TSTP Solution File: ANA022-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ANA022-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.JCIOlq1n9l true
% Computer : n026.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 : Wed Aug 30 17:25:58 EDT 2023
% Result : Unsatisfiable 16.22s 2.90s
% Output : Refutation 16.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA022-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.JCIOlq1n9l true
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 18:58:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.19/0.59 % Total configuration time : 435
% 0.19/0.59 % Estimated wc time : 1092
% 0.19/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.71 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.19/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.19/0.72 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.19/0.72 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.19/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.72 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 16.22/2.90 % Solved by fo/fo6_bce.sh.
% 16.22/2.90 % BCE start: 27
% 16.22/2.90 % BCE eliminated: 0
% 16.22/2.90 % PE start: 27
% 16.22/2.90 logic: eq
% 16.22/2.90 % PE eliminated: 9
% 16.22/2.90 % done 845 iterations in 2.148s
% 16.22/2.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 16.22/2.90 % SZS output start Refutation
% 16.22/2.90 thf(class_OrderedGroup_Opordered__ab__group__add_type, type, class_OrderedGroup_Opordered__ab__group__add:
% 16.22/2.90 $i > $o).
% 16.22/2.90 thf(v_g_type, type, v_g: $i > $i).
% 16.22/2.90 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 16.22/2.90 thf(c_less_type, type, c_less: $i > $i > $i > $o).
% 16.22/2.90 thf(class_Orderings_Oorder_type, type, class_Orderings_Oorder: $i > $o).
% 16.22/2.90 thf(class_OrderedGroup_Olordered__ab__group__abs_type, type, class_OrderedGroup_Olordered__ab__group__abs:
% 16.22/2.90 $i > $o).
% 16.22/2.90 thf(c_minus_type, type, c_minus: $i > $i > $i > $i).
% 16.22/2.90 thf(c_Orderings_Omax_type, type, c_Orderings_Omax: $i > $i > $i > $i).
% 16.22/2.90 thf(v_k_type, type, v_k: $i > $i).
% 16.22/2.90 thf(class_Orderings_Olinorder_type, type, class_Orderings_Olinorder: $i > $o).
% 16.22/2.90 thf(c_uminus_type, type, c_uminus: $i > $i > $i).
% 16.22/2.90 thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type, type,
% 16.22/2.90 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o).
% 16.22/2.90 thf(class_LOrder_Ojoin__semilorder_type, type, class_LOrder_Ojoin__semilorder:
% 16.22/2.90 $i > $o).
% 16.22/2.90 thf(class_OrderedGroup_Oab__group__add_type, type, class_OrderedGroup_Oab__group__add:
% 16.22/2.90 $i > $o).
% 16.22/2.90 thf(c_plus_type, type, c_plus: $i > $i > $i > $i).
% 16.22/2.90 thf(v_x_type, type, v_x: $i).
% 16.22/2.90 thf(class_Ring__and__Field_Oordered__idom_type, type, class_Ring__and__Field_Oordered__idom:
% 16.22/2.90 $i > $o).
% 16.22/2.90 thf(class_OrderedGroup_Ocomm__monoid__add_type, type, class_OrderedGroup_Ocomm__monoid__add:
% 16.22/2.90 $i > $o).
% 16.22/2.90 thf(v_f_type, type, v_f: $i > $i).
% 16.22/2.90 thf(c_HOL_Oabs_type, type, c_HOL_Oabs: $i > $i > $i).
% 16.22/2.90 thf(t_b_type, type, t_b: $i).
% 16.22/2.90 thf(c_0_type, type, c_0: $i).
% 16.22/2.90 thf(clsrel_Ring__and__Field_Oordered__idom_4, axiom,
% 16.22/2.90 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 16.22/2.90 ( class_OrderedGroup_Oab__group__add @ T ))).
% 16.22/2.90 thf(zip_derived_cl25, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Oab__group__add @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 16.22/2.90 thf(cls_OrderedGroup_Odiff__self_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 16.22/2.90 ( ( c_minus @ V_a @ V_a @ T_a ) = ( c_0 ) ))).
% 16.22/2.90 thf(zip_derived_cl13, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 16.22/2.90 | ((c_minus @ X1 @ X1 @ X0) = (c_0)))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_OrderedGroup_Odiff__self_0])).
% 16.22/2.90 thf(zip_derived_cl146, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_minus @ X1 @ X1 @ X0) = (c_0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl13])).
% 16.22/2.90 thf(tfree_tcs, conjecture,
% 16.22/2.90 (~( class_Ring__and__Field_Oordered__idom @ t_b ))).
% 16.22/2.90 thf(zf_stmt_0, negated_conjecture,
% 16.22/2.90 (class_Ring__and__Field_Oordered__idom @ t_b),
% 16.22/2.90 inference('cnf.neg', [status(esa)], [tfree_tcs])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl154, plain,
% 16.22/2.90 (![X0 : $i]: ((c_minus @ X0 @ X0 @ t_b) = (c_0))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl146, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl25, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Oab__group__add @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 16.22/2.90 thf(cls_OrderedGroup_Ominus__diff__eq_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 16.22/2.90 ( ( c_uminus @ ( c_minus @ V_a @ V_b @ T_a ) @ T_a ) =
% 16.22/2.90 ( c_minus @ V_b @ V_a @ T_a ) ))).
% 16.22/2.90 thf(zip_derived_cl14, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 16.22/2.90 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_minus @ X1 @ X2 @ X0)))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_OrderedGroup_Ominus__diff__eq_0])).
% 16.22/2.90 thf(zip_derived_cl147, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_minus @ X1 @ X2 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl14])).
