%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ANA026-2 : TPTP v9.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.gLkWDWgzoi true
% Computer : n020.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 04:28:53 PM UTC 2025
% Result : Unsatisfiable 27.02s 4.47s
% Output : Refutation 27.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ANA026-2 : TPTP v9.2.0. Released v3.2.0.
% 0.04/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.gLkWDWgzoi true
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 15:23:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.55/0.64 % Total configuration time : 435
% 0.55/0.64 % Estimated wc time : 1092
% 0.55/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 27.02/4.47 % Solved by fo/fo13.sh.
% 27.02/4.47 % done 2011 iterations in 3.691s
% 27.02/4.47 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 27.02/4.47 % SZS output start Refutation
% 27.02/4.47 thf(v_x_type, type, v_x: $i).
% 27.02/4.47 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 27.02/4.47 thf(c_less_type, type, c_less: $i > $i > $i > $o).
% 27.02/4.47 thf(class_OrderedGroup_Oab__group__add_type, type, class_OrderedGroup_Oab__group__add:
% 27.02/4.47 $i > $o).
% 27.02/4.47 thf(class_LOrder_Ojoin__semilorder_type, type, class_LOrder_Ojoin__semilorder:
% 27.02/4.47 $i > $o).
% 27.02/4.47 thf(c_minus_type, type, c_minus: $i > $i > $i > $i).
% 27.02/4.47 thf(c_uminus_type, type, c_uminus: $i > $i > $i).
% 27.02/4.47 thf(class_OrderedGroup_Ocomm__monoid__add_type, type, class_OrderedGroup_Ocomm__monoid__add:
% 27.02/4.47 $i > $o).
% 27.02/4.47 thf(class_Orderings_Oorder_type, type, class_Orderings_Oorder: $i > $o).
% 27.02/4.47 thf(c_Orderings_Omax_type, type, c_Orderings_Omax: $i > $i > $i > $i).
% 27.02/4.47 thf(v_g_type, type, v_g: $i > $i).
% 27.02/4.47 thf(class_Orderings_Olinorder_type, type, class_Orderings_Olinorder: $i > $o).
% 27.02/4.47 thf(class_OrderedGroup_Olordered__ab__group__abs_type, type, class_OrderedGroup_Olordered__ab__group__abs:
% 27.02/4.47 $i > $o).
% 27.02/4.47 thf(class_Ring__and__Field_Oordered__idom_type, type, class_Ring__and__Field_Oordered__idom:
% 27.02/4.47 $i > $o).
% 27.02/4.47 thf(v_f_type, type, v_f: $i > $i).
% 27.02/4.47 thf(class_OrderedGroup_Opordered__ab__group__add_type, type, class_OrderedGroup_Opordered__ab__group__add:
% 27.02/4.47 $i > $o).
% 27.02/4.47 thf(c_plus_type, type, c_plus: $i > $i > $i > $i).
% 27.02/4.47 thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type, type,
% 27.02/4.47 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o).
% 27.02/4.47 thf(v_k_type, type, v_k: $i > $i).
% 27.02/4.47 thf(c_HOL_Oabs_type, type, c_HOL_Oabs: $i > $i > $i).
% 27.02/4.47 thf(t_b_type, type, t_b: $i).
% 27.02/4.47 thf(c_0_type, type, c_0: $i).
% 27.02/4.47 thf(clsrel_Ring__and__Field_Oordered__idom_50, axiom,
% 27.02/4.47 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 27.02/4.47 ( class_OrderedGroup_Olordered__ab__group__abs @ T ))).
% 27.02/4.47 thf(zip_derived_cl30, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 27.02/4.47 thf(clsrel_OrderedGroup_Olordered__ab__group__abs_1, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) |
% 27.02/4.47 ( class_OrderedGroup_Opordered__ab__group__add @ T ))).
% 27.02/4.47 thf(zip_derived_cl24, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_OrderedGroup_Olordered__ab__group__abs_1])).
% 27.02/4.47 thf(cls_Orderings_Olinorder__not__le_0, axiom,
% 27.02/4.47 (( ~( class_Orderings_Olinorder @ T_a ) ) | ( c_less @ V_y @ V_x @ T_a ) |
% 27.02/4.47 ( c_lessequals @ V_x @ V_y @ T_a ))).
% 27.02/4.47 thf(zip_derived_cl18, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_Orderings_Olinorder @ X0)
% 27.02/4.47 | (c_less @ X1 @ X2 @ X0)
% 27.02/4.47 | (c_lessequals @ X2 @ X1 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_Orderings_Olinorder__not__le_0])).
% 27.02/4.47 thf(cls_Orderings_Oorder__less__imp__le_0, axiom,
% 27.02/4.47 (( ~( class_Orderings_Oorder @ T_a ) ) |
% 27.02/4.47 ( ~( c_less @ V_x @ V_y @ T_a ) ) | ( c_lessequals @ V_x @ V_y @ T_a ))).
% 27.02/4.47 thf(zip_derived_cl22, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_Orderings_Oorder @ X0)
% 27.02/4.47 | ~ (c_less @ X1 @ X2 @ X0)
% 27.02/4.47 | (c_lessequals @ X1 @ X2 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_Orderings_Oorder__less__imp__le_0])).
% 27.02/4.47 thf(zip_derived_cl40, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ( (c_lessequals @ X1 @ X2 @ X0)
% 27.02/4.47 | ~ (class_Orderings_Olinorder @ X0)
% 27.02/4.47 | ~ (class_Orderings_Oorder @ X0)
% 27.02/4.47 | (c_lessequals @ X2 @ X1 @ X0))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl22])).
% 27.02/4.47 thf(clsrel_Ring__and__Field_Oordered__idom_35, axiom,
% 27.02/4.47 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 27.02/4.47 ( class_LOrder_Ojoin__semilorder @ T ))).
% 27.02/4.47 thf(zip_derived_cl28, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_LOrder_Ojoin__semilorder @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_35])).
% 27.02/4.47 thf(clsrel_LOrder_Ojoin__semilorder_1, axiom,
% 27.02/4.47 (( ~( class_LOrder_Ojoin__semilorder @ T ) ) |
% 27.02/4.47 ( class_Orderings_Oorder @ T ))).
% 27.02/4.47 thf(zip_derived_cl23, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_LOrder_Ojoin__semilorder @ X0)
% 27.02/4.47 | (class_Orderings_Oorder @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [clsrel_LOrder_Ojoin__semilorder_1])).
% 27.02/4.47 thf(zip_derived_cl33, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_Orderings_Oorder @ X0))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl23])).
