TSTP Solution File: GRP026-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP026-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.V4bPvPF19W true
% Computer : n032.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 01:49:34 EDT 2023
% Result : Unsatisfiable 0.99s 0.75s
% Output : Refutation 0.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : GRP026-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% 0.07/0.09 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.V4bPvPF19W true
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Aug 28 22:27:31 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.09/0.28 % Running portfolio for 300 s
% 0.09/0.28 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.28 % Number of cores: 8
% 0.09/0.29 % Python version: Python 3.6.8
% 0.09/0.29 % Running in FO mode
% 0.13/0.51 % Total configuration time : 435
% 0.13/0.51 % Estimated wc time : 1092
% 0.13/0.51 % Estimated cpu time (7 cpus) : 156.0
% 0.13/0.58 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.13/0.58 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.13/0.58 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.13/0.59 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.13/0.59 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.13/0.60 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.13/0.62 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.99/0.75 % Solved by fo/fo13.sh.
% 0.99/0.75 % done 280 iterations in 0.139s
% 0.99/0.75 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.99/0.75 % SZS output start Refutation
% 0.99/0.75 thf(h_type, type, h: $i).
% 0.99/0.75 thf(an_isomorphism_type, type, an_isomorphism: $i > $i).
% 0.99/0.75 thf(d2_type, type, d2: $i).
% 0.99/0.75 thf(b_type, type, b: $i).
% 0.99/0.75 thf(g2_type, type, g2: $i).
% 0.99/0.75 thf(d3_type, type, d3: $i).
% 0.99/0.75 thf(f_type, type, f: $i).
% 0.99/0.75 thf(c_type, type, c: $i).
% 0.99/0.75 thf(g1_type, type, g1: $i).
% 0.99/0.75 thf(group_member_type, type, group_member: $i > $i > $o).
% 0.99/0.75 thf(d1_type, type, d1: $i).
% 0.99/0.75 thf(a_type, type, a: $i).
% 0.99/0.75 thf(g_type, type, g: $i).
% 0.99/0.75 thf(product_type, type, product: $i > $i > $i > $i > $o).
% 0.99/0.75 thf(prove_product_holds_in_group2, conjecture,
% 0.99/0.75 (product @
% 0.99/0.75 g2 @ ( an_isomorphism @ d1 ) @ ( an_isomorphism @ d2 ) @
% 0.99/0.75 ( an_isomorphism @ d3 ))).
% 0.99/0.75 thf(zf_stmt_0, negated_conjecture,
% 0.99/0.75 (~( product @
% 0.99/0.75 g2 @ ( an_isomorphism @ d1 ) @ ( an_isomorphism @ d2 ) @
% 0.99/0.75 ( an_isomorphism @ d3 ) )),
% 0.99/0.75 inference('cnf.neg', [status(esa)], [prove_product_holds_in_group2])).
% 0.99/0.75 thf(zip_derived_cl44, plain,
% 0.99/0.75 (~ (product @ g2 @ (an_isomorphism @ d1) @ (an_isomorphism @ d2) @
% 0.99/0.75 (an_isomorphism @ d3))),
% 0.99/0.75 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.99/0.75 thf(d2_in_group1, axiom, (group_member @ d2 @ g1)).
% 0.99/0.75 thf(zip_derived_cl41, plain, ( (group_member @ d2 @ g1)),
% 0.99/0.75 inference('cnf', [status(esa)], [d2_in_group1])).
% 0.99/0.75 thf(all_of_group1, axiom,
% 0.99/0.75 (( ~( group_member @ X @ g1 ) ) | ( ( X ) = ( a ) ) | ( ( X ) = ( b ) ) |
% 0.99/0.75 ( ( X ) = ( c ) ))).
% 0.99/0.75 thf(zip_derived_cl17, plain,
% 0.99/0.75 (![X0 : $i]:
% 0.99/0.75 (~ (group_member @ X0 @ g1)
% 0.99/0.75 | ((X0) = (a))
% 0.99/0.75 | ((X0) = (b))
% 0.99/0.75 | ((X0) = (c)))),
% 0.99/0.75 inference('cnf', [status(esa)], [all_of_group1])).
% 0.99/0.75 thf(zip_derived_cl132, plain, ((((d2) = (a)) | ((d2) = (b)) | ((d2) = (c)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl17])).
% 0.99/0.75 thf(d1_in_group1, axiom, (group_member @ d1 @ g1)).
% 0.99/0.75 thf(zip_derived_cl40, plain, ( (group_member @ d1 @ g1)),
% 0.99/0.75 inference('cnf', [status(esa)], [d1_in_group1])).
% 0.99/0.75 thf(zip_derived_cl17, plain,
% 0.99/0.75 (![X0 : $i]:
% 0.99/0.75 (~ (group_member @ X0 @ g1)
% 0.99/0.75 | ((X0) = (a))
% 0.99/0.75 | ((X0) = (b))
% 0.99/0.75 | ((X0) = (c)))),
% 0.99/0.75 inference('cnf', [status(esa)], [all_of_group1])).
% 0.99/0.75 thf(zip_derived_cl131, plain, ((((d1) = (a)) | ((d1) = (b)) | ((d1) = (c)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl17])).
% 0.99/0.75 thf(d1_times_d2_is_d3, axiom, (product @ g1 @ d1 @ d2 @ d3)).