% 16.22/2.90 thf(zip_derived_cl240, plain,
% 16.22/2.90 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_uminus @ c_0 @ t_b) = (c_0)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl147])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl243, plain, (((c_uminus @ c_0 @ t_b) = (c_0))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl240, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl25, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Oab__group__add @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 16.22/2.90 thf(cls_OrderedGroup_Odiff__minus__eq__add_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 16.22/2.90 ( ( c_minus @ V_a @ ( c_uminus @ V_b @ T_a ) @ T_a ) =
% 16.22/2.90 ( c_plus @ V_a @ V_b @ T_a ) ))).
% 16.22/2.90 thf(zip_derived_cl12, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 16.22/2.90 | ((c_minus @ X1 @ (c_uminus @ X2 @ X0) @ X0)
% 16.22/2.90 = (c_plus @ X1 @ X2 @ X0)))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [cls_OrderedGroup_Odiff__minus__eq__add_0])).
% 16.22/2.90 thf(zip_derived_cl145, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_minus @ X2 @ (c_uminus @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_plus @ X2 @ X1 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl12])).
% 16.22/2.90 thf(zip_derived_cl246, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_minus @ X0 @ c_0 @ t_b) = (c_plus @ X0 @ c_0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl243, zip_derived_cl145])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl247, plain,
% 16.22/2.90 (![X0 : $i]: ((c_minus @ X0 @ c_0 @ t_b) = (c_plus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl246, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl25, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Oab__group__add @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 16.22/2.90 thf(cls_OrderedGroup_Ocompare__rls__3_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 16.22/2.90 ( ( c_plus @ ( c_minus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) =
% 16.22/2.90 ( c_minus @ ( c_plus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ))).
% 16.22/2.90 thf(zip_derived_cl9, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 16.22/2.90 | ((c_plus @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0)
% 16.22/2.90 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__3_0])).
% 16.22/2.90 thf(zip_derived_cl144, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_plus @ (c_minus @ X3 @ X2 @ X0) @ X1 @ X0)
% 16.22/2.90 = (c_minus @ (c_plus @ X3 @ X1 @ X0) @ X2 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl9])).
% 16.22/2.90 thf(zip_derived_cl250, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X1 @ c_0 @ t_b) @ X0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl144])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl247, plain,
% 16.22/2.90 (![X0 : $i]: ((c_minus @ X0 @ c_0 @ t_b) = (c_plus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl246, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl252, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b)
% 16.22/2.90 = (c_minus @ (c_minus @ X1 @ c_0 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl250, zip_derived_cl2, zip_derived_cl247])).
% 16.22/2.90 thf(zip_derived_cl144, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_plus @ (c_minus @ X3 @ X2 @ X0) @ X1 @ X0)
% 16.22/2.90 = (c_minus @ (c_plus @ X3 @ X1 @ X0) @ X2 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl9])).
% 16.22/2.90 thf(zip_derived_cl341, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_plus @ (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b) @
% 16.22/2.90 X2 @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ (c_minus @ X1 @ c_0 @ t_b) @ X2 @ t_b) @
% 16.22/2.90 X0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl144])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl362, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ((c_plus @ (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b) @ X2 @
% 16.22/2.90 t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ (c_minus @ X1 @ c_0 @ t_b) @ X2 @ t_b) @
% 16.22/2.90 X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl341, zip_derived_cl2])).
% 16.22/2.90 thf(clsrel_Ring__and__Field_Oordered__idom_23, axiom,
% 16.22/2.90 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 16.22/2.90 ( class_OrderedGroup_Ocomm__monoid__add @ T ))).
% 16.22/2.90 thf(zip_derived_cl22, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Ocomm__monoid__add @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_23])).
% 16.22/2.90 thf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Ocomm__monoid__add @ T_a ) ) |
% 16.22/2.90 ( ( c_plus @ c_0 @ V_y @ T_a ) = ( V_y ) ))).
% 16.22/2.90 thf(zip_derived_cl7, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Ocomm__monoid__add @ X0)
% 16.22/2.90 | ((c_plus @ c_0 @ X1 @ X0) = (X1)))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0])).
% 16.22/2.90 thf(zip_derived_cl134, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_plus @ c_0 @ X1 @ X0) = (X1)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl22, zip_derived_cl7])).
% 16.22/2.90 thf(zip_derived_cl154, plain,
% 16.22/2.90 (![X0 : $i]: ((c_minus @ X0 @ X0 @ t_b) = (c_0))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl146, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl144, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_plus @ (c_minus @ X3 @ X2 @ X0) @ X1 @ X0)
% 16.22/2.90 = (c_minus @ (c_plus @ X3 @ X1 @ X0) @ X2 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl9])).
% 16.22/2.90 thf(zip_derived_cl213, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_plus @ c_0 @ X1 @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X0 @ X1 @ t_b) @ X0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl144])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl215, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_plus @ c_0 @ X1 @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X0 @ X1 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl213, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl578, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((X0) = (c_minus @ X0 @ c_0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl215])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl952, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ((c_plus @ (c_minus @ X1 @ X0 @ t_b) @ X2 @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X1 @ X2 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl362, zip_derived_cl582, zip_derived_cl582])).
% 16.22/2.90 thf(clsrel_Ring__and__Field_Oordered__idom_50, axiom,
% 16.22/2.90 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 16.22/2.90 ( class_OrderedGroup_Olordered__ab__group__abs @ T ))).
% 16.22/2.90 thf(zip_derived_cl26, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 16.22/2.90 thf(clsrel_OrderedGroup_Olordered__ab__group__abs_1, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) |
% 16.22/2.90 ( class_OrderedGroup_Opordered__ab__group__add @ T ))).
% 16.22/2.90 thf(zip_derived_cl20, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_OrderedGroup_Olordered__ab__group__abs_1])).
