TSTP Solution File: ANA022-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA022-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 : 600s
% DateTime : Thu Jul 14 19:21:39 EDT 2022
% Result : Unsatisfiable 0.83s 1.09s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA022-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Fri Jul 8 06:06:37 EDT 2022
% 0.20/0.33 % CPUTime :
% 0.43/0.98 ============================== Prover9 ===============================
% 0.43/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98 Process 23852 was started by sandbox on n005.cluster.edu,
% 0.43/0.98 Fri Jul 8 06:06:37 2022
% 0.43/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23696_n005.cluster.edu".
% 0.43/0.98 ============================== end of head ===========================
% 0.43/0.98
% 0.43/0.98 ============================== INPUT =================================
% 0.43/0.98
% 0.43/0.98 % Reading from file /tmp/Prover9_23696_n005.cluster.edu
% 0.43/0.98
% 0.43/0.98 set(prolog_style_variables).
% 0.43/0.98 set(auto2).
% 0.43/0.98 % set(auto2) -> set(auto).
% 0.43/0.98 % set(auto) -> set(auto_inference).
% 0.43/0.98 % set(auto) -> set(auto_setup).
% 0.43/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98 % set(auto) -> set(auto_limits).
% 0.43/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98 % set(auto) -> set(auto_denials).
% 0.43/0.98 % set(auto) -> set(auto_process).
% 0.43/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98 % set(auto2) -> assign(stats, some).
% 0.43/0.98 % set(auto2) -> clear(echo_input).
% 0.43/0.98 % set(auto2) -> set(quiet).
% 0.43/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98 % set(auto2) -> clear(print_given).
% 0.43/0.98 assign(lrs_ticks,-1).
% 0.43/0.98 assign(sos_limit,10000).
% 0.43/0.98 assign(order,kbo).
% 0.43/0.98 set(lex_order_vars).
% 0.43/0.98 clear(print_given).
% 0.43/0.98
% 0.43/0.98 % formulas(sos). % not echoed (27 formulas)
% 0.43/0.98
% 0.43/0.98 ============================== end of input ==========================
% 0.43/0.98
% 0.43/0.98 % From the command line: assign(max_seconds, 300).
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98
% 0.43/0.98 % Formulas that are not ordinary clauses:
% 0.43/0.98
% 0.43/0.98 ============================== end of process non-clausal formulas ===
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.98
% 0.43/0.98 ============================== PREDICATE ELIMINATION =================
% 0.43/0.98 1 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 0.43/0.98 2 class_Ring__and__Field_Oordered__idom(t_b) # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 0.43/0.98 Derived: class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 0.43/0.98 3 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 0.43/0.98 Derived: class_Orderings_Olinorder(t_b). [resolve(3,a,2,a)].
% 0.43/0.98 4 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 0.43/0.98 Derived: class_LOrder_Ojoin__semilorder(t_b). [resolve(4,a,2,a)].
% 0.43/0.98 5 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_4) # label(axiom). [assumption].
% 0.43/0.98 Derived: class_OrderedGroup_Oab__group__add(t_b). [resolve(5,a,2,a)].
% 0.43/0.98 6 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__idom_50) # label(axiom). [assumption].
% 0.43/0.98 Derived: class_OrderedGroup_Olordered__ab__group__abs(t_b). [resolve(6,a,2,a)].
% 0.43/0.98 7 class_LOrder_Ojoin__semilorder(t_b). [resolve(4,a,2,a)].
% 0.43/0.98 8 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 0.43/0.98 Derived: class_Orderings_Oorder(t_b). [resolve(7,a,8,a)].
% 0.43/0.98 9 class_OrderedGroup_Olordered__ab__group__abs(t_b). [resolve(6,a,2,a)].
% 0.43/0.98 10 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_1) # label(axiom). [assumption].
% 0.43/0.98 11 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_6) # label(axiom). [assumption].
% 0.43/0.98 12 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A) # label(cls_OrderedGroup_Oabs__ge__zero_0) # label(axiom). [assumption].