% 0.99/0.75 thf(zip_derived_cl43, plain, ( (product @ g1 @ d1 @ d2 @ d3)),
% 0.99/0.75 inference('cnf', [status(esa)], [d1_times_d2_is_d3])).
% 0.99/0.75 thf(zip_derived_cl181, plain,
% 0.99/0.75 ((((d1) = (b)) | ((d1) = (a)) | (product @ g1 @ c @ d2 @ d3))),
% 0.99/0.75 inference('s_sup+', [status(thm)], [zip_derived_cl131, zip_derived_cl43])).
% 0.99/0.75 thf(zip_derived_cl254, plain,
% 0.99/0.75 ((((d2) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | (product @ g1 @ c @ c @ d3))),
% 0.99/0.75 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl181])).
% 0.99/0.75 thf(c_times_c_is_b, axiom, (product @ g1 @ c @ c @ b)).
% 0.99/0.75 thf(zip_derived_cl27, plain, ( (product @ g1 @ c @ c @ b)),
% 0.99/0.75 inference('cnf', [status(esa)], [c_times_c_is_b])).
% 0.99/0.75 thf(total_function2, axiom,
% 0.99/0.75 (( ~( product @ Xg @ X @ Y @ Z ) ) | ( ~( product @ Xg @ X @ Y @ W ) ) |
% 0.99/0.75 ( ( W ) = ( Z ) ))).
% 0.99/0.75 thf(zip_derived_cl8, plain,
% 0.99/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.75 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.75 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.75 | ((X4) = (X3)))),
% 0.99/0.75 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.75 thf(zip_derived_cl80, plain,
% 0.99/0.75 (![X0 : $i]: (~ (product @ g1 @ c @ c @ X0) | ((X0) = (b)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl8])).
% 0.99/0.75 thf(zip_derived_cl375, plain,
% 0.99/0.75 ((((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ((d2) = (b))
% 0.99/0.75 | ((d3) = (b)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl80])).
% 0.99/0.75 thf(zip_derived_cl132, plain, ((((d2) = (a)) | ((d2) = (b)) | ((d2) = (c)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl17])).
% 0.99/0.75 thf(zip_derived_cl131, plain, ((((d1) = (a)) | ((d1) = (b)) | ((d1) = (c)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl17])).
% 0.99/0.75 thf(zip_derived_cl44, plain,
% 0.99/0.75 (~ (product @ g2 @ (an_isomorphism @ d1) @ (an_isomorphism @ d2) @
% 0.99/0.75 (an_isomorphism @ d3))),
% 0.99/0.75 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.99/0.75 thf(zip_derived_cl182, plain,
% 0.99/0.75 ((((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ~ (product @ g2 @ (an_isomorphism @ c) @ (an_isomorphism @ d2) @
% 0.99/0.75 (an_isomorphism @ d3)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl44])).
% 0.99/0.75 thf(c_maps_to_h, axiom, (( an_isomorphism @ c ) = ( h ))).
% 0.99/0.75 thf(zip_derived_cl39, plain, (((an_isomorphism @ c) = (h))),
% 0.99/0.75 inference('cnf', [status(esa)], [c_maps_to_h])).
% 0.99/0.75 thf(zip_derived_cl186, plain,
% 0.99/0.75 ((((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ~ (product @ g2 @ h @ (an_isomorphism @ d2) @ (an_isomorphism @ d3)))),
% 0.99/0.75 inference('demod', [status(thm)], [zip_derived_cl182, zip_derived_cl39])).
% 0.99/0.75 thf(zip_derived_cl206, plain,
% 0.99/0.75 ((((d2) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ~ (product @ g2 @ h @ (an_isomorphism @ c) @ (an_isomorphism @ d3)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl186])).
% 0.99/0.75 thf(zip_derived_cl39, plain, (((an_isomorphism @ c) = (h))),
% 0.99/0.75 inference('cnf', [status(esa)], [c_maps_to_h])).
% 0.99/0.75 thf(zip_derived_cl208, plain,
% 0.99/0.75 ((((d2) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ~ (product @ g2 @ h @ h @ (an_isomorphism @ d3)))),
% 0.99/0.75 inference('demod', [status(thm)], [zip_derived_cl206, zip_derived_cl39])).
% 0.99/0.75 thf(zip_derived_cl389, plain,
% 0.99/0.75 ((((d2) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ((d2) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ~ (product @ g2 @ h @ h @ (an_isomorphism @ b)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl375, zip_derived_cl208])).
% 0.99/0.75 thf(b_maps_to_g, axiom, (( an_isomorphism @ b ) = ( g ))).
% 0.99/0.75 thf(zip_derived_cl38, plain, (((an_isomorphism @ b) = (g))),
% 0.99/0.75 inference('cnf', [status(esa)], [b_maps_to_g])).
% 0.99/0.75 thf(h_times_h_is_g, axiom, (product @ g2 @ h @ h @ g)).
% 0.99/0.75 thf(zip_derived_cl36, plain, ( (product @ g2 @ h @ h @ g)),
% 0.99/0.75 inference('cnf', [status(esa)], [h_times_h_is_g])).
% 0.99/0.75 thf(zip_derived_cl400, plain,
% 0.99/0.75 ((((d2) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ((d2) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a)))),
% 0.99/0.75 inference('demod', [status(thm)],
% 0.99/0.75 [zip_derived_cl389, zip_derived_cl38, zip_derived_cl36])).