% 16.22/2.90 thf(cls_OrderedGroup_Ocompare__rls__8_1, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Opordered__ab__group__add @ T_a ) ) |
% 16.22/2.90 ( ~( c_lessequals @ V_a @ ( c_plus @ V_c @ V_b @ T_a ) @ T_a ) ) |
% 16.22/2.90 ( c_lessequals @ ( c_minus @ V_a @ V_b @ T_a ) @ V_c @ T_a ))).
% 16.22/2.90 thf(zip_derived_cl10, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X1 @ (c_plus @ X2 @ X3 @ X0) @ X0)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__8_1])).
% 16.22/2.90 thf(zip_derived_cl137, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X3 @ X1 @ X0) @ X2 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X3 @ (c_plus @ X2 @ X1 @ X0) @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl20, zip_derived_cl10])).
% 16.22/2.90 thf(zip_derived_cl152, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X3 @ (c_plus @ X1 @ X2 @ X0) @ X0)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X3 @ X2 @ X0) @ X1 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl26, zip_derived_cl137])).
% 16.22/2.90 thf(zip_derived_cl953, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ X3 @
% 16.22/2.90 (c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b) @ t_b)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X3 @ X1 @ t_b) @
% 16.22/2.90 (c_minus @ X2 @ X0 @ t_b) @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl952, zip_derived_cl152])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl974, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (c_lessequals @ X3 @
% 16.22/2.90 (c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b) @ t_b)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X3 @ X1 @ t_b) @
% 16.22/2.90 (c_minus @ X2 @ X0 @ t_b) @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl953, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl252, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b)
% 16.22/2.90 = (c_minus @ (c_minus @ X1 @ c_0 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl250, zip_derived_cl2, zip_derived_cl247])).
% 16.22/2.90 thf(zip_derived_cl147, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_minus @ X1 @ X2 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl14])).
% 16.22/2.90 thf(zip_derived_cl340, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_uminus @ (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b) @
% 16.22/2.90 t_b) = (c_minus @ X0 @ (c_minus @ X1 @ c_0 @ t_b) @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl147])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl361, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_uminus @ (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ X0 @ (c_minus @ X1 @ c_0 @ t_b) @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl340, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl147, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_minus @ X1 @ X2 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl14])).
% 16.22/2.90 thf(zip_derived_cl613, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_uminus @ X0 @ t_b) = (c_minus @ c_0 @ X0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl582, zip_derived_cl147])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl617, plain,
% 16.22/2.90 (![X0 : $i]: ((c_uminus @ X0 @ t_b) = (c_minus @ c_0 @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl613, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl905, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ X0 @ X1 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl361, zip_derived_cl582, zip_derived_cl617,
% 16.22/2.90 zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl25, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Oab__group__add @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 16.22/2.90 thf(cls_OrderedGroup_Ocompare__rls__2_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 16.22/2.90 ( ( c_plus @ V_a @ ( c_minus @ V_b @ V_c @ T_a ) @ T_a ) =
% 16.22/2.90 ( c_minus @ ( c_plus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ))).
% 16.22/2.90 thf(zip_derived_cl8, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 16.22/2.90 | ((c_plus @ X1 @ (c_minus @ X2 @ X3 @ X0) @ X0)
% 16.22/2.90 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__2_0])).
% 16.22/2.90 thf(zip_derived_cl143, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_plus @ X3 @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_minus @ (c_plus @ X3 @ X2 @ X0) @ X1 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl8])).
% 16.22/2.90 thf(zip_derived_cl912, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X2 @ c_0 @ t_b) @
% 16.22/2.90 (c_minus @ X0 @ X1 @ t_b) @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl905, zip_derived_cl143])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl252, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b)
% 16.22/2.90 = (c_minus @ (c_minus @ X1 @ c_0 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl250, zip_derived_cl2, zip_derived_cl247])).
% 16.22/2.90 thf(zip_derived_cl143, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_plus @ X3 @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_minus @ (c_plus @ X3 @ X2 @ X0) @ X1 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl8])).
% 16.22/2.90 thf(zip_derived_cl339, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_plus @ X2 @
% 16.22/2.90 (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X2 @ (c_minus @ X1 @ c_0 @ t_b) @ t_b) @
% 16.22/2.90 X0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl143])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl360, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ((c_plus @ X2 @ (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b) @
% 16.22/2.90 t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X2 @ (c_minus @ X1 @ c_0 @ t_b) @ t_b) @
% 16.22/2.90 X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl339, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl868, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ((c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl360, zip_derived_cl582, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl247, plain,
% 16.22/2.90 (![X0 : $i]: ((c_minus @ X0 @ c_0 @ t_b) = (c_plus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl246, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl607, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_plus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl247, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl931, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ((c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b)
% 16.22/2.90 = (c_minus @ X2 @ (c_minus @ X0 @ X1 @ t_b) @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl912, zip_derived_cl2, zip_derived_cl868,
% 16.22/2.90 zip_derived_cl607])).
% 16.22/2.90 thf(zip_derived_cl8850, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (c_lessequals @ X3 @
% 16.22/2.90 (c_minus @ X2 @ (c_minus @ X0 @ X1 @ t_b) @ t_b) @ t_b)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X3 @ X1 @ t_b) @
% 16.22/2.90 (c_minus @ X2 @ X0 @ t_b) @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl974, zip_derived_cl931])).
% 16.22/2.90 thf(zip_derived_cl252, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b)
% 16.22/2.90 = (c_minus @ (c_minus @ X1 @ c_0 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl250, zip_derived_cl2, zip_derived_cl247])).
% 16.22/2.90 thf(zip_derived_cl26, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 16.22/2.90 thf(zip_derived_cl20, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_OrderedGroup_Olordered__ab__group__abs_1])).