% 27.02/4.47 thf(zip_derived_cl543, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ( (c_lessequals @ X2 @ X1 @ X0)
% 27.02/4.47 | ~ (class_Orderings_Olinorder @ X0)
% 27.02/4.47 | (c_lessequals @ X1 @ X2 @ X0)
% 27.02/4.47 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl33])).
% 27.02/4.47 thf(clsrel_Ring__and__Field_Oordered__idom_33, axiom,
% 27.02/4.47 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 27.02/4.47 ( class_Orderings_Olinorder @ T ))).
% 27.02/4.47 thf(zip_derived_cl27, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_Orderings_Olinorder @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_33])).
% 27.02/4.47 thf(zip_derived_cl27700, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (c_lessequals @ X1 @ X2 @ X0)
% 27.02/4.47 | (c_lessequals @ X2 @ X1 @ X0))),
% 27.02/4.47 inference('clc', [status(thm)], [zip_derived_cl543, zip_derived_cl27])).
% 27.02/4.47 thf(zip_derived_cl30, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 27.02/4.47 thf(clsrel_Ring__and__Field_Oordered__idom_23, axiom,
% 27.02/4.47 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 27.02/4.47 ( class_OrderedGroup_Ocomm__monoid__add @ T ))).
% 27.02/4.47 thf(zip_derived_cl26, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Ocomm__monoid__add @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_23])).
% 27.02/4.47 thf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Ocomm__monoid__add @ T_a ) ) |
% 27.02/4.47 ( ( c_plus @ c_0 @ V_y @ T_a ) = ( V_y ) ))).
% 27.02/4.47 thf(zip_derived_cl9, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Ocomm__monoid__add @ X0)
% 27.02/4.47 | ((c_plus @ c_0 @ X1 @ X0) = (X1)))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0])).
% 27.02/4.47 thf(zip_derived_cl38, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | ((c_plus @ c_0 @ X1 @ X0) = (X1)))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl9])).
% 27.02/4.47 thf(tfree_tcs, conjecture,
% 27.02/4.47 (~( class_Ring__and__Field_Oordered__idom @ t_b ))).
% 27.02/4.47 thf(zf_stmt_0, negated_conjecture,
% 27.02/4.47 (class_Ring__and__Field_Oordered__idom @ t_b),
% 27.02/4.47 inference('cnf.neg', [status(esa)], [tfree_tcs])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl45, plain,
% 27.02/4.47 (![X0 : $i]: ((c_plus @ c_0 @ X0 @ t_b) = (X0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl2])).
% 27.02/4.47 thf(cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 27.02/4.47 ( ( c_minus @ V_a @ V_b @ T_a ) =
% 27.02/4.47 ( c_plus @ V_a @ ( c_uminus @ V_b @ T_a ) @ T_a ) ))).
% 27.02/4.47 thf(zip_derived_cl3, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X1 @ X2 @ X0)
% 27.02/4.47 = (c_plus @ X1 @ (c_uminus @ X2 @ X0) @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0])).
% 27.02/4.47 thf(zip_derived_cl50, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl3])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(clsrel_Ring__and__Field_Oordered__idom_4, axiom,
% 27.02/4.47 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 27.02/4.47 ( class_OrderedGroup_Oab__group__add @ T ))).
% 27.02/4.47 thf(zip_derived_cl29, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Oab__group__add @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl52, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl31])).
% 27.02/4.47 thf(cls_OrderedGroup_Oabs__of__nonpos_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T_a ) ) |
% 27.02/4.47 ( ~( c_lessequals @ V_a @ c_0 @ T_a ) ) |
% 27.02/4.47 ( ( c_HOL_Oabs @ V_a @ T_a ) = ( c_uminus @ V_a @ T_a ) ))).
% 27.02/4.47 thf(zip_derived_cl6, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ c_0 @ X0)
% 27.02/4.47 | ((c_HOL_Oabs @ X1 @ X0) = (c_uminus @ X1 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__of__nonpos_0])).
% 27.02/4.47 thf(zip_derived_cl67, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X0 @ c_0 @ t_b)
% 27.02/4.47 | ((c_HOL_Oabs @ X0 @ t_b) = (c_minus @ c_0 @ X0 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl6])).
% 27.02/4.47 thf(zip_derived_cl393, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X0 @ c_0 @ t_b)
% 27.02/4.47 | ((c_HOL_Oabs @ X0 @ t_b) = (c_minus @ c_0 @ X0 @ t_b)))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl67])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl397, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (c_lessequals @ X0 @ c_0 @ t_b)
% 27.02/4.47 | ((c_HOL_Oabs @ X0 @ t_b) = (c_minus @ c_0 @ X0 @ t_b)))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl393, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl27721, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ( (c_lessequals @ c_0 @ X0 @ t_b)
% 27.02/4.47 | ~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ((c_HOL_Oabs @ X0 @ t_b) = (c_minus @ c_0 @ X0 @ t_b)))),
% 27.02/4.47 inference('s_sup-', [status(thm)],
% 27.02/4.47 [zip_derived_cl27700, zip_derived_cl397])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl27904, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ( (c_lessequals @ c_0 @ X0 @ t_b)
% 27.02/4.47 | ((c_HOL_Oabs @ X0 @ t_b) = (c_minus @ c_0 @ X0 @ t_b)))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl27721, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl30, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 27.02/4.47 thf(zip_derived_cl24, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_OrderedGroup_Olordered__ab__group__abs_1])).
% 27.02/4.47 thf(zip_derived_cl27, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_Orderings_Olinorder @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_33])).
% 27.02/4.47 thf(cls_conjecture_2, conjecture,
% 27.02/4.47 (c_lessequals @
% 27.02/4.47 ( c_Orderings_Omax @
% 27.02/4.47 ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ c_0 @ t_b ) @
% 27.02/4.47 ( c_HOL_Oabs @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @
% 27.02/4.47 t_b)).
% 27.02/4.47 thf(zf_stmt_1, negated_conjecture,
% 27.02/4.47 (~( c_lessequals @
% 27.02/4.47 ( c_Orderings_Omax @
% 27.02/4.47 ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ c_0 @ t_b ) @
% 27.02/4.47 ( c_HOL_Oabs @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @
% 27.02/4.47 t_b )),
% 27.02/4.47 inference('cnf.neg', [status(esa)], [cls_conjecture_2])).
% 27.02/4.47 thf(zip_derived_cl1, plain,
% 27.02/4.47 (~ (c_lessequals @
% 27.02/4.47 (c_Orderings_Omax @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 c_0 @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_1])).