% 0.43/0.98 13 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A) # label(cls_OrderedGroup_Oabs__minus__cancel_0) # label(axiom). [assumption].
% 0.43/0.98 14 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A) # label(cls_OrderedGroup_Oabs__of__nonpos_0) # label(axiom). [assumption].
% 0.43/0.98 Derived: class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(9,a,10,a)].
% 0.43/0.98 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b). [resolve(9,a,11,a)].
% 0.43/0.98 Derived: c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b). [resolve(9,a,12,a)].
% 0.43/0.98 Derived: c_HOL_Oabs(c_uminus(A,t_b),t_b) = c_HOL_Oabs(A,t_b). [resolve(9,a,13,a)].
% 0.43/0.98 Derived: -c_lessequals(A,c_0,t_b) | c_HOL_Oabs(A,t_b) = c_uminus(A,t_b). [resolve(9,a,14,a)].
% 0.43/0.98 15 class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 0.43/0.98 16 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(c_0,B,A) = B # label(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) # label(axiom). [assumption].
% 0.43/0.98 Derived: c_plus(c_0,A,t_b) = A. [resolve(15,a,16,a)].
% 0.43/0.98 17 class_OrderedGroup_Oab__group__add(t_b). [resolve(5,a,2,a)].
% 0.43/0.98 18 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,B,A) = c_0 # label(cls_OrderedGroup_Odiff__self_0) # label(axiom). [assumption].
% 0.43/0.98 19 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,c_uminus(C,A),A) = c_plus(B,C,A) # label(cls_OrderedGroup_Odiff__minus__eq__add_0) # label(axiom). [assumption].
% 0.43/0.98 20 -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_minus(B,C,A),A) = c_minus(C,B,A) # label(cls_OrderedGroup_Ominus__diff__eq_0) # label(axiom). [assumption].
% 0.43/0.98 21 -class_OrderedGroup_Oab__group__add(A) | c_plus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,C,A),D,A) # label(cls_OrderedGroup_Ocompare__rls__2_0) # label(axiom). [assumption].
% 0.43/0.98 22 -class_OrderedGroup_Oab__group__add(A) | c_plus(c_minus(B,C,A),D,A) = c_minus(c_plus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__3_0) # label(axiom). [assumption].
% 0.43/0.98 Derived: c_minus(A,A,t_b) = c_0. [resolve(17,a,18,a)].
% 0.43/0.98 Derived: c_minus(A,c_uminus(B,t_b),t_b) = c_plus(A,B,t_b). [resolve(17,a,19,a)].
% 0.43/0.98 Derived: c_uminus(c_minus(A,B,t_b),t_b) = c_minus(B,A,t_b). [resolve(17,a,20,a)].
% 0.43/0.98 Derived: c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,B,t_b),C,t_b). [resolve(17,a,21,a)].
% 0.43/0.98 Derived: c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(c_plus(A,C,t_b),B,t_b). [resolve(17,a,22,a)].
% 0.43/0.98 23 class_Orderings_Olinorder(t_b). [resolve(3,a,2,a)].
% 0.43/0.98 24 -class_Orderings_Olinorder(A) | c_less(B,C,A) | c_lessequals(C,B,A) # label(cls_Orderings_Olinorder__not__le_0) # label(axiom). [assumption].
% 0.43/0.98 25 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) # label(axiom). [assumption].
% 0.43/0.98 Derived: c_less(A,B,t_b) | c_lessequals(B,A,t_b). [resolve(23,a,24,a)].
% 0.43/0.98 Derived: -c_lessequals(A,B,t_b) | -c_lessequals(C,B,t_b) | c_lessequals(c_Orderings_Omax(C,A,t_b),B,t_b). [resolve(23,a,25,a)].
% 0.43/0.98 26 class_Orderings_Oorder(t_b). [resolve(7,a,8,a)].
% 0.43/0.98 27 -class_Orderings_Oorder(A) | -c_less(B,C,A) | c_lessequals(B,C,A) # label(cls_Orderings_Oorder__less__imp__le_0) # label(axiom). [assumption].