% 16.22/2.90 thf(cls_OrderedGroup_Odiff__le__0__iff__le_1, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Opordered__ab__group__add @ T_a ) ) |
% 16.22/2.90 ( ~( c_lessequals @ V_a @ V_b @ T_a ) ) |
% 16.22/2.90 ( c_lessequals @ ( c_minus @ V_a @ V_b @ T_a ) @ c_0 @ T_a ))).
% 16.22/2.90 thf(zip_derived_cl11, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X1 @ X2 @ X0)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X1 @ X2 @ X0) @ c_0 @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [cls_OrderedGroup_Odiff__le__0__iff__le_1])).
% 16.22/2.90 thf(zip_derived_cl138, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X2 @ X1 @ X0) @ c_0 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X2 @ X1 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl20, zip_derived_cl11])).
% 16.22/2.90 thf(zip_derived_cl153, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X2 @ X1 @ X0)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X2 @ X1 @ X0) @ c_0 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl26, zip_derived_cl138])).
% 16.22/2.90 thf(zip_derived_cl386, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ X1 @ c_0 @ t_b) @ X0 @ t_b)
% 16.22/2.90 | (c_lessequals @
% 16.22/2.90 (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b) @ c_0 @ t_b))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl153])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl392, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (c_lessequals @ (c_minus @ X1 @ c_0 @ t_b) @ X0 @ t_b)
% 16.22/2.90 | (c_lessequals @
% 16.22/2.90 (c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b) @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl386, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl1131, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (c_lessequals @ X1 @ X0 @ t_b)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl392, zip_derived_cl582, zip_derived_cl582])).
% 16.22/2.90 thf(cls_conjecture_1, conjecture,
% 16.22/2.90 (~( c_lessequals @ ( v_k @ V_U ) @ ( v_f @ V_U ) @ t_b ))).
% 16.22/2.90 thf(zf_stmt_1, negated_conjecture,
% 16.22/2.90 (c_lessequals @ ( v_k @ V_U ) @ ( v_f @ V_U ) @ t_b),
% 16.22/2.90 inference('cnf.neg', [status(esa)], [cls_conjecture_1])).
% 16.22/2.90 thf(zip_derived_cl0, plain,
% 16.22/2.90 (![X0 : $i]: (c_lessequals @ (v_k @ X0) @ (v_f @ X0) @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 16.22/2.90 thf(zip_derived_cl154, plain,
% 16.22/2.90 (![X0 : $i]: ((c_minus @ X0 @ X0 @ t_b) = (c_0))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl146, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl252, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_minus @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b)
% 16.22/2.90 = (c_minus @ (c_minus @ X1 @ c_0 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl250, zip_derived_cl2, zip_derived_cl247])).
% 16.22/2.90 thf(zip_derived_cl354, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 ((c_minus @ (c_minus @ c_0 @ X0 @ t_b) @ c_0 @ t_b)
% 16.22/2.90 = (c_minus @ c_0 @ X0 @ t_b))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl252])).
% 16.22/2.90 thf(zip_derived_cl147, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_uminus @ (c_minus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_minus @ X1 @ X2 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl14])).
% 16.22/2.90 thf(zip_derived_cl367, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ c_0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl354, zip_derived_cl147])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl377, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ c_0 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl367, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl905, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ X0 @ X1 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl361, zip_derived_cl582, zip_derived_cl617,
% 16.22/2.90 zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl1087, plain,
% 16.22/2.90 (![X0 : $i]: ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl377, zip_derived_cl905, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl146, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_minus @ X1 @ X1 @ X0) = (c_0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl13])).
% 16.22/2.90 thf(zip_derived_cl145, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_minus @ X2 @ (c_uminus @ X1 @ X0) @ X0)
% 16.22/2.90 = (c_plus @ X2 @ X1 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl25, zip_derived_cl12])).
% 16.22/2.90 thf(zip_derived_cl226, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_0) = (c_plus @ (c_uminus @ X1 @ X0) @ X1 @ X0)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl146, zip_derived_cl145])).
% 16.22/2.90 thf(zip_derived_cl228, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (((c_0) = (c_plus @ (c_uminus @ X1 @ X0) @ X1 @ X0))
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 16.22/2.90 inference('simplify', [status(thm)], [zip_derived_cl226])).
% 16.22/2.90 thf(zip_derived_cl26, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 16.22/2.90 thf(clsrel_OrderedGroup_Olordered__ab__group__abs_6, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) |
% 16.22/2.90 ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ))).
% 16.22/2.90 thf(zip_derived_cl21, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_OrderedGroup_Olordered__ab__group__abs_6])).
% 16.22/2.90 thf(cls_OrderedGroup_Oadd__le__cancel__right_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a ) ) |
% 16.22/2.90 ( ~( c_lessequals @
% 16.22/2.90 ( c_plus @ V_a @ V_c @ T_a ) @ ( c_plus @ V_b @ V_c @ T_a ) @ T_a ) ) |
% 16.22/2.90 ( c_lessequals @ V_a @ V_b @ T_a ))).
% 16.22/2.90 thf(zip_derived_cl6, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_plus @ X1 @ X2 @ X0) @
% 16.22/2.90 (c_plus @ X3 @ X2 @ X0) @ X0)
% 16.22/2.90 | (c_lessequals @ X1 @ X3 @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [cls_OrderedGroup_Oadd__le__cancel__right_0])).
% 16.22/2.90 thf(zip_derived_cl135, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | (c_lessequals @ X3 @ X2 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_plus @ X3 @ X1 @ X0) @
% 16.22/2.90 (c_plus @ X2 @ X1 @ X0) @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl21, zip_derived_cl6])).