% 0.99/0.75 thf(zip_derived_cl401, plain,
% 0.99/0.75 ((((d1) = (a)) | ((d1) = (b)) | ((d2) = (a)) | ((d2) = (b)))),
% 0.99/0.75 inference('simplify', [status(thm)], [zip_derived_cl400])).
% 0.99/0.75 thf(zip_derived_cl181, plain,
% 0.99/0.75 ((((d1) = (b)) | ((d1) = (a)) | (product @ g1 @ c @ d2 @ d3))),
% 0.99/0.75 inference('s_sup+', [status(thm)], [zip_derived_cl131, zip_derived_cl43])).
% 0.99/0.75 thf(zip_derived_cl420, plain,
% 0.99/0.75 ((((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | (product @ g1 @ c @ b @ d3))),
% 0.99/0.75 inference('s_sup+', [status(thm)], [zip_derived_cl401, zip_derived_cl181])).
% 0.99/0.75 thf(zip_derived_cl430, plain,
% 0.99/0.75 (( (product @ g1 @ c @ b @ d3)
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d2) = (a)))),
% 0.99/0.75 inference('simplify', [status(thm)], [zip_derived_cl420])).
% 0.99/0.75 thf(c_times_b_is_a, axiom, (product @ g1 @ c @ b @ a)).
% 0.99/0.75 thf(zip_derived_cl26, plain, ( (product @ g1 @ c @ b @ a)),
% 0.99/0.75 inference('cnf', [status(esa)], [c_times_b_is_a])).
% 0.99/0.75 thf(zip_derived_cl8, plain,
% 0.99/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.75 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.75 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.75 | ((X4) = (X3)))),
% 0.99/0.75 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.75 thf(zip_derived_cl79, plain,
% 0.99/0.75 (![X0 : $i]: (~ (product @ g1 @ c @ b @ X0) | ((X0) = (a)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl8])).
% 0.99/0.75 thf(zip_derived_cl451, plain,
% 0.99/0.75 ((((d2) = (a)) | ((d1) = (b)) | ((d1) = (a)) | ((d3) = (a)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl430, zip_derived_cl79])).
% 0.99/0.75 thf(zip_derived_cl401, plain,
% 0.99/0.75 ((((d1) = (a)) | ((d1) = (b)) | ((d2) = (a)) | ((d2) = (b)))),
% 0.99/0.75 inference('simplify', [status(thm)], [zip_derived_cl400])).
% 0.99/0.75 thf(zip_derived_cl186, plain,
% 0.99/0.75 ((((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ~ (product @ g2 @ h @ (an_isomorphism @ d2) @ (an_isomorphism @ d3)))),
% 0.99/0.75 inference('demod', [status(thm)], [zip_derived_cl182, zip_derived_cl39])).
% 0.99/0.75 thf(zip_derived_cl422, plain,
% 0.99/0.75 ((((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ~ (product @ g2 @ h @ (an_isomorphism @ b) @ (an_isomorphism @ d3)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl401, zip_derived_cl186])).
% 0.99/0.75 thf(zip_derived_cl38, plain, (((an_isomorphism @ b) = (g))),
% 0.99/0.75 inference('cnf', [status(esa)], [b_maps_to_g])).
% 0.99/0.75 thf(zip_derived_cl432, plain,
% 0.99/0.75 ((((d2) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ~ (product @ g2 @ h @ g @ (an_isomorphism @ d3)))),
% 0.99/0.75 inference('demod', [status(thm)], [zip_derived_cl422, zip_derived_cl38])).
% 0.99/0.75 thf(zip_derived_cl433, plain,
% 0.99/0.75 ((~ (product @ g2 @ h @ g @ (an_isomorphism @ d3))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d2) = (a)))),
% 0.99/0.75 inference('simplify', [status(thm)], [zip_derived_cl432])).
% 0.99/0.75 thf(zip_derived_cl473, plain,
% 0.99/0.75 ((((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d2) = (a))
% 0.99/0.75 | ~ (product @ g2 @ h @ g @ (an_isomorphism @ a))
% 0.99/0.75 | ((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.75 | ((d2) = (a)))),
% 0.99/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl451, zip_derived_cl433])).
% 0.99/0.75 thf(a_maps_to_f, axiom, (( an_isomorphism @ a ) = ( f ))).
% 0.99/0.75 thf(zip_derived_cl37, plain, (((an_isomorphism @ a) = (f))),
% 0.99/0.75 inference('cnf', [status(esa)], [a_maps_to_f])).
% 0.99/0.75 thf(h_times_g_is_f, axiom, (product @ g2 @ h @ g @ f)).
% 0.99/0.75 thf(zip_derived_cl35, plain, ( (product @ g2 @ h @ g @ f)),
% 0.99/0.75 inference('cnf', [status(esa)], [h_times_g_is_f])).
% 0.99/0.75 thf(zip_derived_cl487, plain,
% 0.99/0.75 ((((d1) = (a))
% 0.99/0.75 | ((d1) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d2) = (a)))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl473, zip_derived_cl37, zip_derived_cl35])).
% 0.99/0.76 thf(zip_derived_cl488, plain, ((((d2) = (a)) | ((d1) = (b)) | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl487])).
% 0.99/0.76 thf(zip_derived_cl181, plain,
% 0.99/0.76 ((((d1) = (b)) | ((d1) = (a)) | (product @ g1 @ c @ d2 @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl131, zip_derived_cl43])).