% 27.02/4.47 thf(zip_derived_cl52, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl31])).
% 27.02/4.47 thf(cls_OrderedGroup_Ominus__diff__eq_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 27.02/4.47 ( ( c_uminus @ ( c_minus @ V_a @ V_b @ T_a ) @ T_a ) =
% 27.02/4.47 ( c_minus @ V_b @ V_a @ T_a ) ))).
% 27.02/4.47 thf(zip_derived_cl17, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ X1 @ X2 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ominus__diff__eq_0])).
% 27.02/4.47 thf(zip_derived_cl76, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl17])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl80, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl30, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 27.02/4.47 thf(zip_derived_cl52, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl31])).
% 27.02/4.47 thf(cls_OrderedGroup_Oabs__minus__cancel_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T_a ) ) |
% 27.02/4.47 ( ( c_HOL_Oabs @ ( c_uminus @ V_a @ T_a ) @ T_a ) =
% 27.02/4.47 ( c_HOL_Oabs @ V_a @ T_a ) ))).
% 27.02/4.47 thf(zip_derived_cl5, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | ((c_HOL_Oabs @ (c_uminus @ X1 @ X0) @ X0) = (c_HOL_Oabs @ X1 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__minus__cancel_0])).
% 27.02/4.47 thf(zip_derived_cl66, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 27.02/4.47 | ((c_HOL_Oabs @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_HOL_Oabs @ X0 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl5])).
% 27.02/4.47 thf(zip_derived_cl297, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ((c_HOL_Oabs @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_HOL_Oabs @ X0 @ t_b)))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl66])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl303, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ((c_HOL_Oabs @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_HOL_Oabs @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl297, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl327, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_HOL_Oabs @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_HOL_Oabs @ (c_minus @ X0 @ X1 @ t_b) @ t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl303])).
% 27.02/4.47 thf(zip_derived_cl346, plain,
% 27.02/4.47 (~ (c_lessequals @
% 27.02/4.47 (c_Orderings_Omax @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 c_0 @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl327])).
% 27.02/4.47 thf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, axiom,
% 27.02/4.47 (( ~( class_Orderings_Olinorder @ T_b ) ) |
% 27.02/4.47 ( ~( c_lessequals @ V_y @ V_z @ T_b ) ) |
% 27.02/4.47 ( ~( c_lessequals @ V_x @ V_z @ T_b ) ) |
% 27.02/4.47 ( c_lessequals @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ V_z @ T_b ))).
% 27.02/4.47 thf(zip_derived_cl20, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_Orderings_Olinorder @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ X2 @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X3 @ X2 @ X0)
% 27.02/4.47 | (c_lessequals @ (c_Orderings_Omax @ X3 @ X1 @ X0) @ X2 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2])).
% 27.02/4.47 thf(zip_derived_cl412, plain,
% 27.02/4.47 ((~ (class_Orderings_Olinorder @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ c_0 @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl346, zip_derived_cl20])).
% 27.02/4.47 thf(zip_derived_cl452, plain,
% 27.02/4.47 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ c_0 @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl412])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl453, plain,
% 27.02/4.47 ((~ (c_lessequals @ c_0 @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl452, zip_derived_cl2])).
% 27.02/4.47 thf(cls_OrderedGroup_Ocompare__rls__8_1, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Opordered__ab__group__add @ T_a ) ) |
% 27.02/4.47 ( ~( c_lessequals @ V_a @ ( c_plus @ V_c @ V_b @ T_a ) @ T_a ) ) |
% 27.02/4.47 ( c_lessequals @ ( c_minus @ V_a @ V_b @ T_a ) @ V_c @ T_a ))).
% 27.02/4.47 thf(zip_derived_cl15, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ (c_plus @ X2 @ X3 @ X0) @ X0)
% 27.02/4.47 | (c_lessequals @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__8_1])).
% 27.02/4.47 thf(zip_derived_cl457, plain,
% 27.02/4.47 ((~ (c_lessequals @ c_0 @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)
% 27.02/4.47 | ~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 (v_k @ v_x) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl453, zip_derived_cl15])).
% 27.02/4.47 thf(zip_derived_cl494, plain,
% 27.02/4.47 ((~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ c_0 @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)
% 27.02/4.47 | ~ (c_lessequals @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 (v_k @ v_x) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl457])).
% 27.02/4.47 thf(cls_OrderedGroup_Oabs__ge__zero_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T_a ) ) |
% 27.02/4.47 ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ))).
% 27.02/4.47 thf(zip_derived_cl4, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | (c_lessequals @ c_0 @ (c_HOL_Oabs @ X1 @ X0) @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__ge__zero_0])).
% 27.02/4.47 thf(zip_derived_cl519, plain,
% 27.02/4.47 ((~ (c_lessequals @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 (v_k @ v_x) @ t_b) @
% 27.02/4.47 t_b)
% 27.02/4.47 | ~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b))),
% 27.02/4.47 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl4])).
% 27.02/4.47 thf(zip_derived_cl520, plain,
% 27.02/4.47 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 (v_k @ v_x) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl519])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl521, plain,
% 27.02/4.47 (~ (c_lessequals @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 (v_k @ v_x) @ t_b) @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl520, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl3, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X1 @ X2 @ X0)
% 27.02/4.47 = (c_plus @ X1 @ (c_uminus @ X2 @ X0) @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(cls_OrderedGroup_Odiff__self_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 27.02/4.47 ( ( c_minus @ V_a @ V_a @ T_a ) = ( c_0 ) ))).
% 27.02/4.47 thf(zip_derived_cl16, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X1 @ X1 @ X0) = (c_0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Odiff__self_0])).
% 27.02/4.47 thf(zip_derived_cl34, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ X0 @ X0 @ t_b) = (c_0))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl16])).
% 27.02/4.47 thf(cls_OrderedGroup_Ocompare__rls__3_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 27.02/4.47 ( ( c_plus @ ( c_minus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) =
% 27.02/4.47 ( c_minus @ ( c_plus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ))).
% 27.02/4.47 thf(zip_derived_cl12, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_plus @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__3_0])).
% 27.02/4.47 thf(zip_derived_cl193, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_plus @ c_0 @ X1 @ t_b)
% 27.02/4.47 = (c_minus @ (c_plus @ X0 @ X1 @ t_b) @ X0 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl12])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl45, plain,
% 27.02/4.47 (![X0 : $i]: ((c_plus @ c_0 @ X0 @ t_b) = (X0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl199, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((X1) = (c_minus @ (c_plus @ X0 @ X1 @ t_b) @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl193, zip_derived_cl31, zip_derived_cl45])).