% 16.22/2.90 thf(zip_derived_cl151, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_plus @ X2 @ X3 @ X0) @
% 16.22/2.90 (c_plus @ X1 @ X3 @ X0) @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ X1 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl26, zip_derived_cl135])).
% 16.22/2.90 thf(zip_derived_cl1235, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_plus @ X2 @ X1 @ X0) @ c_0 @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ (c_uminus @ X1 @ X0) @ X0))),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl228, zip_derived_cl151])).
% 16.22/2.90 thf(zip_derived_cl1262, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ( (c_lessequals @ X2 @ (c_uminus @ X1 @ X0) @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_plus @ X2 @ X1 @ X0) @ c_0 @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 16.22/2.90 inference('simplify', [status(thm)], [zip_derived_cl1235])).
% 16.22/2.90 thf(clsrel_Ring__and__Field_Oordered__idom_35, axiom,
% 16.22/2.90 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 16.22/2.90 ( class_LOrder_Ojoin__semilorder @ T ))).
% 16.22/2.90 thf(zip_derived_cl24, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_LOrder_Ojoin__semilorder @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_35])).
% 16.22/2.90 thf(clsrel_LOrder_Ojoin__semilorder_1, axiom,
% 16.22/2.90 (( ~( class_LOrder_Ojoin__semilorder @ T ) ) |
% 16.22/2.90 ( class_Orderings_Oorder @ T ))).
% 16.22/2.90 thf(zip_derived_cl19, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_LOrder_Ojoin__semilorder @ X0)
% 16.22/2.90 | (class_Orderings_Oorder @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)], [clsrel_LOrder_Ojoin__semilorder_1])).
% 16.22/2.90 thf(zip_derived_cl133, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_Orderings_Oorder @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl24, zip_derived_cl19])).
% 16.22/2.90 thf(cls_Orderings_Oorder__class_Oorder__trans_0, axiom,
% 16.22/2.90 (( ~( class_Orderings_Oorder @ T_a ) ) |
% 16.22/2.90 ( ~( c_lessequals @ V_y @ V_z @ T_a ) ) |
% 16.22/2.90 ( ~( c_lessequals @ V_x @ V_y @ T_a ) ) |
% 16.22/2.90 ( c_lessequals @ V_x @ V_z @ T_a ))).
% 16.22/2.90 thf(zip_derived_cl17, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Orderings_Oorder @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X1 @ X2 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X3 @ X1 @ X0)
% 16.22/2.90 | (c_lessequals @ X3 @ X2 @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [cls_Orderings_Oorder__class_Oorder__trans_0])).
% 16.22/2.90 thf(zip_derived_cl141, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (c_lessequals @ X3 @ X1 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X3 @ X2 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X2 @ X1 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl133, zip_derived_cl17])).
% 16.22/2.90 thf(zip_derived_cl1444, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_plus @ X2 @ X1 @ X0) @ c_0 @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ X3 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_uminus @ X1 @ X0) @ X3 @ X0))),
% 16.22/2.90 inference('s_sup-', [status(thm)],
% 16.22/2.90 [zip_derived_cl1262, zip_derived_cl141])).
% 16.22/2.90 thf(zip_derived_cl1469, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (c_lessequals @ (c_uminus @ X1 @ X0) @ X3 @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ X3 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_plus @ X2 @ X1 @ X0) @ c_0 @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 16.22/2.90 inference('simplify', [status(thm)], [zip_derived_cl1444])).
% 16.22/2.90 thf(zip_derived_cl1571, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (c_lessequals @ X0 @ X1 @ t_b)
% 16.22/2.90 | (c_lessequals @ X2 @ X1 @ t_b)
% 16.22/2.90 | ~ (c_lessequals @
% 16.22/2.90 (c_plus @ X2 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) @ c_0 @ t_b)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)],
% 16.22/2.90 [zip_derived_cl1087, zip_derived_cl1469])).
% 16.22/2.90 thf(zip_derived_cl868, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ((c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl360, zip_derived_cl582, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl607, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_plus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl247, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl1590, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (c_lessequals @ X0 @ X1 @ t_b)
% 16.22/2.90 | (c_lessequals @ X2 @ X1 @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ X2 @ X0 @ t_b) @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl1571, zip_derived_cl868, zip_derived_cl607,
% 16.22/2.90 zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl2723, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ( (c_lessequals @ X1 @ (v_f @ X0) @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ X1 @ (v_k @ X0) @ t_b) @ c_0 @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl1590])).
% 16.22/2.90 thf(zip_derived_cl3052, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (c_lessequals @ X1 @ (v_k @ X0) @ t_b)
% 16.22/2.90 | (c_lessequals @ X1 @ (v_f @ X0) @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)],
% 16.22/2.90 [zip_derived_cl1131, zip_derived_cl2723])).
% 16.22/2.90 thf(zip_derived_cl1131, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (c_lessequals @ X1 @ X0 @ t_b)
% 16.22/2.90 | (c_lessequals @ (c_minus @ X1 @ X0 @ t_b) @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl392, zip_derived_cl582, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl1087, plain,
% 16.22/2.90 (![X0 : $i]: ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl377, zip_derived_cl905, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl26, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 16.22/2.90 thf(cls_OrderedGroup_Oabs__of__nonpos_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T_a ) ) |
% 16.22/2.90 ( ~( c_lessequals @ V_a @ c_0 @ T_a ) ) |
% 16.22/2.90 ( ( c_HOL_Oabs @ V_a @ T_a ) = ( c_uminus @ V_a @ T_a ) ))).
% 16.22/2.90 thf(zip_derived_cl5, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X1 @ c_0 @ X0)
% 16.22/2.90 | ((c_HOL_Oabs @ X1 @ X0) = (c_uminus @ X1 @ X0)))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__of__nonpos_0])).