% 0.43/0.98 28 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_lessequals(D,C,A) # label(cls_Orderings_Oorder__class_Oorder__trans_0) # label(axiom). [assumption].
% 0.43/0.98 Derived: -c_less(A,B,t_b) | c_lessequals(A,B,t_b). [resolve(26,a,27,a)].
% 0.43/0.98 Derived: -c_lessequals(A,B,t_b) | -c_lessequals(C,A,t_b) | c_lessequals(C,B,t_b). [resolve(26,a,28,a)].
% 0.43/0.98 29 class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(9,a,10,a)].
% 0.43/0.98 30 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_minus(B,C,A),c_0,A) # label(cls_OrderedGroup_Odiff__le__0__iff__le_1) # label(axiom). [assumption].
% 0.83/1.09 31 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_plus(C,D,A),A) | c_lessequals(c_minus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__8_1) # label(axiom). [assumption].
% 0.83/1.09 Derived: -c_lessequals(A,B,t_b) | c_lessequals(c_minus(A,B,t_b),c_0,t_b). [resolve(29,a,30,a)].
% 0.83/1.09 Derived: -c_lessequals(A,c_plus(B,C,t_b),t_b) | c_lessequals(c_minus(A,C,t_b),B,t_b). [resolve(29,a,31,a)].
% 0.83/1.09 32 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b). [resolve(9,a,11,a)].
% 0.83/1.09 33 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A) # label(cls_OrderedGroup_Oadd__le__cancel__right_0) # label(axiom). [assumption].
% 0.83/1.09 Derived: -c_lessequals(c_plus(A,B,t_b),c_plus(C,B,t_b),t_b) | c_lessequals(A,C,t_b). [resolve(32,a,33,a)].
% 0.83/1.09
% 0.83/1.09 ============================== end predicate elimination =============
% 0.83/1.09
% 0.83/1.09 Auto_denials: (non-Horn, no changes).
% 0.83/1.09
% 0.83/1.09 Term ordering decisions:
% 0.83/1.09 Function symbol KB weights: t_b=1. c_0=1. v_x=1. c_HOL_Oabs=1. c_uminus=1. v_f=1. v_k=1. v_g=1. c_minus=1. c_plus=1. c_Orderings_Omax=1.
% 0.83/1.09
% 0.83/1.09 ============================== end of process initial clauses ========
% 0.83/1.09
% 0.83/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.09
% 0.83/1.09 ============================== end of clauses for search =============
% 0.83/1.09
% 0.83/1.09 ============================== SEARCH ================================
% 0.83/1.09
% 0.83/1.09 % Starting search at 0.01 seconds.
% 0.83/1.09
% 0.83/1.09 ============================== PROOF =================================
% 0.83/1.09 % SZS status Unsatisfiable
% 0.83/1.09 % SZS output start Refutation
% 0.83/1.09
% 0.83/1.09 % Proof 1 at 0.12 (+ 0.00) seconds.
% 0.83/1.09 % Length of proof is 82.
% 0.83/1.09 % Level of proof is 13.
% 0.83/1.09 % Maximum clause weight is 19.000.
% 0.83/1.09 % Given clauses 191.
% 0.83/1.09
% 0.83/1.09 1 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 0.83/1.09 2 class_Ring__and__Field_Oordered__idom(t_b) # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 0.83/1.09 3 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 0.83/1.09 4 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 0.83/1.09 5 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_4) # label(axiom). [assumption].
% 0.83/1.09 6 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__idom_50) # label(axiom). [assumption].
% 0.83/1.09 7 class_LOrder_Ojoin__semilorder(t_b). [resolve(4,a,2,a)].
% 0.83/1.09 8 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 0.83/1.09 9 class_OrderedGroup_Olordered__ab__group__abs(t_b). [resolve(6,a,2,a)].
% 0.83/1.09 10 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_1) # label(axiom). [assumption].
% 0.83/1.09 11 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_6) # label(axiom). [assumption].
% 0.83/1.09 12 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A) # label(cls_OrderedGroup_Oabs__ge__zero_0) # label(axiom). [assumption].