% 0.99/0.76 thf(zip_derived_cl495, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | (product @ g1 @ c @ a @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl488, zip_derived_cl181])).
% 0.99/0.76 thf(zip_derived_cl507, plain,
% 0.99/0.76 (( (product @ g1 @ c @ a @ d3) | ((d1) = (b)) | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl495])).
% 0.99/0.76 thf(c_times_a_is_c, axiom, (product @ g1 @ c @ a @ c)).
% 0.99/0.76 thf(zip_derived_cl23, plain, ( (product @ g1 @ c @ a @ c)),
% 0.99/0.76 inference('cnf', [status(esa)], [c_times_a_is_c])).
% 0.99/0.76 thf(zip_derived_cl8, plain,
% 0.99/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.76 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.76 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.76 | ((X4) = (X3)))),
% 0.99/0.76 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.76 thf(zip_derived_cl69, plain,
% 0.99/0.76 (![X0 : $i]: (~ (product @ g1 @ c @ a @ X0) | ((X0) = (c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl8])).
% 0.99/0.76 thf(zip_derived_cl608, plain, ((((d1) = (a)) | ((d1) = (b)) | ((d3) = (c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl507, zip_derived_cl69])).
% 0.99/0.76 thf(zip_derived_cl488, plain, ((((d2) = (a)) | ((d1) = (b)) | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl487])).
% 0.99/0.76 thf(zip_derived_cl186, plain,
% 0.99/0.76 ((((d1) = (b))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ h @ (an_isomorphism @ d2) @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl182, zip_derived_cl39])).
% 0.99/0.76 thf(zip_derived_cl497, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ h @ (an_isomorphism @ a) @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl488, zip_derived_cl186])).
% 0.99/0.76 thf(zip_derived_cl37, plain, (((an_isomorphism @ a) = (f))),
% 0.99/0.76 inference('cnf', [status(esa)], [a_maps_to_f])).
% 0.99/0.76 thf(zip_derived_cl509, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ h @ f @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl497, zip_derived_cl37])).
% 0.99/0.76 thf(zip_derived_cl510, plain,
% 0.99/0.76 ((~ (product @ g2 @ h @ f @ (an_isomorphism @ d3))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl509])).
% 0.99/0.76 thf(zip_derived_cl631, plain,
% 0.99/0.76 ((((d1) = (b))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ h @ f @ (an_isomorphism @ c))
% 0.99/0.76 | ((d1) = (b))
% 0.99/0.76 | ((d1) = (a)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl608, zip_derived_cl510])).
% 0.99/0.76 thf(zip_derived_cl39, plain, (((an_isomorphism @ c) = (h))),
% 0.99/0.76 inference('cnf', [status(esa)], [c_maps_to_h])).
% 0.99/0.76 thf(h_times_f_is_h, axiom, (product @ g2 @ h @ f @ h)).
% 0.99/0.76 thf(zip_derived_cl32, plain, ( (product @ g2 @ h @ f @ h)),
% 0.99/0.76 inference('cnf', [status(esa)], [h_times_f_is_h])).
% 0.99/0.76 thf(zip_derived_cl645, plain,
% 0.99/0.76 ((((d1) = (b)) | ((d1) = (a)) | ((d1) = (b)) | ((d1) = (a)))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl631, zip_derived_cl39, zip_derived_cl32])).
% 0.99/0.76 thf(zip_derived_cl646, plain, ((((d1) = (a)) | ((d1) = (b)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl645])).
% 0.99/0.76 thf(zip_derived_cl132, plain, ((((d2) = (a)) | ((d2) = (b)) | ((d2) = (c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl17])).
% 0.99/0.76 thf(zip_derived_cl43, plain, ( (product @ g1 @ d1 @ d2 @ d3)),
% 0.99/0.76 inference('cnf', [status(esa)], [d1_times_d2_is_d3])).
% 0.99/0.76 thf(zip_derived_cl188, plain,
% 0.99/0.76 ((((d2) = (b)) | ((d2) = (a)) | (product @ g1 @ d1 @ c @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl43])).
% 0.99/0.76 thf(zip_derived_cl655, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | (product @ g1 @ b @ c @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl188])).
% 0.99/0.76 thf(b_times_c_is_a, axiom, (product @ g1 @ b @ c @ a)).
% 0.99/0.76 thf(zip_derived_cl25, plain, ( (product @ g1 @ b @ c @ a)),
% 0.99/0.76 inference('cnf', [status(esa)], [b_times_c_is_a])).
% 0.99/0.76 thf(zip_derived_cl8, plain,
% 0.99/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.76 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.76 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.76 | ((X4) = (X3)))),
% 0.99/0.76 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.76 thf(zip_derived_cl78, plain,
% 0.99/0.76 (![X0 : $i]: (~ (product @ g1 @ b @ c @ X0) | ((X0) = (a)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl8])).
% 0.99/0.76 thf(zip_derived_cl754, plain,
% 0.99/0.76 ((((d2) = (a)) | ((d2) = (b)) | ((d1) = (a)) | ((d3) = (a)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl655, zip_derived_cl78])).
% 0.99/0.76 thf(zip_derived_cl646, plain, ((((d1) = (a)) | ((d1) = (b)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl645])).
% 0.99/0.76 thf(zip_derived_cl132, plain, ((((d2) = (a)) | ((d2) = (b)) | ((d2) = (c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl17])).