% 16.22/2.90 thf(zip_derived_cl150, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_HOL_Oabs @ X1 @ X0) = (c_uminus @ X1 @ X0))
% 16.22/2.90 | ~ (c_lessequals @ X1 @ c_0 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl26, zip_derived_cl5])).
% 16.22/2.90 thf(zip_derived_cl1090, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_HOL_Oabs @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ c_0 @ X0 @ t_b) @ c_0 @ t_b))),
% 16.22/2.90 inference('s_sup+', [status(thm)],
% 16.22/2.90 [zip_derived_cl1087, zip_derived_cl150])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl1102, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (((c_HOL_Oabs @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ c_0 @ X0 @ t_b) @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl1090, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl617, plain,
% 16.22/2.90 (![X0 : $i]: ((c_uminus @ X0 @ t_b) = (c_minus @ c_0 @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl613, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl26, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 16.22/2.90 thf(cls_OrderedGroup_Oabs__minus__cancel_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T_a ) ) |
% 16.22/2.90 ( ( c_HOL_Oabs @ ( c_uminus @ V_a @ T_a ) @ T_a ) =
% 16.22/2.90 ( c_HOL_Oabs @ V_a @ T_a ) ))).
% 16.22/2.90 thf(zip_derived_cl4, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | ((c_HOL_Oabs @ (c_uminus @ X1 @ X0) @ X0) = (c_HOL_Oabs @ X1 @ X0)))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__minus__cancel_0])).
% 16.22/2.90 thf(zip_derived_cl149, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ((c_HOL_Oabs @ (c_uminus @ X1 @ X0) @ X0) = (c_HOL_Oabs @ X1 @ X0)))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl26, zip_derived_cl4])).
% 16.22/2.90 thf(zip_derived_cl748, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ((c_HOL_Oabs @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_HOL_Oabs @ X0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl617, zip_derived_cl149])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl754, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 ((c_HOL_Oabs @ (c_minus @ c_0 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_HOL_Oabs @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl748, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl2051, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (c_lessequals @ (c_minus @ c_0 @ X0 @ t_b) @ c_0 @ t_b)
% 16.22/2.90 | ((X0) = (c_HOL_Oabs @ X0 @ t_b)))),
% 16.22/2.90 inference('s_sup+', [status(thm)],
% 16.22/2.90 [zip_derived_cl1102, zip_derived_cl754])).
% 16.22/2.90 thf(zip_derived_cl26, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 16.22/2.90 thf(cls_OrderedGroup_Oabs__ge__zero_0, axiom,
% 16.22/2.90 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T_a ) ) |
% 16.22/2.90 ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ))).
% 16.22/2.90 thf(zip_derived_cl3, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 16.22/2.90 | (c_lessequals @ c_0 @ (c_HOL_Oabs @ X1 @ X0) @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__ge__zero_0])).
% 16.22/2.90 thf(zip_derived_cl148, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (c_lessequals @ c_0 @ (c_HOL_Oabs @ X1 @ X0) @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl26, zip_derived_cl3])).
% 16.22/2.90 thf(clsrel_Ring__and__Field_Oordered__idom_33, axiom,
% 16.22/2.90 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 16.22/2.90 ( class_Orderings_Olinorder @ T ))).
% 16.22/2.90 thf(zip_derived_cl23, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_Orderings_Olinorder @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_33])).
% 16.22/2.90 thf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, axiom,
% 16.22/2.90 (( ~( class_Orderings_Olinorder @ T_b ) ) |
% 16.22/2.90 ( ~( c_lessequals @ V_y @ V_z @ T_b ) ) |
% 16.22/2.90 ( ~( c_lessequals @ V_x @ V_z @ T_b ) ) |
% 16.22/2.90 ( c_lessequals @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ V_z @ T_b ))).
% 16.22/2.90 thf(zip_derived_cl16, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Orderings_Olinorder @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X1 @ X2 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X3 @ X2 @ X0)
% 16.22/2.90 | (c_lessequals @ (c_Orderings_Omax @ X3 @ X1 @ X0) @ X2 @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2])).
% 16.22/2.90 thf(zip_derived_cl139, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (c_lessequals @ (c_Orderings_Omax @ X3 @ X2 @ X0) @ X1 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X3 @ X1 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X2 @ X1 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl23, zip_derived_cl16])).
% 16.22/2.90 thf(cls_conjecture_2, conjecture,
% 16.22/2.90 (c_lessequals @
% 16.22/2.90 ( c_Orderings_Omax @
% 16.22/2.90 ( c_minus @ ( v_k @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ c_0 @ t_b ) @
% 16.22/2.90 ( c_HOL_Oabs @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @
% 16.22/2.90 t_b)).
% 16.22/2.90 thf(zf_stmt_2, negated_conjecture,
% 16.22/2.90 (~( c_lessequals @
% 16.22/2.90 ( c_Orderings_Omax @
% 16.22/2.90 ( c_minus @ ( v_k @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ c_0 @ t_b ) @
% 16.22/2.90 ( c_HOL_Oabs @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @
% 16.22/2.90 t_b )),
% 16.22/2.90 inference('cnf.neg', [status(esa)], [cls_conjecture_2])).
% 16.22/2.90 thf(zip_derived_cl1, plain,
% 16.22/2.90 (~ (c_lessequals @
% 16.22/2.90 (c_Orderings_Omax @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 c_0 @ t_b) @
% 16.22/2.90 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_2])).