% 27.02/4.47 thf(zip_derived_cl221, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_uminus @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ X1 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl199])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl52, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl227, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl221, zip_derived_cl31, zip_derived_cl52])).
% 27.02/4.47 thf(zip_derived_cl17, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ X1 @ X2 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ominus__diff__eq_0])).
% 27.02/4.47 thf(zip_derived_cl425, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X1 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl227, zip_derived_cl17])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl447, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X1 @ (c_minus @ X1 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl425, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl227, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl221, zip_derived_cl31, zip_derived_cl52])).
% 27.02/4.47 thf(zip_derived_cl80, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl426, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X1 @ (c_minus @ X1 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl227, zip_derived_cl80])).
% 27.02/4.47 thf(zip_derived_cl34, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ X0 @ X0 @ t_b) = (c_0))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl16])).
% 27.02/4.47 thf(zip_derived_cl17, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ X1 @ X2 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ominus__diff__eq_0])).
% 27.02/4.47 thf(zip_derived_cl78, plain,
% 27.02/4.47 ((~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_uminus @ c_0 @ t_b) = (c_0)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl17])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl82, plain, (((c_uminus @ c_0 @ t_b) = (c_0))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl3, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X1 @ X2 @ X0)
% 27.02/4.47 = (c_plus @ X1 @ (c_uminus @ X2 @ X0) @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0])).
% 27.02/4.47 thf(zip_derived_cl85, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_minus @ X0 @ c_0 @ t_b) = (c_plus @ X0 @ c_0 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl82, zip_derived_cl3])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl89, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ X0 @ c_0 @ t_b) = (c_plus @ X0 @ c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl31])).
% 27.02/4.47 thf(cls_OrderedGroup_Ocompare__rls__10_1, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 27.02/4.47 ( ( c_minus @ ( c_plus @ V_c @ V_b @ T_a ) @ V_b @ T_a ) = ( V_c ) ))).
% 27.02/4.47 thf(zip_derived_cl10, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ (c_plus @ X1 @ X2 @ X0) @ X2 @ X0) = (X1)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__10_1])).
% 27.02/4.47 thf(zip_derived_cl94, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_minus @ (c_minus @ X0 @ c_0 @ t_b) @ c_0 @ t_b) = (X0)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl10])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl96, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ (c_minus @ X0 @ c_0 @ t_b) @ c_0 @ t_b) = (X0))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl17, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ X1 @ X2 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ominus__diff__eq_0])).
% 27.02/4.47 thf(zip_derived_cl120, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_uminus @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ c_0 @ (c_minus @ X0 @ c_0 @ t_b) @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl17])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl52, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl126, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ c_0 @ (c_minus @ X0 @ c_0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl120, zip_derived_cl31, zip_derived_cl52])).
% 27.02/4.47 thf(zip_derived_cl17, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ X1 @ X2 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ominus__diff__eq_0])).
% 27.02/4.47 thf(zip_derived_cl127, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ (c_minus @ X0 @ c_0 @ t_b) @ c_0 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl17])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl52, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl96, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ (c_minus @ X0 @ c_0 @ t_b) @ c_0 @ t_b) = (X0))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl132, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl127, zip_derived_cl31, zip_derived_cl52,
% 27.02/4.47 zip_derived_cl96])).
% 27.02/4.47 thf(zip_derived_cl448, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((X0) = (c_minus @ X1 @ (c_minus @ X1 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl426, zip_derived_cl132])).
% 27.02/4.47 thf(zip_derived_cl503, plain,
% 27.02/4.47 (![X0 : $i]: ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl447, zip_derived_cl448])).
% 27.02/4.47 thf(zip_derived_cl3, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X1 @ X2 @ X0)
% 27.02/4.47 = (c_plus @ X1 @ (c_uminus @ X2 @ X0) @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0])).
% 27.02/4.47 thf(zip_derived_cl504, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_minus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_plus @ X1 @ X0 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl503, zip_derived_cl3])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl516, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_plus @ X1 @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl132, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl127, zip_derived_cl31, zip_derived_cl52,
% 27.02/4.47 zip_derived_cl96])).
% 27.02/4.47 thf(zip_derived_cl12, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_plus @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__3_0])).
% 27.02/4.47 thf(zip_derived_cl195, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_plus @ X0 @ X1 @ t_b)
% 27.02/4.47 = (c_minus @ (c_plus @ c_0 @ X1 @ t_b) @
% 27.02/4.47 (c_minus @ c_0 @ X0 @ t_b) @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl12])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl45, plain,
% 27.02/4.47 (![X0 : $i]: ((c_plus @ c_0 @ X0 @ t_b) = (X0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl201, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_plus @ X0 @ X1 @ t_b)
% 27.02/4.47 = (c_minus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl195, zip_derived_cl31, zip_derived_cl45])).
% 27.02/4.47 thf(zip_derived_cl1480, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_plus @ X0 @ X1 @ t_b) = (c_plus @ X1 @ X0 @ t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl516, zip_derived_cl201])).
% 27.02/4.47 thf(zip_derived_cl1527, plain,
% 27.02/4.47 (~ (c_lessequals @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @ (v_k @ v_x) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl521, zip_derived_cl1480])).
% 27.02/4.47 thf(zip_derived_cl201, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_plus @ X0 @ X1 @ t_b)
% 27.02/4.47 = (c_minus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl195, zip_derived_cl31, zip_derived_cl45])).
% 27.02/4.47 thf(zip_derived_cl34, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ X0 @ X0 @ t_b) = (c_0))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl16])).
% 27.02/4.47 thf(zip_derived_cl1122, plain,
% 27.02/4.47 (![X0 : $i]: ((c_plus @ X0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (c_0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl201, zip_derived_cl34])).
% 27.02/4.47 thf(cls_OrderedGroup_Ocompare__rls__2_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 27.02/4.47 ( ( c_plus @ V_a @ ( c_minus @ V_b @ V_c @ T_a ) @ T_a ) =
% 27.02/4.47 ( c_minus @ ( c_plus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ))).
% 27.02/4.47 thf(zip_derived_cl11, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_plus @ X1 @ (c_minus @ X2 @ X3 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__2_0])).
% 27.02/4.47 thf(zip_derived_cl30, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 27.02/4.47 thf(zip_derived_cl24, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_OrderedGroup_Olordered__ab__group__abs_1])).
% 27.02/4.47 thf(zip_derived_cl448, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((X0) = (c_minus @ X1 @ (c_minus @ X1 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl426, zip_derived_cl132])).