% 0.99/0.76 thf(zip_derived_cl44, plain,
% 0.99/0.76 (~ (product @ g2 @ (an_isomorphism @ d1) @ (an_isomorphism @ d2) @
% 0.99/0.76 (an_isomorphism @ d3))),
% 0.99/0.76 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.99/0.76 thf(zip_derived_cl189, plain,
% 0.99/0.76 ((((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ (an_isomorphism @ d1) @ (an_isomorphism @ c) @
% 0.99/0.76 (an_isomorphism @ d3)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl44])).
% 0.99/0.76 thf(zip_derived_cl39, plain, (((an_isomorphism @ c) = (h))),
% 0.99/0.76 inference('cnf', [status(esa)], [c_maps_to_h])).
% 0.99/0.76 thf(zip_derived_cl193, plain,
% 0.99/0.76 ((((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ (an_isomorphism @ d1) @ h @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl189, zip_derived_cl39])).
% 0.99/0.76 thf(zip_derived_cl657, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ (an_isomorphism @ b) @ h @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl646, zip_derived_cl193])).
% 0.99/0.76 thf(zip_derived_cl38, plain, (((an_isomorphism @ b) = (g))),
% 0.99/0.76 inference('cnf', [status(esa)], [b_maps_to_g])).
% 0.99/0.76 thf(zip_derived_cl664, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ h @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl657, zip_derived_cl38])).
% 0.99/0.76 thf(zip_derived_cl774, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ h @ (an_isomorphism @ a)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl754, zip_derived_cl664])).
% 0.99/0.76 thf(zip_derived_cl37, plain, (((an_isomorphism @ a) = (f))),
% 0.99/0.76 inference('cnf', [status(esa)], [a_maps_to_f])).
% 0.99/0.76 thf(g_times_h_is_f, axiom, (product @ g2 @ g @ h @ f)).
% 0.99/0.76 thf(zip_derived_cl34, plain, ( (product @ g2 @ g @ h @ f)),
% 0.99/0.76 inference('cnf', [status(esa)], [g_times_h_is_f])).
% 0.99/0.76 thf(zip_derived_cl787, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ((d2) = (b))
% 0.99/0.76 | ((d2) = (a)))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl774, zip_derived_cl37, zip_derived_cl34])).
% 0.99/0.76 thf(zip_derived_cl788, plain, ((((d2) = (a)) | ((d2) = (b)) | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl787])).
% 0.99/0.76 thf(zip_derived_cl646, plain, ((((d1) = (a)) | ((d1) = (b)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl645])).
% 0.99/0.76 thf(zip_derived_cl43, plain, ( (product @ g1 @ d1 @ d2 @ d3)),
% 0.99/0.76 inference('cnf', [status(esa)], [d1_times_d2_is_d3])).
% 0.99/0.76 thf(zip_derived_cl651, plain,
% 0.99/0.76 ((((d1) = (a)) | (product @ g1 @ b @ d2 @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl43])).
% 0.99/0.76 thf(zip_derived_cl799, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | (product @ g1 @ b @ b @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl788, zip_derived_cl651])).
% 0.99/0.76 thf(zip_derived_cl806, plain,
% 0.99/0.76 (( (product @ g1 @ b @ b @ d3) | ((d2) = (a)) | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl799])).
% 0.99/0.76 thf(b_times_b_is_c, axiom, (product @ g1 @ b @ b @ c)).
% 0.99/0.76 thf(zip_derived_cl24, plain, ( (product @ g1 @ b @ b @ c)),
% 0.99/0.76 inference('cnf', [status(esa)], [b_times_b_is_c])).
% 0.99/0.76 thf(zip_derived_cl8, plain,
% 0.99/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.76 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.76 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.76 | ((X4) = (X3)))),
% 0.99/0.76 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.76 thf(zip_derived_cl70, plain,
% 0.99/0.76 (![X0 : $i]: (~ (product @ g1 @ b @ b @ X0) | ((X0) = (c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl8])).
% 0.99/0.76 thf(zip_derived_cl897, plain, ((((d1) = (a)) | ((d2) = (a)) | ((d3) = (c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl806, zip_derived_cl70])).
% 0.99/0.76 thf(zip_derived_cl788, plain, ((((d2) = (a)) | ((d2) = (b)) | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl787])).
% 0.99/0.76 thf(zip_derived_cl646, plain, ((((d1) = (a)) | ((d1) = (b)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl645])).
% 0.99/0.76 thf(zip_derived_cl44, plain,
% 0.99/0.76 (~ (product @ g2 @ (an_isomorphism @ d1) @ (an_isomorphism @ d2) @
% 0.99/0.76 (an_isomorphism @ d3))),
% 0.99/0.76 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.99/0.76 thf(zip_derived_cl652, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ (an_isomorphism @ b) @ (an_isomorphism @ d2) @
% 0.99/0.76 (an_isomorphism @ d3)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl646, zip_derived_cl44])).
% 0.99/0.76 thf(zip_derived_cl38, plain, (((an_isomorphism @ b) = (g))),
% 0.99/0.76 inference('cnf', [status(esa)], [b_maps_to_g])).
% 0.99/0.76 thf(zip_derived_cl663, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ (an_isomorphism @ d2) @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl652, zip_derived_cl38])).
% 0.99/0.76 thf(zip_derived_cl801, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ (an_isomorphism @ b) @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl788, zip_derived_cl663])).
% 0.99/0.76 thf(zip_derived_cl38, plain, (((an_isomorphism @ b) = (g))),
% 0.99/0.76 inference('cnf', [status(esa)], [b_maps_to_g])).
