TSTP Solution File: ANA028-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ANA028-1 : 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.j9SpfjnW7i true
% Computer : n004.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 17:26:00 EDT 2023
% Result : Unsatisfiable 83.91s 12.60s
% Output : Refutation 83.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA028-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.j9SpfjnW7i true
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 18:03:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.79 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 83.91/12.60 % Solved by fo/fo6_bce.sh.
% 83.91/12.60 % BCE start: 2809
% 83.91/12.60 % BCE eliminated: 331
% 83.91/12.60 % PE start: 2478
% 83.91/12.60 logic: eq
% 83.91/12.60 % PE eliminated: -98
% 83.91/12.60 % done 7825 iterations in 11.839s
% 83.91/12.60 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 83.91/12.60 % SZS output start Refutation
% 83.91/12.60 thf(c_minus_type, type, c_minus: $i > $i > $i > $i).
% 83.91/12.60 thf(class_OrderedGroup_Oab__group__add_type, type, class_OrderedGroup_Oab__group__add:
% 83.91/12.60 $i > $o).
% 83.91/12.60 thf(v_f_type, type, v_f: $i > $i).
% 83.91/12.60 thf(v_k_type, type, v_k: $i > $i).
% 83.91/12.60 thf(class_Orderings_Olinorder_type, type, class_Orderings_Olinorder: $i > $o).
% 83.91/12.60 thf(v_g_type, type, v_g: $i > $i).
% 83.91/12.60 thf(t_b_type, type, t_b: $i).
% 83.91/12.60 thf(c_plus_type, type, c_plus: $i > $i > $i > $i).
% 83.91/12.60 thf(class_OrderedGroup_Olordered__ab__group__abs_type, type, class_OrderedGroup_Olordered__ab__group__abs:
% 83.91/12.60 $i > $o).
% 83.91/12.60 thf(c_HOL_Oabs_type, type, c_HOL_Oabs: $i > $i > $i).
% 83.91/12.60 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 83.91/12.60 thf(c_less_type, type, c_less: $i > $i > $i > $o).
% 83.91/12.60 thf(class_Orderings_Oorder_type, type, class_Orderings_Oorder: $i > $o).
% 83.91/12.60 thf(class_Ring__and__Field_Oordered__idom_type, type, class_Ring__and__Field_Oordered__idom:
% 83.91/12.60 $i > $o).
% 83.91/12.60 thf(c_0_type, type, c_0: $i).
% 83.91/12.60 thf(v_x_type, type, v_x: $i).
% 83.91/12.60 thf(class_OrderedGroup_Opordered__ab__group__add_type, type, class_OrderedGroup_Opordered__ab__group__add:
% 83.91/12.60 $i > $o).
% 83.91/12.60 thf(cls_conjecture_3, conjecture,
% 83.91/12.60 (c_lessequals @
% 83.91/12.60 ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @
% 83.91/12.60 ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b)).
% 83.91/12.60 thf(zf_stmt_0, negated_conjecture,
% 83.91/12.60 (~( c_lessequals @
% 83.91/12.60 ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @
% 83.91/12.60 ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b )),
% 83.91/12.60 inference('cnf.neg', [status(esa)], [cls_conjecture_3])).
% 83.91/12.60 thf(zip_derived_cl2807, plain,
% 83.91/12.60 (~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_0])).
% 83.91/12.60 thf(clsrel_Ring__and__Field_Oordered__idom_4, axiom,
% 83.91/12.60 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 83.91/12.60 ( class_OrderedGroup_Oab__group__add @ T ))).
% 83.91/12.60 thf(zip_derived_cl2450, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Oab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 83.91/12.60 thf(clsrel_Ring__and__Field_Oordered__idom_50, axiom,
% 83.91/12.60 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 83.91/12.60 ( class_OrderedGroup_Olordered__ab__group__abs @ T ))).
% 83.91/12.60 thf(zip_derived_cl2462, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 83.91/12.60 thf(zip_derived_cl2462, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Olordered__ab__group__abs @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_50])).
