13])).
% 1.04/0.85 thf(zip_derived_cl17, plain, (~ (subgroup_member @ d)),
% 1.04/0.85 inference('cnf', [status(esa)], [d_in_subgroup])).
% 1.04/0.85 thf(zip_derived_cl15, plain, (~ (subgroup_member @ a)),
% 1.04/0.85 inference('cnf', [status(esa)], [a_in_subgroup])).
% 1.04/0.85 thf(zip_derived_cl147, plain, ( (subgroup_member @ c)),
% 1.04/0.85 inference('demod', [status(thm)],
% 1.04/0.85 [zip_derived_cl145, zip_derived_cl17, zip_derived_cl15])).
% 1.04/0.85 thf(zip_derived_cl17, plain, (~ (subgroup_member @ d)),
% 1.04/0.85 inference('cnf', [status(esa)], [d_in_subgroup])).
% 1.04/0.85 thf(zip_derived_cl700, plain, (~ (subgroup_member @ (inverse @ a))),
% 1.04/0.85 inference('demod', [status(thm)],
% 1.04/0.85 [zip_derived_cl690, zip_derived_cl147, zip_derived_cl17])).
% 1.04/0.85 thf(zip_derived_cl4, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 1.04/0.85 inference('cnf', [status(esa)], [total_function1])).
% 1.04/0.85 thf(b_times_a_inverse_is_c, axiom, (product @ b @ ( inverse @ a ) @ c)).
% 1.04/0.85 thf(zip_derived_cl18, plain, ( (product @ b @ (inverse @ a) @ c)),
% 1.04/0.85 inference('cnf', [status(esa)], [b_times_a_inverse_is_c])).
% 1.04/0.85 thf(zip_derived_cl5, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/0.85 (~ (product @ X0 @ X1 @ X2)
% 1.04/0.85 | ~ (product @ X0 @ X1 @ X3)
% 1.04/0.85 | ((X2) = (X3)))),
% 1.04/0.85 inference('cnf', [status(esa)], [total_function2])).
% 1.04/0.85 thf(zip_derived_cl56, plain,
% 1.04/0.85 (![X0 : $i]: (~ (product @ b @ (inverse @ a) @ X0) | ((c) = (X0)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl5])).
% 1.04/0.85 thf(zip_derived_cl198, plain, (((c) = (multiply @ b @ (inverse @ a)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl56])).
% 1.04/0.85 thf(zip_derived_cl677, plain,
% 1.04/0.85 (![X0 : $i, X1 : $i]:
% 1.04/0.85 (~ (subgroup_member @ X0)
% 1.04/0.85 | ~ (subgroup_member @ (multiply @ X0 @ X1))
% 1.04/0.85 | (subgroup_member @ X1))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl628])).
% 1.04/0.85 thf(zip_derived_cl693, plain,
% 1.04/0.85 ((~ (subgroup_member @ b)
% 1.04/0.85 | ~ (subgroup_member @ c)
% 1.04/0.85 | (subgroup_member @ (inverse @ a)))),
% 1.04/0.85 inference('s_sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl677])).
% 1.04/0.85 thf(b_is_in_subgroup, axiom, (subgroup_member @ b)).
% 1.04/0.85 thf(zip_derived_cl16, plain, ( (subgroup_member @ b)),
% 1.04/0.85 inference('cnf', [status(esa)], [b_is_in_subgroup])).
% 1.04/0.85 thf(zip_derived_cl147, plain, ( (subgroup_member @ c)),
% 1.04/0.85 inference('demod', [status(thm)],
% 1.04/0.85 [zip_derived_cl145, zip_derived_cl17, zip_derived_cl15])).
% 1.04/0.85 thf(zip_derived_cl704, plain, ( (subgroup_member @ (inverse @ a))),
% 1.04/0.85 inference('demod', [status(thm)],
% 1.04/0.85 [zip_derived_cl693, zip_derived_cl16, zip_derived_cl147])).
% 1.04/0.85 thf(zip_derived_cl706, plain, ($false),
% 1.04/0.85 inference('demod', [status(thm)], [zip_derived_cl700, zip_derived_cl704])).
% 1.04/0.85
% 1.04/0.85 % SZS output end Refutation
% 1.04/0.85
% 1.04/0.85
% 1.04/0.85 % Terminating...
% 1.84/1.03 % Runner terminated.
% 1.84/1.04 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------