% 0.83/1.09 13 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A) # label(cls_OrderedGroup_Oabs__minus__cancel_0) # label(axiom). [assumption].
% 0.83/1.09 14 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A) # label(cls_OrderedGroup_Oabs__of__nonpos_0) # label(axiom). [assumption].
% 0.83/1.09 15 class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 0.83/1.09 16 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(c_0,B,A) = B # label(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) # label(axiom). [assumption].
% 0.83/1.09 17 class_OrderedGroup_Oab__group__add(t_b). [resolve(5,a,2,a)].
% 0.83/1.09 18 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,B,A) = c_0 # label(cls_OrderedGroup_Odiff__self_0) # label(axiom). [assumption].
% 0.83/1.09 19 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,c_uminus(C,A),A) = c_plus(B,C,A) # label(cls_OrderedGroup_Odiff__minus__eq__add_0) # label(axiom). [assumption].
% 0.83/1.09 20 -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_minus(B,C,A),A) = c_minus(C,B,A) # label(cls_OrderedGroup_Ominus__diff__eq_0) # label(axiom). [assumption].
% 0.83/1.09 21 -class_OrderedGroup_Oab__group__add(A) | c_plus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,C,A),D,A) # label(cls_OrderedGroup_Ocompare__rls__2_0) # label(axiom). [assumption].
% 0.83/1.09 22 -class_OrderedGroup_Oab__group__add(A) | c_plus(c_minus(B,C,A),D,A) = c_minus(c_plus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__3_0) # label(axiom). [assumption].
% 0.83/1.09 23 class_Orderings_Olinorder(t_b). [resolve(3,a,2,a)].
% 0.83/1.09 24 -class_Orderings_Olinorder(A) | c_less(B,C,A) | c_lessequals(C,B,A) # label(cls_Orderings_Olinorder__not__le_0) # label(axiom). [assumption].
% 0.83/1.09 25 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) # label(axiom). [assumption].
% 0.83/1.09 26 class_Orderings_Oorder(t_b). [resolve(7,a,8,a)].
% 0.83/1.09 27 -class_Orderings_Oorder(A) | -c_less(B,C,A) | c_lessequals(B,C,A) # label(cls_Orderings_Oorder__less__imp__le_0) # label(axiom). [assumption].
% 0.83/1.09 28 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_lessequals(D,C,A) # label(cls_Orderings_Oorder__class_Oorder__trans_0) # label(axiom). [assumption].
% 0.83/1.09 29 class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(9,a,10,a)].
% 0.83/1.09 30 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_minus(B,C,A),c_0,A) # label(cls_OrderedGroup_Odiff__le__0__iff__le_1) # label(axiom). [assumption].
% 0.83/1.09 31 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_plus(C,D,A),A) | c_lessequals(c_minus(B,D,A),C,A) # label(cls_OrderedGroup_Ocompare__rls__8_1) # label(axiom). [assumption].
% 0.83/1.09 32 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b). [resolve(9,a,11,a)].
% 0.83/1.09 33 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A) # label(cls_OrderedGroup_Oadd__le__cancel__right_0) # label(axiom). [assumption].
% 0.83/1.09 34 c_lessequals(v_k(A),v_f(A),t_b) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 0.83/1.09 35 -c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 0.83/1.09 36 c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b). [resolve(9,a,12,a)].
% 0.83/1.09 37 c_HOL_Oabs(c_uminus(A,t_b),t_b) = c_HOL_Oabs(A,t_b). [resolve(9,a,13,a)].
% 0.83/1.09 38 -c_lessequals(A,c_0,t_b) | c_HOL_Oabs(A,t_b) = c_uminus(A,t_b). [resolve(9,a,14,a)].
% 0.83/1.09 39 -c_lessequals(A,c_0,t_b) | c_uminus(A,t_b) = c_HOL_Oabs(A,t_b). [copy(38),flip(b)].
% 0.83/1.09 40 c_plus(c_0,A,t_b) = A. [resolve(15,a,16,a)].