% 83.91/12.60 thf(zip_derived_cl2450, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Oab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 83.91/12.60 thf(cls_OrderedGroup_Odiff__self_0, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 83.91/12.60 ( ( c_minus @ V_a @ V_a @ T_a ) = ( c_0 ) ))).
% 83.91/12.60 thf(zip_derived_cl1098, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 83.91/12.60 | ((c_minus @ X1 @ X1 @ X0) = (c_0)))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_OrderedGroup_Odiff__self_0])).
% 83.91/12.60 thf(clsrel_Ring__and__Field_Oordered__idom_54, axiom,
% 83.91/12.60 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 83.91/12.60 ( class_OrderedGroup_Opordered__ab__group__add @ T ))).
% 83.91/12.60 thf(zip_derived_cl2466, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_54])).
% 83.91/12.60 thf(zip_derived_cl2450, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Oab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 83.91/12.60 thf(cls_OrderedGroup_Ocompare__rls__3_0, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 83.91/12.60 ( ( c_plus @ ( c_minus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) =
% 83.91/12.60 ( c_minus @ ( c_plus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ))).
% 83.91/12.60 thf(zip_derived_cl2786, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 83.91/12.60 | ((c_plus @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0)
% 83.91/12.60 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__3_0])).
% 83.91/12.60 thf(zip_derived_cl2450, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Oab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 83.91/12.60 thf(cls_OrderedGroup_Ocompare__rls__5_0, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 83.91/12.60 ( ( c_minus @ V_a @ ( c_minus @ V_b @ V_c @ T_a ) @ T_a ) =
% 83.91/12.60 ( c_minus @ ( c_plus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ))).
% 83.91/12.60 thf(zip_derived_cl2788, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 83.91/12.60 | ((c_minus @ X1 @ (c_minus @ X3 @ X2 @ X0) @ X0)
% 83.91/12.60 = (c_minus @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__5_0])).
% 83.91/12.60 thf(zip_derived_cl2466, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_54])).
% 83.91/12.60 thf(zip_derived_cl2466, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_54])).
% 83.91/12.60 thf(zip_derived_cl2450, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Oab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_4])).
% 83.91/12.60 thf(cls_OrderedGroup_Ocompare__rls__4_0, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 83.91/12.60 ( ( c_minus @ ( c_minus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) =
% 83.91/12.60 ( c_minus @ V_a @ ( c_plus @ V_b @ V_c @ T_a ) @ T_a ) ))).
% 83.91/12.60 thf(zip_derived_cl2787, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 83.91/12.60 | ((c_minus @ (c_minus @ X1 @ X2 @ X0) @ X3 @ X0)
% 83.91/12.60 = (c_minus @ X1 @ (c_plus @ X2 @ X3 @ X0) @ X0)))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__4_0])).
% 83.91/12.60 thf(zip_derived_cl2466, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_54])).
% 83.91/12.60 thf(clsrel_Ring__and__Field_Oordered__idom_44, axiom,
% 83.91/12.60 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 83.91/12.60 ( class_Orderings_Oorder @ T ))).
% 83.91/12.60 thf(zip_derived_cl2455, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_Orderings_Oorder @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_44])).
% 83.91/12.60 thf(clsrel_Ring__and__Field_Oordered__idom_33, axiom,
% 83.91/12.60 (( ~( class_Ring__and__Field_Oordered__idom @ T ) ) |
% 83.91/12.60 ( class_Orderings_Olinorder @ T ))).
% 83.91/12.60 thf(zip_derived_cl2443, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_Orderings_Olinorder @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_33])).
% 83.91/12.60 thf(cls_Orderings_Olinorder__not__le_0, axiom,
% 83.91/12.60 (( ~( class_Orderings_Olinorder @ T_a ) ) | ( c_less @ V_y @ V_x @ T_a ) |
% 83.91/12.60 ( c_lessequals @ V_x @ V_y @ T_a ))).