% 0.99/0.76 thf(zip_derived_cl808, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ g @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl801, zip_derived_cl38])).
% 0.99/0.76 thf(zip_derived_cl809, plain,
% 0.99/0.76 ((~ (product @ g2 @ g @ g @ (an_isomorphism @ d3))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl808])).
% 0.99/0.76 thf(zip_derived_cl921, plain,
% 0.99/0.76 ((((d2) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ g @ (an_isomorphism @ c))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d1) = (a)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl897, zip_derived_cl809])).
% 0.99/0.76 thf(zip_derived_cl39, plain, (((an_isomorphism @ c) = (h))),
% 0.99/0.76 inference('cnf', [status(esa)], [c_maps_to_h])).
% 0.99/0.76 thf(g_times_g_is_h, axiom, (product @ g2 @ g @ g @ h)).
% 0.99/0.76 thf(zip_derived_cl33, plain, ( (product @ g2 @ g @ g @ h)),
% 0.99/0.76 inference('cnf', [status(esa)], [g_times_g_is_h])).
% 0.99/0.76 thf(zip_derived_cl939, plain,
% 0.99/0.76 ((((d2) = (a)) | ((d1) = (a)) | ((d2) = (a)) | ((d1) = (a)))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl921, zip_derived_cl39, zip_derived_cl33])).
% 0.99/0.76 thf(zip_derived_cl940, plain, ((((d1) = (a)) | ((d2) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl939])).
% 0.99/0.76 thf(zip_derived_cl651, plain,
% 0.99/0.76 ((((d1) = (a)) | (product @ g1 @ b @ d2 @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl43])).
% 0.99/0.76 thf(zip_derived_cl955, plain,
% 0.99/0.76 ((((d1) = (a)) | ((d1) = (a)) | (product @ g1 @ b @ a @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl940, zip_derived_cl651])).
% 0.99/0.76 thf(zip_derived_cl961, plain,
% 0.99/0.76 (( (product @ g1 @ b @ a @ d3) | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl955])).
% 0.99/0.76 thf(b_times_a_is_b, axiom, (product @ g1 @ b @ a @ b)).
% 0.99/0.76 thf(zip_derived_cl21, plain, ( (product @ g1 @ b @ a @ b)),
% 0.99/0.76 inference('cnf', [status(esa)], [b_times_a_is_b])).
% 0.99/0.76 thf(zip_derived_cl8, plain,
% 0.99/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.76 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.76 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.76 | ((X4) = (X3)))),
% 0.99/0.76 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.76 thf(zip_derived_cl67, plain,
% 0.99/0.76 (![X0 : $i]: (~ (product @ g1 @ b @ a @ X0) | ((X0) = (b)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl8])).
% 0.99/0.76 thf(zip_derived_cl997, plain, ((((d1) = (a)) | ((d3) = (b)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl961, zip_derived_cl67])).
% 0.99/0.76 thf(zip_derived_cl940, plain, ((((d1) = (a)) | ((d2) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl939])).
% 0.99/0.76 thf(zip_derived_cl663, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ (an_isomorphism @ d2) @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl652, zip_derived_cl38])).
% 0.99/0.76 thf(zip_derived_cl957, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ (an_isomorphism @ a) @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl940, zip_derived_cl663])).
% 0.99/0.76 thf(zip_derived_cl37, plain, (((an_isomorphism @ a) = (f))),
% 0.99/0.76 inference('cnf', [status(esa)], [a_maps_to_f])).
% 0.99/0.76 thf(zip_derived_cl963, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ f @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl957, zip_derived_cl37])).
% 0.99/0.76 thf(zip_derived_cl964, plain,
% 0.99/0.76 ((~ (product @ g2 @ g @ f @ (an_isomorphism @ d3)) | ((d1) = (a)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl963])).
% 0.99/0.76 thf(zip_derived_cl1014, plain,
% 0.99/0.76 ((((d1) = (a))
% 0.99/0.76 | ~ (product @ g2 @ g @ f @ (an_isomorphism @ b))
% 0.99/0.76 | ((d1) = (a)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl997, zip_derived_cl964])).
% 0.99/0.76 thf(zip_derived_cl38, plain, (((an_isomorphism @ b) = (g))),
% 0.99/0.76 inference('cnf', [status(esa)], [b_maps_to_g])).
% 0.99/0.76 thf(g_times_f_is_g, axiom, (product @ g2 @ g @ f @ g)).
% 0.99/0.76 thf(zip_derived_cl30, plain, ( (product @ g2 @ g @ f @ g)),
% 0.99/0.76 inference('cnf', [status(esa)], [g_times_f_is_g])).
% 0.99/0.76 thf(zip_derived_cl1025, plain, ((((d1) = (a)) | ((d1) = (a)))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl1014, zip_derived_cl38, zip_derived_cl30])).
% 0.99/0.76 thf(zip_derived_cl1026, plain, (((d1) = (a))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl1025])).
% 0.99/0.76 thf(zip_derived_cl37, plain, (((an_isomorphism @ a) = (f))),
% 0.99/0.76 inference('cnf', [status(esa)], [a_maps_to_f])).
% 0.99/0.76 thf(zip_derived_cl1029, plain,
% 0.99/0.76 (~ (product @ g2 @ f @ (an_isomorphism @ d2) @ (an_isomorphism @ d3))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl44, zip_derived_cl1026, zip_derived_cl37])).