% 27.02/4.47 thf(zip_derived_cl15, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ (c_plus @ X2 @ X3 @ X0) @ X0)
% 27.02/4.47 | (c_lessequals @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__8_1])).
% 27.02/4.47 thf(zip_derived_cl463, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X2 @
% 27.02/4.47 (c_plus @ X1 @ (c_minus @ X2 @ X0 @ t_b) @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl448, zip_derived_cl15])).
% 27.02/4.47 thf(zip_derived_cl608, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X1 @
% 27.02/4.47 (c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ X2 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl463])).
% 27.02/4.47 thf(zip_derived_cl711, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X1 @
% 27.02/4.47 (c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ X2 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl608])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl712, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (c_lessequals @ X1 @
% 27.02/4.47 (c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ X2 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl711, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl731, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X1 @
% 27.02/4.47 (c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ X2 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl712])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl747, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (c_lessequals @ X1 @
% 27.02/4.47 (c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ X2 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl731, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl30, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 27.02/4.47 thf(clsrel_OrderedGroup_Olordered__ab__group__abs_6, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) |
% 27.02/4.47 ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ))).
% 27.02/4.47 thf(zip_derived_cl25, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_OrderedGroup_Olordered__ab__group__abs_6])).
% 27.02/4.47 thf(zip_derived_cl45, plain,
% 27.02/4.47 (![X0 : $i]: ((c_plus @ c_0 @ X0 @ t_b) = (X0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl2])).
% 27.02/4.47 thf(cls_OrderedGroup_Oadd__le__cancel__right_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a ) ) |
% 27.02/4.47 ( ~( c_lessequals @
% 27.02/4.47 ( c_plus @ V_a @ V_c @ T_a ) @ ( c_plus @ V_b @ V_c @ T_a ) @ T_a ) ) |
% 27.02/4.47 ( c_lessequals @ V_a @ V_b @ T_a ))).
% 27.02/4.47 thf(zip_derived_cl8, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ X0)
% 27.02/4.47 | ~ (c_lessequals @ (c_plus @ X1 @ X2 @ X0) @
% 27.02/4.47 (c_plus @ X3 @ X2 @ X0) @ X0)
% 27.02/4.47 | (c_lessequals @ X1 @ X3 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Oadd__le__cancel__right_0])).
% 27.02/4.47 thf(zip_derived_cl106, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X0 @ (c_plus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ c_0 @ X1 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl8])).
% 27.02/4.47 thf(zip_derived_cl110, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X0 @ (c_plus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ c_0 @ X1 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl106])).
% 27.02/4.47 thf(zip_derived_cl262, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X0 @ (c_plus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ c_0 @ X1 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl110])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl263, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (c_lessequals @ X0 @ (c_plus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ c_0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl262, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl763, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ( (c_lessequals @ X0 @ X1 @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X2 @
% 27.02/4.47 (c_plus @ (c_minus @ (c_plus @ X1 @ c_0 @ t_b) @ X0 @ t_b) @
% 27.02/4.47 X2 @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl747, zip_derived_cl263])).
% 27.02/4.47 thf(zip_derived_cl89, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ X0 @ c_0 @ t_b) = (c_plus @ X0 @ c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl126, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ c_0 @ (c_minus @ X0 @ c_0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl120, zip_derived_cl31, zip_derived_cl52])).
% 27.02/4.47 thf(zip_derived_cl132, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl127, zip_derived_cl31, zip_derived_cl52,
% 27.02/4.47 zip_derived_cl96])).
% 27.02/4.47 thf(zip_derived_cl137, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ c_0 @ t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl132])).
% 27.02/4.47 thf(zip_derived_cl132, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl127, zip_derived_cl31, zip_derived_cl52,
% 27.02/4.47 zip_derived_cl96])).
% 27.02/4.47 thf(zip_derived_cl139, plain,
% 27.02/4.47 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl137, zip_derived_cl132])).
% 27.02/4.47 thf(zip_derived_cl165, plain,
% 27.02/4.47 (![X0 : $i]: ((X0) = (c_plus @ X0 @ c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl139])).
% 27.02/4.47 thf(zip_derived_cl786, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ( (c_lessequals @ X0 @ X1 @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X2 @
% 27.02/4.47 (c_plus @ (c_minus @ X1 @ X0 @ t_b) @ X2 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl763, zip_derived_cl165])).
% 27.02/4.47 thf(zip_derived_cl1226, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ( (c_lessequals @ X0 @ X1 @ t_b)
% 27.02/4.47 | ~ (c_lessequals @
% 27.02/4.47 (c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b) @ c_0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)],
% 27.02/4.47 [zip_derived_cl1122, zip_derived_cl786])).
% 27.02/4.47 thf(zip_derived_cl80, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl1246, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ( (c_lessequals @ X0 @ X1 @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ X0 @ X1 @ t_b) @ c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl1226, zip_derived_cl80])).
% 27.02/4.47 thf(zip_derived_cl1637, plain,
% 27.02/4.47 (~ (c_lessequals @
% 27.02/4.47 (c_minus @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @ (v_k @ v_x) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 c_0 @ t_b)),
% 27.02/4.47 inference('s_sup+', [status(thm)],
% 27.02/4.47 [zip_derived_cl1527, zip_derived_cl1246])).
% 27.02/4.47 thf(zip_derived_cl28491, plain,
% 27.02/4.47 (( (c_lessequals @ c_0 @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @
% 27.02/4.47 t_b)
% 27.02/4.47 | ~ (c_lessequals @
% 27.02/4.47 (c_minus @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @ (v_k @ v_x) @
% 27.02/4.47 (c_minus @ c_0 @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 c_0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)],
% 27.02/4.47 [zip_derived_cl27904, zip_derived_cl1637])).
% 27.02/4.47 thf(zip_derived_cl448, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((X0) = (c_minus @ X1 @ (c_minus @ X1 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl426, zip_derived_cl132])).
% 27.02/4.47 thf(zip_derived_cl17, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ X1 @ X2 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ominus__diff__eq_0])).
% 27.02/4.47 thf(zip_derived_cl3, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X1 @ X2 @ X0)
% 27.02/4.47 = (c_plus @ X1 @ (c_uminus @ X2 @ X0) @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0])).
% 27.02/4.47 thf(zip_derived_cl73, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X3 @ (c_minus @ X1 @ X2 @ X0) @ X0)
% 27.02/4.47 = (c_plus @ X3 @ (c_minus @ X2 @ X1 @ X0) @ X0)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl3])).