% 83.91/12.60 thf(zip_derived_cl2800, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.91/12.60 (~ (class_Orderings_Olinorder @ X0)
% 83.91/12.60 | (c_less @ X1 @ X2 @ X0)
% 83.91/12.60 | (c_lessequals @ X2 @ X1 @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_Orderings_Olinorder__not__le_0])).
% 83.91/12.60 thf(zip_derived_cl2807, plain,
% 83.91/12.60 (~ (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_0])).
% 83.91/12.60 thf(zip_derived_cl57900, plain,
% 83.91/12.60 (( (c_less @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b)
% 83.91/12.60 | ~ (class_Orderings_Olinorder @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2800, zip_derived_cl2807])).
% 83.91/12.60 thf(zip_derived_cl60847, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_less @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2443, zip_derived_cl57900])).
% 83.91/12.60 thf(tfree_tcs, conjecture,
% 83.91/12.60 (~( class_Ring__and__Field_Oordered__idom @ t_b ))).
% 83.91/12.60 thf(zf_stmt_1, negated_conjecture,
% 83.91/12.60 (class_Ring__and__Field_Oordered__idom @ t_b),
% 83.91/12.60 inference('cnf.neg', [status(esa)], [tfree_tcs])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl60848, plain,
% 83.91/12.60 ( (c_less @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl60847, zip_derived_cl2808])).
% 83.91/12.60 thf(cls_Orderings_Oorder__less__imp__le_0, axiom,
% 83.91/12.60 (( ~( class_Orderings_Oorder @ T_a ) ) |
% 83.91/12.60 ( ~( c_less @ V_x @ V_y @ T_a ) ) | ( c_lessequals @ V_x @ V_y @ T_a ))).
% 83.91/12.60 thf(zip_derived_cl2803, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.91/12.60 (~ (class_Orderings_Oorder @ X0)
% 83.91/12.60 | ~ (c_less @ X1 @ X2 @ X0)
% 83.91/12.60 | (c_lessequals @ X1 @ X2 @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_Orderings_Oorder__less__imp__le_0])).
% 83.91/12.60 thf(zip_derived_cl60860, plain,
% 83.91/12.60 ((~ (class_Orderings_Oorder @ t_b)
% 83.91/12.60 | (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl60848, zip_derived_cl2803])).
% 83.91/12.60 thf(zip_derived_cl60889, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2455, zip_derived_cl60860])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl60892, plain,
% 83.91/12.60 ( (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl60889, zip_derived_cl2808])).
% 83.91/12.60 thf(cls_OrderedGroup_Odiff__le__0__iff__le_1, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Opordered__ab__group__add @ T_a ) ) |
% 83.91/12.60 ( ~( c_lessequals @ V_a @ V_b @ T_a ) ) |
% 83.91/12.60 ( c_lessequals @ ( c_minus @ V_a @ V_b @ T_a ) @ c_0 @ T_a ))).
% 83.91/12.60 thf(zip_derived_cl1094, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 83.91/12.60 | ~ (c_lessequals @ X1 @ X2 @ X0)
% 83.91/12.60 | (c_lessequals @ (c_minus @ X1 @ X2 @ X0) @ c_0 @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [cls_OrderedGroup_Odiff__le__0__iff__le_1])).
% 83.91/12.60 thf(zip_derived_cl60901, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_minus @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 c_0 @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl60892, zip_derived_cl1094])).
% 83.91/12.60 thf(zip_derived_cl60908, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_minus @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 c_0 @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2466, zip_derived_cl60901])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl60909, plain,
% 83.91/12.60 ( (c_lessequals @
% 83.91/12.60 (c_minus @ (c_minus @ (v_f @ v_x) @ (v_g @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 c_0 @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl60908, zip_derived_cl2808])).
% 83.91/12.60 thf(zip_derived_cl60927, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Oab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @
% 83.91/12.60 (c_plus @ (v_g @ v_x) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 t_b) @
% 83.91/12.60 c_0 @ t_b))),
% 83.91/12.60 inference('s_sup+', [status(thm)],
% 83.91/12.60 [zip_derived_cl2787, zip_derived_cl60909])).