% 0.99/0.76 thf(zip_derived_cl188, plain,
% 0.99/0.76 ((((d2) = (b)) | ((d2) = (a)) | (product @ g1 @ d1 @ c @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl43])).
% 0.99/0.76 thf(zip_derived_cl1026, plain, (((d1) = (a))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl1025])).
% 0.99/0.76 thf(zip_derived_cl1032, plain,
% 0.99/0.76 ((((d2) = (b)) | ((d2) = (a)) | (product @ g1 @ a @ c @ d3))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl188, zip_derived_cl1026])).
% 0.99/0.76 thf(a_times_c_is_c, axiom, (product @ g1 @ a @ c @ c)).
% 0.99/0.76 thf(zip_derived_cl22, plain, ( (product @ g1 @ a @ c @ c)),
% 0.99/0.76 inference('cnf', [status(esa)], [a_times_c_is_c])).
% 0.99/0.76 thf(zip_derived_cl8, plain,
% 0.99/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.76 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.76 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.76 | ((X4) = (X3)))),
% 0.99/0.76 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.76 thf(zip_derived_cl68, plain,
% 0.99/0.76 (![X0 : $i]: (~ (product @ g1 @ a @ c @ X0) | ((X0) = (c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl8])).
% 0.99/0.76 thf(zip_derived_cl1136, plain,
% 0.99/0.76 ((((d2) = (a)) | ((d2) = (b)) | ((d3) = (c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl1032, zip_derived_cl68])).
% 0.99/0.76 thf(zip_derived_cl193, plain,
% 0.99/0.76 ((((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ (an_isomorphism @ d1) @ h @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl189, zip_derived_cl39])).
% 0.99/0.76 thf(zip_derived_cl1026, plain, (((d1) = (a))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl1025])).
% 0.99/0.76 thf(zip_derived_cl37, plain, (((an_isomorphism @ a) = (f))),
% 0.99/0.76 inference('cnf', [status(esa)], [a_maps_to_f])).
% 0.99/0.76 thf(zip_derived_cl1034, plain,
% 0.99/0.76 ((((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ f @ h @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl193, zip_derived_cl1026, zip_derived_cl37])).
% 0.99/0.76 thf(zip_derived_cl1148, plain,
% 0.99/0.76 ((((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ((d2) = (b))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ f @ h @ (an_isomorphism @ c)))),
% 0.99/0.76 inference('s_sup-', [status(thm)],
% 0.99/0.76 [zip_derived_cl1136, zip_derived_cl1034])).
% 0.99/0.76 thf(zip_derived_cl39, plain, (((an_isomorphism @ c) = (h))),
% 0.99/0.76 inference('cnf', [status(esa)], [c_maps_to_h])).
% 0.99/0.76 thf(f_times_h_is_h, axiom, (product @ g2 @ f @ h @ h)).
% 0.99/0.76 thf(zip_derived_cl31, plain, ( (product @ g2 @ f @ h @ h)),
% 0.99/0.76 inference('cnf', [status(esa)], [f_times_h_is_h])).
% 0.99/0.76 thf(zip_derived_cl1154, plain,
% 0.99/0.76 ((((d2) = (b)) | ((d2) = (a)) | ((d2) = (b)) | ((d2) = (a)))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl1148, zip_derived_cl39, zip_derived_cl31])).
% 0.99/0.76 thf(zip_derived_cl1155, plain, ((((d2) = (a)) | ((d2) = (b)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl1154])).
% 0.99/0.76 thf(zip_derived_cl43, plain, ( (product @ g1 @ d1 @ d2 @ d3)),
% 0.99/0.76 inference('cnf', [status(esa)], [d1_times_d2_is_d3])).
% 0.99/0.76 thf(zip_derived_cl1026, plain, (((d1) = (a))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl1025])).
% 0.99/0.76 thf(zip_derived_cl1028, plain, ( (product @ g1 @ a @ d2 @ d3)),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl1026])).
% 0.99/0.76 thf(zip_derived_cl1160, plain,
% 0.99/0.76 ((((d2) = (a)) | (product @ g1 @ a @ b @ d3))),
% 0.99/0.76 inference('s_sup+', [status(thm)],
% 0.99/0.76 [zip_derived_cl1155, zip_derived_cl1028])).
% 0.99/0.76 thf(a_times_b_is_b, axiom, (product @ g1 @ a @ b @ b)).
% 0.99/0.76 thf(zip_derived_cl20, plain, ( (product @ g1 @ a @ b @ b)),
% 0.99/0.76 inference('cnf', [status(esa)], [a_times_b_is_b])).
% 0.99/0.76 thf(zip_derived_cl8, plain,
% 0.99/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.76 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.76 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.76 | ((X4) = (X3)))),
% 0.99/0.76 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.76 thf(zip_derived_cl50, plain,
% 0.99/0.76 (![X0 : $i]: (~ (product @ g1 @ a @ b @ X0) | ((X0) = (b)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl8])).
% 0.99/0.76 thf(zip_derived_cl1188, plain, ((((d2) = (a)) | ((d3) = (b)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl1160, zip_derived_cl50])).
% 0.99/0.76 thf(zip_derived_cl1155, plain, ((((d2) = (a)) | ((d2) = (b)))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl1154])).