% 27.02/4.47 thf(zip_derived_cl84, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (((c_minus @ X3 @ (c_minus @ X1 @ X2 @ X0) @ X0)
% 27.02/4.47 = (c_plus @ X3 @ (c_minus @ X2 @ X1 @ X0) @ X0))
% 27.02/4.47 | ~ (class_OrderedGroup_Oab__group__add @ X0))),
% 27.02/4.47 inference('simplify', [status(thm)], [zip_derived_cl73])).
% 27.02/4.47 thf(zip_derived_cl33, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_Orderings_Oorder @ X0))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl23])).
% 27.02/4.47 thf(zip_derived_cl30, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 27.02/4.47 thf(zip_derived_cl30, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 27.02/4.47 thf(zip_derived_cl24, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [clsrel_OrderedGroup_Olordered__ab__group__abs_1])).
% 27.02/4.47 thf(cls_OrderedGroup_Ocompare__rls__4_0, axiom,
% 27.02/4.47 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 27.02/4.47 ( ( c_minus @ ( c_minus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) =
% 27.02/4.47 ( c_minus @ V_a @ ( c_plus @ V_b @ V_c @ T_a ) @ T_a ) ))).
% 27.02/4.47 thf(zip_derived_cl13, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ (c_minus @ X1 @ X2 @ X0) @ X3 @ X0)
% 27.02/4.47 = (c_minus @ X1 @ (c_plus @ X2 @ X3 @ X0) @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__4_0])).
% 27.02/4.47 thf(zip_derived_cl1637, plain,
% 27.02/4.47 (~ (c_lessequals @
% 27.02/4.47 (c_minus @ (v_f @ v_x) @
% 27.02/4.47 (c_plus @ (v_k @ v_x) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 c_0 @ t_b)),
% 27.02/4.47 inference('s_sup+', [status(thm)],
% 27.02/4.47 [zip_derived_cl1527, zip_derived_cl1246])).
% 27.02/4.47 thf(zip_derived_cl1656, plain,
% 27.02/4.47 ((~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ~ (c_lessequals @
% 27.02/4.47 (c_minus @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 c_0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl1637])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl1657, plain,
% 27.02/4.47 (~ (c_lessequals @
% 27.02/4.47 (c_minus @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 c_0 @ t_b)),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl1656, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl15, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ (c_plus @ X2 @ X3 @ X0) @ X0)
% 27.02/4.47 | (c_lessequals @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__8_1])).
% 27.02/4.47 thf(zip_derived_cl1678, plain,
% 27.02/4.47 ((~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_plus @ c_0 @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl1657, zip_derived_cl15])).
% 27.02/4.47 thf(zip_derived_cl45, plain,
% 27.02/4.47 (![X0 : $i]: ((c_plus @ c_0 @ X0 @ t_b) = (X0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl1687, plain,
% 27.02/4.47 ((~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl1678, zip_derived_cl45])).
% 27.02/4.47 thf(zip_derived_cl1757, plain,
% 27.02/4.47 ((~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl1687])).
% 27.02/4.47 thf(zip_derived_cl1758, plain,
% 27.02/4.47 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl1757])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl1759, plain,
% 27.02/4.47 (~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 (c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl1758, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl4, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | (c_lessequals @ c_0 @ (c_HOL_Oabs @ X1 @ X0) @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__ge__zero_0])).
% 27.02/4.47 thf(cls_Orderings_Oorder__class_Oorder__trans_0, axiom,
% 27.02/4.47 (( ~( class_Orderings_Oorder @ T_a ) ) |
% 27.02/4.47 ( ~( c_lessequals @ V_y @ V_z @ T_a ) ) |
% 27.02/4.47 ( ~( c_lessequals @ V_x @ V_y @ T_a ) ) |
% 27.02/4.47 ( c_lessequals @ V_x @ V_z @ T_a ))).
% 27.02/4.47 thf(zip_derived_cl21, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_Orderings_Oorder @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ X2 @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X3 @ X1 @ X0)
% 27.02/4.47 | (c_lessequals @ X3 @ X2 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_Orderings_Oorder__class_Oorder__trans_0])).
% 27.02/4.47 thf(zip_derived_cl70, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 27.02/4.47 | ~ (class_Orderings_Oorder @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X2 @ c_0 @ X0)
% 27.02/4.47 | (c_lessequals @ X2 @ (c_HOL_Oabs @ X1 @ X0) @ X0))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl21])).
% 27.02/4.47 thf(zip_derived_cl1774, plain,
% 27.02/4.47 ((~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 27.02/4.47 | ~ (class_Orderings_Oorder @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 c_0 @ t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl1759, zip_derived_cl70])).
% 27.02/4.47 thf(zip_derived_cl1784, plain,
% 27.02/4.47 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (class_Orderings_Oorder @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 c_0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl1774])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl1785, plain,
% 27.02/4.47 ((~ (class_Orderings_Oorder @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl1784, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl1786, plain,
% 27.02/4.47 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 c_0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl1785])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl1787, plain,
% 27.02/4.47 (~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ c_0 @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl1786, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl199, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((X1) = (c_minus @ (c_plus @ X0 @ X1 @ t_b) @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl193, zip_derived_cl31, zip_derived_cl45])).
% 27.02/4.47 thf(zip_derived_cl448, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((X0) = (c_minus @ X1 @ (c_minus @ X1 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl426, zip_derived_cl132])).
% 27.02/4.47 thf(zip_derived_cl480, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((X1) = (c_minus @ (c_plus @ X1 @ X0 @ t_b) @ X0 @ t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl199, zip_derived_cl448])).
% 27.02/4.47 thf(zip_derived_cl45, plain,
% 27.02/4.47 (![X0 : $i]: ((c_plus @ c_0 @ X0 @ t_b) = (X0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl712, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (c_lessequals @ X1 @
% 27.02/4.47 (c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ X2 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl711, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl735, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (c_lessequals @ X1 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ c_0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl712])).
% 27.02/4.47 thf(zip_derived_cl933, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (c_lessequals @ (c_plus @ X0 @ X1 @ t_b) @ X0 @ t_b)
% 27.02/4.47 | (c_lessequals @ X1 @ c_0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl480, zip_derived_cl735])).
% 27.02/4.47 thf(zip_derived_cl1800, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ~ (c_lessequals @
% 27.02/4.47 (c_plus @ X0 @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 X0 @ t_b)),
% 27.02/4.47 inference('s_sup+', [status(thm)],
% 27.02/4.47 [zip_derived_cl1787, zip_derived_cl933])).