% 83.91/12.60 thf(zip_derived_cl67223, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @
% 83.91/12.60 (c_plus @ (v_g @ v_x) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 t_b) @
% 83.91/12.60 c_0 @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2450, zip_derived_cl60927])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67225, plain,
% 83.91/12.60 ( (c_lessequals @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @
% 83.91/12.60 (c_plus @ (v_g @ v_x) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 t_b) @
% 83.91/12.60 c_0 @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67223, zip_derived_cl2808])).
% 83.91/12.60 thf(cls_OrderedGroup_Odiff__le__0__iff__le_0, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Opordered__ab__group__add @ T_a ) ) |
% 83.91/12.60 ( ~( c_lessequals @ ( c_minus @ V_a @ V_b @ T_a ) @ c_0 @ T_a ) ) |
% 83.91/12.60 ( c_lessequals @ V_a @ V_b @ T_a ))).
% 83.91/12.60 thf(zip_derived_cl1093, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 83.91/12.60 | ~ (c_lessequals @ (c_minus @ X1 @ X2 @ X0) @ c_0 @ X0)
% 83.91/12.60 | (c_lessequals @ X1 @ X2 @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [cls_OrderedGroup_Odiff__le__0__iff__le_0])).
% 83.91/12.60 thf(zip_derived_cl67241, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @ (v_f @ v_x) @
% 83.91/12.60 (c_plus @ (v_g @ v_x) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl67225, zip_derived_cl1093])).
% 83.91/12.60 thf(zip_derived_cl67253, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @ (v_f @ v_x) @
% 83.91/12.60 (c_plus @ (v_g @ v_x) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2466, zip_derived_cl67241])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67254, plain,
% 83.91/12.60 ( (c_lessequals @ (v_f @ v_x) @
% 83.91/12.60 (c_plus @ (v_g @ v_x) @ (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 83.91/12.60 t_b) @
% 83.91/12.60 t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67253, zip_derived_cl2808])).
% 83.91/12.60 thf(cls_OrderedGroup_Ocompare__rls__8_1, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Opordered__ab__group__add @ T_a ) ) |
% 83.91/12.60 ( ~( c_lessequals @ V_a @ ( c_plus @ V_c @ V_b @ T_a ) @ T_a ) ) |
% 83.91/12.60 ( c_lessequals @ ( c_minus @ V_a @ V_b @ T_a ) @ V_c @ T_a ))).
% 83.91/12.60 thf(zip_derived_cl2794, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 83.91/12.60 | ~ (c_lessequals @ X1 @ (c_plus @ X2 @ X3 @ X0) @ X0)
% 83.91/12.60 | (c_lessequals @ (c_minus @ X1 @ X3 @ X0) @ X2 @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__8_1])).
% 83.91/12.60 thf(zip_derived_cl67271, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl67254, zip_derived_cl2794])).
% 83.91/12.60 thf(zip_derived_cl67274, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2466, zip_derived_cl67271])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67275, plain,
% 83.91/12.60 ( (c_lessequals @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @
% 83.91/12.60 (c_minus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67274, zip_derived_cl2808])).
% 83.91/12.60 thf(zip_derived_cl67288, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Oab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_minus @ (c_plus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 83.91/12.60 (v_f @ v_x) @ t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b))),
% 83.91/12.60 inference('s_sup+', [status(thm)],
% 83.91/12.60 [zip_derived_cl2788, zip_derived_cl67275])).
% 83.91/12.60 thf(zip_derived_cl67362, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_minus @ (c_plus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @
% 83.91/12.60 (v_f @ v_x) @ t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2450, zip_derived_cl67288])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67364, plain,
% 83.91/12.60 ( (c_lessequals @
% 83.91/12.60 (c_minus @ (c_plus @ (v_f @ v_x) @ (v_k @ v_x) @ t_b) @ (v_f @ v_x) @
% 83.91/12.60 t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67362, zip_derived_cl2808])).