% 0.99/0.76 thf(zip_derived_cl1029, plain,
% 0.99/0.76 (~ (product @ g2 @ f @ (an_isomorphism @ d2) @ (an_isomorphism @ d3))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl44, zip_derived_cl1026, zip_derived_cl37])).
% 0.99/0.76 thf(zip_derived_cl1161, plain,
% 0.99/0.76 ((((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ f @ (an_isomorphism @ b) @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('s_sup-', [status(thm)],
% 0.99/0.76 [zip_derived_cl1155, zip_derived_cl1029])).
% 0.99/0.76 thf(zip_derived_cl38, plain, (((an_isomorphism @ b) = (g))),
% 0.99/0.76 inference('cnf', [status(esa)], [b_maps_to_g])).
% 0.99/0.76 thf(zip_derived_cl1165, plain,
% 0.99/0.76 ((((d2) = (a)) | ~ (product @ g2 @ f @ g @ (an_isomorphism @ d3)))),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl1161, zip_derived_cl38])).
% 0.99/0.76 thf(zip_derived_cl1197, plain,
% 0.99/0.76 ((((d2) = (a))
% 0.99/0.76 | ((d2) = (a))
% 0.99/0.76 | ~ (product @ g2 @ f @ g @ (an_isomorphism @ b)))),
% 0.99/0.76 inference('s_sup-', [status(thm)],
% 0.99/0.76 [zip_derived_cl1188, zip_derived_cl1165])).
% 0.99/0.76 thf(zip_derived_cl38, plain, (((an_isomorphism @ b) = (g))),
% 0.99/0.76 inference('cnf', [status(esa)], [b_maps_to_g])).
% 0.99/0.76 thf(f_times_g_is_g, axiom, (product @ g2 @ f @ g @ g)).
% 0.99/0.76 thf(zip_derived_cl29, plain, ( (product @ g2 @ f @ g @ g)),
% 0.99/0.76 inference('cnf', [status(esa)], [f_times_g_is_g])).
% 0.99/0.76 thf(zip_derived_cl1200, plain, ((((d2) = (a)) | ((d2) = (a)))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl1197, zip_derived_cl38, zip_derived_cl29])).
% 0.99/0.76 thf(zip_derived_cl1201, plain, (((d2) = (a))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl1200])).
% 0.99/0.76 thf(zip_derived_cl37, plain, (((an_isomorphism @ a) = (f))),
% 0.99/0.76 inference('cnf', [status(esa)], [a_maps_to_f])).
% 0.99/0.76 thf(zip_derived_cl1206, plain,
% 0.99/0.76 (~ (product @ g2 @ f @ f @ (an_isomorphism @ d3))),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl1029, zip_derived_cl1201, zip_derived_cl37])).
% 0.99/0.76 thf(zip_derived_cl1028, plain, ( (product @ g1 @ a @ d2 @ d3)),
% 0.99/0.76 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl1026])).
% 0.99/0.76 thf(zip_derived_cl1201, plain, (((d2) = (a))),
% 0.99/0.76 inference('simplify', [status(thm)], [zip_derived_cl1200])).
% 0.99/0.76 thf(zip_derived_cl1205, plain, ( (product @ g1 @ a @ a @ d3)),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl1028, zip_derived_cl1201])).
% 0.99/0.76 thf(a_times_a_is_a, axiom, (product @ g1 @ a @ a @ a)).
% 0.99/0.76 thf(zip_derived_cl19, plain, ( (product @ g1 @ a @ a @ a)),
% 0.99/0.76 inference('cnf', [status(esa)], [a_times_a_is_a])).
% 0.99/0.76 thf(zip_derived_cl8, plain,
% 0.99/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.99/0.76 (~ (product @ X0 @ X1 @ X2 @ X3)
% 0.99/0.76 | ~ (product @ X0 @ X1 @ X2 @ X4)
% 0.99/0.76 | ((X4) = (X3)))),
% 0.99/0.76 inference('cnf', [status(esa)], [total_function2])).
% 0.99/0.76 thf(zip_derived_cl49, plain,
% 0.99/0.76 (![X0 : $i]: (~ (product @ g1 @ a @ a @ X0) | ((X0) = (a)))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl8])).
% 0.99/0.76 thf(zip_derived_cl1216, plain, (((d3) = (a))),
% 0.99/0.76 inference('s_sup-', [status(thm)], [zip_derived_cl1205, zip_derived_cl49])).
% 0.99/0.76 thf(zip_derived_cl37, plain, (((an_isomorphism @ a) = (f))),
% 0.99/0.76 inference('cnf', [status(esa)], [a_maps_to_f])).
% 0.99/0.76 thf(f_times_f_is_f, axiom, (product @ g2 @ f @ f @ f)).
% 0.99/0.76 thf(zip_derived_cl28, plain, ( (product @ g2 @ f @ f @ f)),
% 0.99/0.76 inference('cnf', [status(esa)], [f_times_f_is_f])).
% 0.99/0.76 thf(zip_derived_cl1233, plain, ($false),
% 0.99/0.76 inference('demod', [status(thm)],
% 0.99/0.76 [zip_derived_cl1206, zip_derived_cl1216, zip_derived_cl37,
% 0.99/0.76 zip_derived_cl28])).
% 0.99/0.76
% 0.99/0.76 % SZS output end Refutation
% 0.99/0.76
% 0.99/0.76
% 0.99/0.76 % Terminating...
% 1.17/0.82 % Runner terminated.
% 1.69/0.83 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------