% 0.83/1.09 41 c_minus(A,A,t_b) = c_0. [resolve(17,a,18,a)].
% 0.83/1.09 42 c_minus(A,c_uminus(B,t_b),t_b) = c_plus(A,B,t_b). [resolve(17,a,19,a)].
% 0.83/1.09 43 c_uminus(c_minus(A,B,t_b),t_b) = c_minus(B,A,t_b). [resolve(17,a,20,a)].
% 0.83/1.09 44 c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,B,t_b),C,t_b). [resolve(17,a,21,a)].
% 0.83/1.09 45 c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(c_plus(A,C,t_b),B,t_b). [resolve(17,a,22,a)].
% 0.83/1.09 46 c_less(A,B,t_b) | c_lessequals(B,A,t_b). [resolve(23,a,24,a)].
% 0.83/1.09 47 -c_lessequals(A,B,t_b) | -c_lessequals(C,B,t_b) | c_lessequals(c_Orderings_Omax(C,A,t_b),B,t_b). [resolve(23,a,25,a)].
% 0.83/1.09 48 -c_less(A,B,t_b) | c_lessequals(A,B,t_b). [resolve(26,a,27,a)].
% 0.83/1.09 49 -c_lessequals(A,B,t_b) | -c_lessequals(C,A,t_b) | c_lessequals(C,B,t_b). [resolve(26,a,28,a)].
% 0.83/1.09 50 -c_lessequals(A,B,t_b) | c_lessequals(c_minus(A,B,t_b),c_0,t_b). [resolve(29,a,30,a)].
% 0.83/1.09 51 -c_lessequals(A,c_plus(B,C,t_b),t_b) | c_lessequals(c_minus(A,C,t_b),B,t_b). [resolve(29,a,31,a)].
% 0.83/1.09 52 -c_lessequals(c_plus(A,B,t_b),c_plus(C,B,t_b),t_b) | c_lessequals(A,C,t_b). [resolve(32,a,33,a)].
% 0.83/1.09 57 c_minus(c_plus(A,B,t_b),C,t_b) = c_minus(A,c_minus(C,B,t_b),t_b). [para(43(a,1),42(a,1,2)),rewrite([44(8)]),flip(a)].
% 0.83/1.09 58 c_minus(c_uminus(A,t_b),B,t_b) = c_uminus(c_plus(B,A,t_b),t_b). [para(42(a,1),43(a,1,1)),flip(a)].
% 0.83/1.09 59 c_uminus(c_uminus(c_plus(A,B,t_b),t_b),t_b) = c_plus(A,B,t_b). [para(42(a,1),43(a,2)),rewrite([58(4)])].
% 0.83/1.09 60 c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_minus(B,C,t_b),t_b). [back_rewrite(45),rewrite([57(8)])].
% 0.83/1.09 61 c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(A,c_minus(C,B,t_b),t_b). [back_rewrite(44),rewrite([57(8)])].
% 0.83/1.09 66 -c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b). [ur(47,a,36,a,c,35,a)].
% 0.83/1.09 67 c_lessequals(A,B,t_b) | c_lessequals(B,A,t_b). [resolve(48,a,46,a)].
% 0.83/1.09 69 c_lessequals(A,A,t_b). [factor(67,a,b)].
% 0.83/1.09 74 -c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_0,t_b). [ur(49,a,36,a,c,35,a)].
% 0.83/1.09 76 c_lessequals(c_minus(v_k(A),v_f(A),t_b),c_0,t_b). [resolve(50,a,34,a)].
% 0.83/1.09 78 -c_lessequals(A,c_plus(B,A,t_b),t_b) | c_lessequals(c_0,B,t_b). [para(40(a,1),52(a,1))].
% 0.83/1.09 98 -c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b). [ur(47,a,69,a,c,74,a)].
% 0.83/1.09 111 -c_lessequals(c_minus(v_k(v_x),c_minus(v_g(v_x),A,t_b),t_b),A,t_b). [ur(52,b,98,a),rewrite([60(8),40(11)])].