% 83.91/12.60 thf(zip_derived_cl67388, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Oab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_plus @ (c_minus @ (v_f @ v_x) @ (v_f @ v_x) @ t_b) @
% 83.91/12.60 (v_k @ v_x) @ t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b))),
% 83.91/12.60 inference('s_sup+', [status(thm)],
% 83.91/12.60 [zip_derived_cl2786, zip_derived_cl67364])).
% 83.91/12.60 thf(zip_derived_cl67520, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @
% 83.91/12.60 (c_plus @ (c_minus @ (v_f @ v_x) @ (v_f @ v_x) @ t_b) @
% 83.91/12.60 (v_k @ v_x) @ t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2450, zip_derived_cl67388])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67522, plain,
% 83.91/12.60 ( (c_lessequals @
% 83.91/12.60 (c_plus @ (c_minus @ (v_f @ v_x) @ (v_f @ v_x) @ t_b) @ (v_k @ v_x) @
% 83.91/12.60 t_b) @
% 83.91/12.60 (v_g @ v_x) @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67520, zip_derived_cl2808])).
% 83.91/12.60 thf(cls_OrderedGroup_Ocompare__rls__9_1, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Opordered__ab__group__add @ T_a ) ) |
% 83.91/12.60 ( ~( c_lessequals @ ( c_plus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) |
% 83.91/12.60 ( c_lessequals @ V_a @ ( c_minus @ V_c @ V_b @ T_a ) @ T_a ))).
% 83.91/12.60 thf(zip_derived_cl2796, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 83.91/12.60 | ~ (c_lessequals @ (c_plus @ X1 @ X2 @ X0) @ X3 @ X0)
% 83.91/12.60 | (c_lessequals @ X1 @ (c_minus @ X3 @ X2 @ X0) @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_OrderedGroup_Ocompare__rls__9_1])).
% 83.91/12.60 thf(zip_derived_cl67534, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_f @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl67522, zip_derived_cl2796])).
% 83.91/12.60 thf(zip_derived_cl67536, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_f @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @ t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2466, zip_derived_cl67534])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67537, plain,
% 83.91/12.60 ( (c_lessequals @ (c_minus @ (v_f @ v_x) @ (v_f @ v_x) @ t_b) @
% 83.91/12.60 (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67536, zip_derived_cl2808])).
% 83.91/12.60 thf(zip_derived_cl67561, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Oab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @ c_0 @ (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @
% 83.91/12.60 t_b))),
% 83.91/12.60 inference('s_sup+', [status(thm)],
% 83.91/12.60 [zip_derived_cl1098, zip_derived_cl67537])).
% 83.91/12.60 thf(zip_derived_cl67564, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @ c_0 @ (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @
% 83.91/12.60 t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2450, zip_derived_cl67561])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67566, plain,
% 83.91/12.60 ( (c_lessequals @ c_0 @ (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67564, zip_derived_cl2808])).
% 83.91/12.60 thf(cls_OrderedGroup_Oabs__of__nonneg_0, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T_a ) ) |
% 83.91/12.60 ( ~( c_lessequals @ c_0 @ V_y @ T_a ) ) |
% 83.91/12.60 ( ( c_HOL_Oabs @ V_y @ T_a ) = ( V_y ) ))).
% 83.91/12.60 thf(zip_derived_cl1076, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 83.91/12.60 | ~ (c_lessequals @ c_0 @ X1 @ X0)
% 83.91/12.60 | ((c_HOL_Oabs @ X1 @ X0) = (X1)))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__of__nonneg_0])).
% 83.91/12.60 thf(zip_derived_cl67579, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 83.91/12.60 | ((c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @ t_b)
% 83.91/12.60 = (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b)))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl67566, zip_derived_cl1076])).
% 83.91/12.60 thf(zip_derived_cl67715, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | ((c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @ t_b)
% 83.91/12.60 = (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b)))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2462, zip_derived_cl67579])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67717, plain,
% 83.91/12.60 (((c_HOL_Oabs @ (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @ t_b)
% 83.91/12.60 = (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b))),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67715, zip_derived_cl2808])).