% 16.22/2.90 thf(zip_derived_cl156, plain,
% 16.22/2.90 ((~ (c_lessequals @ c_0 @
% 16.22/2.90 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl1])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl157, plain,
% 16.22/2.90 ((~ (c_lessequals @ c_0 @
% 16.22/2.90 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl156, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl166, plain,
% 16.22/2.90 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl157])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl167, plain,
% 16.22/2.90 (~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b)),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl2268, plain,
% 16.22/2.90 ((~ (c_lessequals @
% 16.22/2.90 (c_minus @ c_0 @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 c_0 @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)],
% 16.22/2.90 [zip_derived_cl2051, zip_derived_cl167])).
% 16.22/2.90 thf(zip_derived_cl905, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ((c_minus @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ X0 @ X1 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl361, zip_derived_cl582, zip_derived_cl617,
% 16.22/2.90 zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl2278, plain,
% 16.22/2.90 ((~ (c_lessequals @ (c_minus @ (v_g @ v_x) @ (v_f @ v_x) @ t_b) @ c_0 @
% 16.22/2.90 t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl2268, zip_derived_cl905])).
% 16.22/2.90 thf(zip_derived_cl2290, plain,
% 16.22/2.90 ((~ (c_lessequals @ (v_g @ v_x) @ (v_f @ v_x) @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)],
% 16.22/2.90 [zip_derived_cl1131, zip_derived_cl2278])).
% 16.22/2.90 thf(zip_derived_cl3133, plain,
% 16.22/2.90 ((~ (c_lessequals @ (v_g @ v_x) @ (v_k @ v_x) @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)],
% 16.22/2.90 [zip_derived_cl3052, zip_derived_cl2290])).
% 16.22/2.90 thf(zip_derived_cl133, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_Orderings_Oorder @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl24, zip_derived_cl19])).
% 16.22/2.90 thf(zip_derived_cl23, plain,
% 16.22/2.90 (![X0 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (class_Orderings_Olinorder @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)],
% 16.22/2.90 [clsrel_Ring__and__Field_Oordered__idom_33])).
% 16.22/2.90 thf(cls_Orderings_Olinorder__not__le_0, axiom,
% 16.22/2.90 (( ~( class_Orderings_Olinorder @ T_a ) ) | ( c_less @ V_y @ V_x @ T_a ) |
% 16.22/2.90 ( c_lessequals @ V_x @ V_y @ T_a ))).
% 16.22/2.90 thf(zip_derived_cl15, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Orderings_Olinorder @ X0)
% 16.22/2.90 | (c_less @ X1 @ X2 @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ X1 @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_Orderings_Olinorder__not__le_0])).
% 16.22/2.90 thf(cls_Orderings_Oorder__less__imp__le_0, axiom,
% 16.22/2.90 (( ~( class_Orderings_Oorder @ T_a ) ) |
% 16.22/2.90 ( ~( c_less @ V_x @ V_y @ T_a ) ) | ( c_lessequals @ V_x @ V_y @ T_a ))).
% 16.22/2.90 thf(zip_derived_cl18, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Orderings_Oorder @ X0)
% 16.22/2.90 | ~ (c_less @ X1 @ X2 @ X0)
% 16.22/2.90 | (c_lessequals @ X1 @ X2 @ X0))),
% 16.22/2.90 inference('cnf', [status(esa)], [cls_Orderings_Oorder__less__imp__le_0])).
% 16.22/2.90 thf(zip_derived_cl136, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ( (c_lessequals @ X1 @ X2 @ X0)
% 16.22/2.90 | ~ (class_Orderings_Olinorder @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ X1 @ X0)
% 16.22/2.90 | ~ (class_Orderings_Oorder @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl15, zip_derived_cl18])).
% 16.22/2.90 thf(zip_derived_cl140, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (class_Orderings_Oorder @ X0)
% 16.22/2.90 | (c_lessequals @ X1 @ X2 @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ X1 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl23, zip_derived_cl136])).
% 16.22/2.90 thf(zip_derived_cl142, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (c_lessequals @ X1 @ X2 @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ X1 @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl133, zip_derived_cl140])).
% 16.22/2.90 thf(zip_derived_cl168, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ( (c_lessequals @ X2 @ X1 @ X0)
% 16.22/2.90 | (c_lessequals @ X1 @ X2 @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 16.22/2.90 inference('simplify', [status(thm)], [zip_derived_cl142])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl175, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ( (c_lessequals @ X1 @ X0 @ t_b) | (c_lessequals @ X0 @ X1 @ t_b))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl168, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl148, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (c_lessequals @ c_0 @ (c_HOL_Oabs @ X1 @ X0) @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl26, zip_derived_cl3])).
% 16.22/2.90 thf(zip_derived_cl141, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (c_lessequals @ X3 @ X1 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X3 @ X2 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ X2 @ X1 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl133, zip_derived_cl17])).
% 16.22/2.90 thf(zip_derived_cl160, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | (c_lessequals @ c_0 @ X2 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_HOL_Oabs @ X1 @ X0) @ X2 @ X0))),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl141])).
% 16.22/2.90 thf(zip_derived_cl165, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (c_lessequals @ (c_HOL_Oabs @ X1 @ X0) @ X2 @ X0)
% 16.22/2.90 | (c_lessequals @ c_0 @ X2 @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 16.22/2.90 inference('simplify', [status(thm)], [zip_derived_cl160])).
% 16.22/2.90 thf(zip_derived_cl412, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ( (c_lessequals @ X0 @ (c_HOL_Oabs @ X1 @ t_b) @ t_b)
% 16.22/2.90 | (c_lessequals @ c_0 @ X0 @ t_b)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ t_b))),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl175, zip_derived_cl165])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl425, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ( (c_lessequals @ X0 @ (c_HOL_Oabs @ X1 @ t_b) @ t_b)
% 16.22/2.90 | (c_lessequals @ c_0 @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl412, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl167, plain,
% 16.22/2.90 (~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_HOL_Oabs @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b)),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl1376, plain,
% 16.22/2.90 ( (c_lessequals @ c_0 @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @ t_b)),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl425, zip_derived_cl167])).