% 27.02/4.47 thf(zip_derived_cl3567, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ~ (c_lessequals @
% 27.02/4.47 (c_minus @ X0 @ (c_minus @ (v_k @ v_x) @ (v_f @ v_x) @ t_b) @
% 27.02/4.47 t_b) @
% 27.02/4.47 X0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl1800])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl3574, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ~ (c_lessequals @
% 27.02/4.47 (c_minus @ X0 @ (c_minus @ (v_k @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 X0 @ t_b)),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl3567, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl33, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 27.02/4.47 | (class_Orderings_Oorder @ X0))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl23])).
% 27.02/4.47 thf(cls_conjecture_1, conjecture,
% 27.02/4.47 (~( c_lessequals @ ( v_g @ V_U ) @ ( v_k @ V_U ) @ t_b ))).
% 27.02/4.47 thf(zf_stmt_2, negated_conjecture,
% 27.02/4.47 (c_lessequals @ ( v_g @ V_U ) @ ( v_k @ V_U ) @ t_b),
% 27.02/4.47 inference('cnf.neg', [status(esa)], [cls_conjecture_1])).
% 27.02/4.47 thf(zip_derived_cl0, plain,
% 27.02/4.47 (![X0 : $i]: (c_lessequals @ (v_g @ X0) @ (v_k @ X0) @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_2])).
% 27.02/4.47 thf(zip_derived_cl21, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_Orderings_Oorder @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ X2 @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X3 @ X1 @ X0)
% 27.02/4.47 | (c_lessequals @ X3 @ X2 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_Orderings_Oorder__class_Oorder__trans_0])).
% 27.02/4.47 thf(zip_derived_cl69, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_Orderings_Oorder @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ (v_g @ X0) @ t_b)
% 27.02/4.47 | (c_lessequals @ X1 @ (v_k @ X0) @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl21])).
% 27.02/4.47 thf(zip_derived_cl71, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ (v_g @ X0) @ t_b)
% 27.02/4.47 | (c_lessequals @ X1 @ (v_k @ X0) @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl69])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl72, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (c_lessequals @ X1 @ (v_g @ X0) @ t_b)
% 27.02/4.47 | (c_lessequals @ X1 @ (v_k @ X0) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl71, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl4495, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ~ (c_lessequals @
% 27.02/4.47 (c_minus @ (v_k @ X0) @
% 27.02/4.47 (c_minus @ (v_k @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 (v_g @ X0) @ t_b)),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl3574, zip_derived_cl72])).
% 27.02/4.47 thf(zip_derived_cl1246, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ( (c_lessequals @ X0 @ X1 @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (c_minus @ X0 @ X1 @ t_b) @ c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl1226, zip_derived_cl80])).
% 27.02/4.47 thf(zip_derived_cl5350, plain,
% 27.02/4.47 (![X0 : $i]:
% 27.02/4.47 ~ (c_lessequals @
% 27.02/4.47 (c_minus @
% 27.02/4.47 (c_minus @ (v_k @ X0) @
% 27.02/4.47 (c_minus @ (v_k @ v_x) @ (v_f @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 (v_g @ X0) @ t_b) @
% 27.02/4.47 c_0 @ t_b)),
% 27.02/4.47 inference('s_sup+', [status(thm)],
% 27.02/4.47 [zip_derived_cl4495, zip_derived_cl1246])).
% 27.02/4.47 thf(zip_derived_cl13946, plain,
% 27.02/4.47 (~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ c_0 @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)],
% 27.02/4.47 [zip_derived_cl448, zip_derived_cl5350])).
% 27.02/4.47 thf(zip_derived_cl165, plain,
% 27.02/4.47 (![X0 : $i]: ((X0) = (c_plus @ X0 @ c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl139])).
% 27.02/4.47 thf(zip_derived_cl747, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (c_lessequals @ X1 @
% 27.02/4.47 (c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X0 @ X2 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl731, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl773, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (c_lessequals @ c_0 @ (c_minus @ X0 @ X1 @ t_b) @ t_b)
% 27.02/4.47 | (c_lessequals @ X1 @ X0 @ t_b))),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl165, zip_derived_cl747])).
% 27.02/4.47 thf(zip_derived_cl13972, plain,
% 27.02/4.47 (~ (c_lessequals @ c_0 @
% 27.02/4.47 (c_minus @ c_0 @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('s_sup+', [status(thm)],
% 27.02/4.47 [zip_derived_cl13946, zip_derived_cl773])).
% 27.02/4.47 thf(zip_derived_cl80, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl13992, plain,
% 27.02/4.47 (~ (c_lessequals @ c_0 @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl13972, zip_derived_cl80])).
% 27.02/4.47 thf(zip_derived_cl80, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl80, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl11, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_plus @ X1 @ (c_minus @ X2 @ X3 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__2_0])).
% 27.02/4.47 thf(zip_derived_cl275, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ (c_plus @ X2 @ c_0 @ t_b) @
% 27.02/4.47 (c_minus @ X0 @ X1 @ t_b) @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl11])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl165, plain,
% 27.02/4.47 (![X0 : $i]: ((X0) = (c_plus @ X0 @ c_0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl139])).
% 27.02/4.47 thf(zip_derived_cl293, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ((c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X2 @ (c_minus @ X0 @ X1 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl275, zip_derived_cl31, zip_derived_cl165])).
% 27.02/4.47 thf(zip_derived_cl227, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl221, zip_derived_cl31, zip_derived_cl52])).
% 27.02/4.47 thf(zip_derived_cl11, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_plus @ X1 @ (c_minus @ X2 @ X3 @ X0) @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__2_0])).
% 27.02/4.47 thf(zip_derived_cl422, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_plus @ X2 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ (c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b) @
% 27.02/4.47 X1 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl227, zip_derived_cl11])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl445, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ((c_plus @ X2 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ (c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b) @ X1 @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl52, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl3, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X1 @ X2 @ X0)
% 27.02/4.47 = (c_plus @ X1 @ (c_uminus @ X2 @ X0) @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0])).
% 27.02/4.47 thf(zip_derived_cl65, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_minus @ X1 @ X0 @ t_b)
% 27.02/4.47 = (c_plus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl3])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl68, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ X1 @ X0 @ t_b)
% 27.02/4.47 = (c_plus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl293, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ((c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X2 @ (c_minus @ X0 @ X1 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl275, zip_derived_cl31, zip_derived_cl165])).
% 27.02/4.47 thf(zip_derived_cl68, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ X1 @ X0 @ t_b)
% 27.02/4.47 = (c_plus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl12, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_plus @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__3_0])).