% 83.91/12.60 thf(cls_OrderedGroup_Oabs__le__zero__iff_0, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Olordered__ab__group__abs @ T_a ) ) |
% 83.91/12.60 ( ~( c_lessequals @ ( c_HOL_Oabs @ V_a @ T_a ) @ c_0 @ T_a ) ) |
% 83.91/12.60 ( ( V_a ) = ( c_0 ) ))).
% 83.91/12.60 thf(zip_derived_cl1072, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Olordered__ab__group__abs @ X0)
% 83.91/12.60 | ~ (c_lessequals @ (c_HOL_Oabs @ X1 @ X0) @ c_0 @ X0)
% 83.91/12.60 | ((X1) = (c_0)))),
% 83.91/12.60 inference('cnf', [status(esa)], [cls_OrderedGroup_Oabs__le__zero__iff_0])).
% 83.91/12.60 thf(zip_derived_cl67722, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 83.91/12.60 | ~ (c_lessequals @ (c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) @
% 83.91/12.60 c_0 @ t_b)
% 83.91/12.60 | ((c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) = (c_0)))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl67717, zip_derived_cl1072])).
% 83.91/12.60 thf(zip_derived_cl2466, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_OrderedGroup_Opordered__ab__group__add @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_54])).
% 83.91/12.60 thf(cls_conjecture_1, conjecture,
% 83.91/12.60 (~( c_lessequals @ ( v_g @ V_U ) @ ( v_k @ V_U ) @ t_b ))).
% 83.91/12.60 thf(zf_stmt_2, negated_conjecture,
% 83.91/12.60 (c_lessequals @ ( v_g @ V_U ) @ ( v_k @ V_U ) @ t_b),
% 83.91/12.60 inference('cnf.neg', [status(esa)], [cls_conjecture_1])).
% 83.91/12.60 thf(zip_derived_cl2805, plain,
% 83.91/12.60 (![X0 : $i]: (c_lessequals @ (v_g @ X0) @ (v_k @ X0) @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_2])).
% 83.91/12.60 thf(zip_derived_cl1094, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Opordered__ab__group__add @ X0)
% 83.91/12.60 | ~ (c_lessequals @ X1 @ X2 @ X0)
% 83.91/12.60 | (c_lessequals @ (c_minus @ X1 @ X2 @ X0) @ c_0 @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [cls_OrderedGroup_Odiff__le__0__iff__le_1])).
% 83.91/12.60 thf(zip_derived_cl38870, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Opordered__ab__group__add @ t_b)
% 83.91/12.60 | (c_lessequals @ (c_minus @ (v_g @ X0) @ (v_k @ X0) @ t_b) @ c_0 @
% 83.91/12.60 t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2805, zip_derived_cl1094])).
% 83.91/12.60 thf(zip_derived_cl47328, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | (c_lessequals @ (c_minus @ (v_g @ X0) @ (v_k @ X0) @ t_b) @ c_0 @
% 83.91/12.60 t_b))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2466, zip_derived_cl38870])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl47329, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (c_lessequals @ (c_minus @ (v_g @ X0) @ (v_k @ X0) @ t_b) @ c_0 @ t_b)),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl47328, zip_derived_cl2808])).
% 83.91/12.60 thf(zip_derived_cl67727, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Olordered__ab__group__abs @ t_b)
% 83.91/12.60 | ((c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) = (c_0)))),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67722, zip_derived_cl47329])).
% 83.91/12.60 thf(zip_derived_cl67728, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | ((c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) = (c_0)))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2462, zip_derived_cl67727])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67730, plain,
% 83.91/12.60 (((c_minus @ (v_g @ v_x) @ (v_k @ v_x) @ t_b) = (c_0))),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67728, zip_derived_cl2808])).
% 83.91/12.60 thf(cls_OrderedGroup_Odiff__eq__0__iff__eq_0, axiom,
% 83.91/12.60 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 83.91/12.60 ( ( c_minus @ V_a @ V_b @ T_a ) != ( c_0 ) ) | ( ( V_a ) = ( V_b ) ))).