% 16.22/2.90 thf(zip_derived_cl1087, plain,
% 16.22/2.90 (![X0 : $i]: ((c_uminus @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) = (X0))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl377, zip_derived_cl905, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl228, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 (((c_0) = (c_plus @ (c_uminus @ X1 @ X0) @ X1 @ X0))
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 16.22/2.90 inference('simplify', [status(thm)], [zip_derived_cl226])).
% 16.22/2.90 thf(zip_derived_cl151, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (c_lessequals @ (c_plus @ X2 @ X3 @ X0) @
% 16.22/2.90 (c_plus @ X1 @ X3 @ X0) @ X0)
% 16.22/2.90 | (c_lessequals @ X2 @ X1 @ X0))),
% 16.22/2.90 inference('dp-resolution', [status(thm)],
% 16.22/2.90 [zip_derived_cl26, zip_derived_cl135])).
% 16.22/2.90 thf(zip_derived_cl1233, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0)
% 16.22/2.90 | ~ (c_lessequals @ c_0 @ (c_plus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 | (c_lessequals @ (c_uminus @ X1 @ X0) @ X2 @ X0))),
% 16.22/2.90 inference('s_sup-', [status(thm)], [zip_derived_cl228, zip_derived_cl151])).
% 16.22/2.90 thf(zip_derived_cl1260, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ( (c_lessequals @ (c_uminus @ X1 @ X0) @ X2 @ X0)
% 16.22/2.90 | ~ (c_lessequals @ c_0 @ (c_plus @ X2 @ X1 @ X0) @ X0)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ X0))),
% 16.22/2.90 inference('simplify', [status(thm)], [zip_derived_cl1233])).
% 16.22/2.90 thf(zip_derived_cl1350, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ( (c_lessequals @ X0 @ X1 @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ c_0 @
% 16.22/2.90 (c_plus @ X1 @ (c_minus @ c_0 @ X0 @ t_b) @ t_b) @ t_b)
% 16.22/2.90 | ~ (class_Ring__and__Field_Oordered__idom @ t_b))),
% 16.22/2.90 inference('s_sup+', [status(thm)],
% 16.22/2.90 [zip_derived_cl1087, zip_derived_cl1260])).
% 16.22/2.90 thf(zip_derived_cl868, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.22/2.90 ((c_plus @ X2 @ (c_minus @ X1 @ X0 @ t_b) @ t_b)
% 16.22/2.90 = (c_minus @ (c_plus @ X2 @ X1 @ t_b) @ X0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl360, zip_derived_cl582, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl607, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_plus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl247, zip_derived_cl582])).
% 16.22/2.90 thf(zip_derived_cl2, plain, ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.22/2.90 thf(zip_derived_cl1356, plain,
% 16.22/2.90 (![X0 : $i, X1 : $i]:
% 16.22/2.90 ( (c_lessequals @ X0 @ X1 @ t_b)
% 16.22/2.90 | ~ (c_lessequals @ c_0 @ (c_minus @ X1 @ X0 @ t_b) @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl1350, zip_derived_cl868, zip_derived_cl607,
% 16.22/2.90 zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl3566, plain,
% 16.22/2.90 ( (c_lessequals @ (v_g @ v_x) @ (v_k @ v_x) @ t_b)),
% 16.22/2.90 inference('s_sup-', [status(thm)],
% 16.22/2.90 [zip_derived_cl1376, zip_derived_cl1356])).
% 16.22/2.90 thf(zip_derived_cl3622, plain,
% 16.22/2.90 (~ (c_lessequals @ (c_minus @ (v_k @ v_x) @ (v_g @ v_x) @ t_b) @
% 16.22/2.90 (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b)),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl3133, zip_derived_cl3566])).
% 16.22/2.90 thf(zip_derived_cl8865, plain,
% 16.22/2.90 (~ (c_lessequals @ (v_k @ v_x) @
% 16.22/2.90 (c_minus @ (v_f @ v_x) @
% 16.22/2.90 (c_minus @ (v_g @ v_x) @ (v_g @ v_x) @ t_b) @ t_b) @
% 16.22/2.90 t_b)),
% 16.22/2.90 inference('s_sup-', [status(thm)],
% 16.22/2.90 [zip_derived_cl8850, zip_derived_cl3622])).
% 16.22/2.90 thf(zip_derived_cl154, plain,
% 16.22/2.90 (![X0 : $i]: ((c_minus @ X0 @ X0 @ t_b) = (c_0))),
% 16.22/2.90 inference('s_sup+', [status(thm)], [zip_derived_cl146, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl582, plain,
% 16.22/2.90 (![X0 : $i]: ((X0) = (c_minus @ X0 @ c_0 @ t_b))),
% 16.22/2.90 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl2])).
% 16.22/2.90 thf(zip_derived_cl0, plain,
% 16.22/2.90 (![X0 : $i]: (c_lessequals @ (v_k @ X0) @ (v_f @ X0) @ t_b)),
% 16.22/2.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 16.22/2.90 thf(zip_derived_cl8938, plain, ($false),
% 16.22/2.90 inference('demod', [status(thm)],
% 16.22/2.90 [zip_derived_cl8865, zip_derived_cl154, zip_derived_cl582,
% 16.22/2.90 zip_derived_cl0])).
% 16.22/2.90
% 16.22/2.90 % SZS output end Refutation
% 16.22/2.90
% 16.22/2.90
% 16.22/2.90 % Terminating...
% 16.22/3.06 % Runner terminated.
% 16.22/3.08 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------