% 0.83/1.09 146 c_lessequals(A,B,t_b) | c_lessequals(c_minus(B,A,t_b),c_0,t_b). [resolve(67,a,50,a)].
% 0.83/1.09 163 c_minus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_plus(C,B,t_b),t_b). [para(57(a,1),43(a,1,1)),rewrite([43(6)])].
% 0.83/1.09 237 c_uminus(c_uminus(A,t_b),t_b) = A. [para(40(a,1),59(a,1,1,1)),rewrite([40(7)])].
% 0.83/1.09 286 c_minus(A,c_minus(A,B,t_b),t_b) = B. [para(41(a,1),60(a,1,1)),rewrite([40(3)]),flip(a)].
% 0.83/1.09 307 c_minus(A,c_0,t_b) = A. [para(41(a,1),286(a,1,2))].
% 0.83/1.09 310 -c_lessequals(c_minus(v_k(v_x),A,t_b),c_minus(v_g(v_x),A,t_b),t_b). [para(286(a,1),111(a,1,2))].
% 0.83/1.09 311 c_plus(A,B,t_b) = c_plus(B,A,t_b). [para(286(a,1),60(a,1,1)),rewrite([163(6),286(8)])].
% 0.83/1.09 341 -c_lessequals(A,c_plus(A,B,t_b),t_b) | c_lessequals(c_0,B,t_b). [back_rewrite(78),rewrite([311(2)])].
% 0.83/1.09 346 c_minus(c_0,A,t_b) = c_uminus(A,t_b). [para(307(a,1),43(a,1,1)),flip(a)].
% 0.83/1.09 361 -c_lessequals(c_0,c_minus(v_g(v_x),v_f(v_x),t_b),t_b). [ur(49,b,76,a,c,310,a)].
% 0.83/1.09 529 -c_lessequals(v_k(v_x),c_plus(v_g(v_x),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b). [ur(51,b,66,a),rewrite([311(14)])].
% 0.83/1.09 908 c_lessequals(A,c_0,t_b) | c_lessequals(c_uminus(A,t_b),c_0,t_b). [para(346(a,1),146(b,1))].
% 0.83/1.09 943 c_lessequals(A,c_0,t_b) | c_HOL_Oabs(A,t_b) = A. [resolve(908,b,39,a),rewrite([237(7),37(7)]),flip(b)].
% 0.83/1.09 1090 -c_lessequals(A,c_minus(A,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b). [ur(341,b,361,a),rewrite([61(8)])].
% 0.83/1.09 1266 -c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b). [para(41(a,1),1090(a,2))].
% 0.83/1.09 1268 c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = c_minus(v_f(v_x),v_g(v_x),t_b). [resolve(1266,a,943,a)].
% 0.83/1.09 1291 $F. [back_rewrite(529),rewrite([1268(12),61(12),286(12)]),unit_del(a,34)].
% 0.83/1.09
% 0.83/1.09 % SZS output end Refutation
% 0.83/1.09 ============================== end of proof ==========================
% 0.83/1.09
% 0.83/1.09 ============================== STATISTICS ============================
% 0.83/1.09
% 0.83/1.09 Given=191. Generated=2371. Kept=1256. proofs=1.
% 0.83/1.09 Usable=168. Sos=922. Demods=36. Limbo=23, Disabled=194. Hints=0.
% 0.83/1.09 Megabytes=1.33.
% 0.83/1.09 User_CPU=0.12, System_CPU=0.00, Wall_clock=1.
% 0.83/1.09
% 0.83/1.09 ============================== end of statistics =====================
% 0.83/1.09
% 0.83/1.09 ============================== end of search =========================
% 0.83/1.09
% 0.83/1.09 THEOREM PROVED
% 0.83/1.09 % SZS status Unsatisfiable
% 0.83/1.09
% 0.83/1.09 Exiting with 1 proof.
% 0.83/1.09
% 0.83/1.09 Process 23852 exit (max_proofs) Fri Jul 8 06:06:38 2022
% 0.83/1.09 Prover9 interrupted
%------------------------------------------------------------------------------