% 83.91/12.60 thf(zip_derived_cl1092, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.91/12.60 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 83.91/12.60 | ((c_minus @ X1 @ X2 @ X0) != (c_0))
% 83.91/12.60 | ((X1) = (X2)))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [cls_OrderedGroup_Odiff__eq__0__iff__eq_0])).
% 83.91/12.60 thf(zip_derived_cl67744, plain,
% 83.91/12.60 ((~ (class_OrderedGroup_Oab__group__add @ t_b)
% 83.91/12.60 | ((c_0) != (c_0))
% 83.91/12.60 | ((v_g @ v_x) = (v_k @ v_x)))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl67730, zip_derived_cl1092])).
% 83.91/12.60 thf(zip_derived_cl67756, plain,
% 83.91/12.60 ((((v_g @ v_x) = (v_k @ v_x))
% 83.91/12.60 | ~ (class_OrderedGroup_Oab__group__add @ t_b))),
% 83.91/12.60 inference('simplify', [status(thm)], [zip_derived_cl67744])).
% 83.91/12.60 thf(zip_derived_cl67800, plain,
% 83.91/12.60 ((~ (class_Ring__and__Field_Oordered__idom @ t_b)
% 83.91/12.60 | ((v_g @ v_x) = (v_k @ v_x)))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2450, zip_derived_cl67756])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl67802, plain, (((v_g @ v_x) = (v_k @ v_x))),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl67800, zip_derived_cl2808])).
% 83.91/12.60 thf(zip_derived_cl2455, plain,
% 83.91/12.60 (![X0 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (class_Orderings_Oorder @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [clsrel_Ring__and__Field_Oordered__idom_44])).
% 83.91/12.60 thf(cls_Orderings_Oorder__class_Oaxioms__1_0, axiom,
% 83.91/12.60 (( ~( class_Orderings_Oorder @ T_a ) ) | ( c_lessequals @ V_x @ V_x @ T_a ))).
% 83.91/12.60 thf(zip_derived_cl1688, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i]:
% 83.91/12.60 (~ (class_Orderings_Oorder @ X0) | (c_lessequals @ X1 @ X1 @ X0))),
% 83.91/12.60 inference('cnf', [status(esa)],
% 83.91/12.60 [cls_Orderings_Oorder__class_Oaxioms__1_0])).
% 83.91/12.60 thf(zip_derived_cl52960, plain,
% 83.91/12.60 (![X0 : $i, X1 : $i]:
% 83.91/12.60 (~ (class_Ring__and__Field_Oordered__idom @ X0)
% 83.91/12.60 | (c_lessequals @ X1 @ X1 @ X0))),
% 83.91/12.60 inference('s_sup-', [status(thm)],
% 83.91/12.60 [zip_derived_cl2455, zip_derived_cl1688])).
% 83.91/12.60 thf(zip_derived_cl2808, plain,
% 83.91/12.60 ( (class_Ring__and__Field_Oordered__idom @ t_b)),
% 83.91/12.60 inference('cnf', [status(esa)], [zf_stmt_1])).
% 83.91/12.60 thf(zip_derived_cl53058, plain,
% 83.91/12.60 (![X0 : $i]: (c_lessequals @ X0 @ X0 @ t_b)),
% 83.91/12.60 inference('s_sup+', [status(thm)],
% 83.91/12.60 [zip_derived_cl52960, zip_derived_cl2808])).
% 83.91/12.60 thf(zip_derived_cl67804, plain, ($false),
% 83.91/12.60 inference('demod', [status(thm)],
% 83.91/12.60 [zip_derived_cl2807, zip_derived_cl67802, zip_derived_cl53058])).
% 83.91/12.60
% 83.91/12.60 % SZS output end Refutation
% 83.91/12.60
% 83.91/12.60
% 83.91/12.60 % Terminating...
% 84.50/12.69 % Runner terminated.
% 84.50/12.71 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------