% 27.02/4.47 thf(zip_derived_cl1722, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_minus @ (c_minus @ X2 @ X1 @ t_b) @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ (c_plus @ X2 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) @
% 27.02/4.47 X1 @ t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl68, zip_derived_cl12])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl68, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ X1 @ X0 @ t_b)
% 27.02/4.47 = (c_plus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl1754, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ((c_minus @ (c_minus @ X2 @ X1 @ t_b) @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ (c_minus @ X2 @ X0 @ t_b) @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl1722, zip_derived_cl31, zip_derived_cl68])).
% 27.02/4.47 thf(zip_derived_cl12, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_plus @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__3_0])).
% 27.02/4.47 thf(zip_derived_cl3, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ X1 @ X2 @ X0)
% 27.02/4.47 = (c_plus @ X1 @ (c_uminus @ X2 @ X0) @ X0)))),
% 27.02/4.47 inference('cnf', [status(esa)],
% 27.02/4.47 [cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0])).
% 27.02/4.47 thf(zip_derived_cl190, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ~ (class_OrderedGroup_Oab__group__add @ X0)
% 27.02/4.47 | ((c_minus @ (c_minus @ X3 @ X1 @ X0) @ X2 @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X3 @ (c_uminus @ X2 @ X0) @ X0) @ X1 @ X0)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl3])).
% 27.02/4.47 thf(zip_derived_cl206, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (((c_minus @ (c_minus @ X3 @ X1 @ X0) @ X2 @ X0)
% 27.02/4.47 = (c_minus @ (c_plus @ X3 @ (c_uminus @ X2 @ X0) @ X0) @ X1 @ X0))
% 27.02/4.47 | ~ (class_OrderedGroup_Oab__group__add @ X0))),
% 27.02/4.47 inference('simplify', [status(thm)], [zip_derived_cl190])).
% 27.02/4.47 thf(zip_derived_cl80, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl8087, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Oab__group__add @ t_b)
% 27.02/4.47 | ((c_minus @ c_0 @
% 27.02/4.47 (c_minus @ (c_minus @ X2 @ X1 @ t_b) @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X1 @ (c_plus @ X2 @ (c_uminus @ X0 @ t_b) @ t_b) @
% 27.02/4.47 t_b)))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl206, zip_derived_cl80])).
% 27.02/4.47 thf(zip_derived_cl31, plain, ( (class_OrderedGroup_Oab__group__add @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 27.02/4.47 thf(zip_derived_cl80, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X0 @ X1 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl52, plain,
% 27.02/4.47 (![X0 : $i]: ((c_minus @ c_0 @ X0 @ t_b) = (c_uminus @ X0 @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl68, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i]:
% 27.02/4.47 ((c_minus @ X1 @ X0 @ t_b)
% 27.02/4.47 = (c_plus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl31])).
% 27.02/4.47 thf(zip_derived_cl8210, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ((c_minus @ X0 @ (c_minus @ X2 @ X1 @ t_b) @ t_b)
% 27.02/4.47 = (c_minus @ X1 @ (c_minus @ X2 @ X0 @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl8087, zip_derived_cl31, zip_derived_cl80,
% 27.02/4.47 zip_derived_cl52, zip_derived_cl68])).
% 27.02/4.47 thf(zip_derived_cl23492, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.02/4.47 ((c_minus @ X2 @ X0 @ t_b)
% 27.02/4.47 = (c_minus @ X1 @
% 27.02/4.47 (c_minus @ X0 @ (c_minus @ X2 @ X1 @ t_b) @ t_b) @ t_b))),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl445, zip_derived_cl68, zip_derived_cl293,
% 27.02/4.47 zip_derived_cl1754, zip_derived_cl8210])).
% 27.02/4.47 thf(zip_derived_cl28550, plain,
% 27.02/4.47 (~ (c_lessequals @ (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @ c_0 @
% 27.02/4.47 t_b)),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl28491, zip_derived_cl13992, zip_derived_cl80,
% 27.02/4.47 zip_derived_cl293, zip_derived_cl23492])).
% 27.02/4.47 thf(zip_derived_cl15, plain,
% 27.02/4.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.02/4.47 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 27.02/4.47 | ~ (c_lessequals @ X1 @ (c_plus @ X2 @ X3 @ X0) @ X0)
% 27.02/4.47 | (c_lessequals @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0))),
% 27.02/4.47 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__8_1])).
% 27.02/4.47 thf(zip_derived_cl28603, plain,
% 27.02/4.47 ((~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 27.02/4.47 | ~ (c_lessequals @ (v_g @ v_x) @ (c_plus @ c_0 @ (v_k @ v_x) @ t_b) @
% 27.02/4.47 t_b))),
% 27.02/4.47 inference('s_sup+', [status(thm)],
% 27.02/4.47 [zip_derived_cl28550, zip_derived_cl15])).
% 27.02/4.47 thf(zip_derived_cl45, plain,
% 27.02/4.47 (![X0 : $i]: ((c_plus @ c_0 @ X0 @ t_b) = (X0))),
% 27.02/4.47 inference('s_sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl2])).
% 27.02/4.47 thf(zip_derived_cl0, plain,
% 27.02/4.47 (![X0 : $i]: (c_lessequals @ (v_g @ X0) @ (v_k @ X0) @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_2])).
% 27.02/4.47 thf(zip_derived_cl28631, plain,
% 27.02/4.47 (~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)),
% 27.02/4.47 inference('demod', [status(thm)],
% 27.02/4.47 [zip_derived_cl28603, zip_derived_cl45, zip_derived_cl0])).
% 27.02/4.47 thf(zip_derived_cl28636, plain,
% 27.02/4.47 (~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)],
% 27.02/4.47 [zip_derived_cl24, zip_derived_cl28631])).
% 27.02/4.47 thf(zip_derived_cl28699, plain,
% 27.02/4.47 (~ (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('s_sup-', [status(thm)],
% 27.02/4.47 [zip_derived_cl30, zip_derived_cl28636])).
% 27.02/4.47 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 27.02/4.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.02/4.47 thf(zip_derived_cl28700, plain, ($false),
% 27.02/4.47 inference('demod', [status(thm)], [zip_derived_cl28699, zip_derived_cl2])).
% 27.02/4.47
% 27.02/4.47 % SZS output end Refutation
% 27.02/4.47
% 27.02/4.47
% 27.02/4.47 % Terminating...
% 27.33/4.56 % Runner terminated.
% 27.35/4.57 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------