TSTP Solution File: ANA026-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA026-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 19:21:43 EDT 2022
% Result : Unsatisfiable 1.13s 1.40s
% Output : Refutation 1.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ANA026-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n029.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 : 600
% 0.14/0.35 % DateTime : Fri Jul 8 04:57:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.78/1.03 ============================== Prover9 ===============================
% 0.78/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.03 Process 366 was started by sandbox on n029.cluster.edu,
% 0.78/1.03 Fri Jul 8 04:57:30 2022
% 0.78/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32681_n029.cluster.edu".
% 0.78/1.03 ============================== end of head ===========================
% 0.78/1.03
% 0.78/1.03 ============================== INPUT =================================
% 0.78/1.03
% 0.78/1.03 % Reading from file /tmp/Prover9_32681_n029.cluster.edu
% 0.78/1.03
% 0.78/1.03 set(prolog_style_variables).
% 0.78/1.03 set(auto2).
% 0.78/1.03 % set(auto2) -> set(auto).
% 0.78/1.03 % set(auto) -> set(auto_inference).
% 0.78/1.03 % set(auto) -> set(auto_setup).
% 0.78/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.03 % set(auto) -> set(auto_limits).
% 0.78/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.03 % set(auto) -> set(auto_denials).
% 0.78/1.03 % set(auto) -> set(auto_process).
% 0.78/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.03 % set(auto2) -> assign(stats, some).
% 0.78/1.03 % set(auto2) -> clear(echo_input).
% 0.78/1.03 % set(auto2) -> set(quiet).
% 0.78/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.03 % set(auto2) -> clear(print_given).
% 0.78/1.03 assign(lrs_ticks,-1).
% 0.78/1.03 assign(sos_limit,10000).
% 0.78/1.03 assign(order,kbo).
% 0.78/1.03 set(lex_order_vars).
% 0.78/1.03 clear(print_given).
% 0.78/1.03
% 0.78/1.03 % formulas(sos). % not echoed (31 formulas)
% 0.78/1.03
% 0.78/1.03 ============================== end of input ==========================
% 0.78/1.03
% 0.78/1.03 % From the command line: assign(max_seconds, 300).
% 0.78/1.03
% 0.78/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.03
% 0.78/1.03 % Formulas that are not ordinary clauses:
% 0.78/1.03
% 0.78/1.03 ============================== end of process non-clausal formulas ===
% 0.78/1.03
% 0.78/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.78/1.03
% 0.78/1.03 ============================== PREDICATE ELIMINATION =================
% 0.78/1.03 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].
% 0.78/1.03 2 class_Ring__and__Field_Oordered__idom(t_b) # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 0.78/1.03 Derived: class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 0.78/1.03 3 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 0.78/1.03 Derived: class_Orderings_Olinorder(t_b). [resolve(3,a,2,a)].
% 0.78/1.03 4 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 0.78/1.03 Derived: class_LOrder_Ojoin__semilorder(t_b). [resolve(4,a,2,a)].
% 0.78/1.03 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].
% 0.78/1.03 Derived: class_OrderedGroup_Oab__group__add(t_b). [resolve(5,a,2,a)].
% 0.78/1.03 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].
% 0.78/1.03 Derived: class_OrderedGroup_Olordered__ab__group__abs(t_b). [resolve(6,a,2,a)].
% 0.78/1.03 7 class_Orderings_Olinorder(t_b). [resolve(3,a,2,a)].
% 0.78/1.03 8 -class_Orderings_Olinorder(A) | -c_less(B,C,A) | -c_lessequals(C,B,A) # label(cls_Orderings_Olinorder__not__le_1) # label(axiom). [assumption].
% 0.78/1.03 9 -class_Orderings_Olinorder(A) | c_less(B,C,A) | c_lessequals(C,B,A) # label(cls_Orderings_Olinorder__not__le_0) # label(axiom). [assumption].
% 0.78/1.03 10 -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].
% 0.78/1.03 Derived: -c_less(A,B,t_b) | -c_lessequals(B,A,t_b). [resolve(7,a,8,a)].
% 0.78/1.03 Derived: c_less(A,B,t_b) | c_lessequals(B,A,t_b). [resolve(7,a,9,a)].
% 0.78/1.03 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(7,a,10,a)].
% 0.78/1.03 11 class_LOrder_Ojoin__semilorder(t_b). [resolve(4,a,2,a)].
% 0.78/1.03 12 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 0.78/1.03 Derived: class_Orderings_Oorder(t_b). [resolve(11,a,12,a)].
% 0.78/1.03 13 class_OrderedGroup_Olordered__ab__group__abs(t_b). [resolve(6,a,2,a)].
% 0.78/1.03 14 -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].
% 0.78/1.03 15 -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].
% 0.78/1.03 16 -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].
% 0.78/1.03 17 -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].
% 0.78/1.03 18 -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].
% 0.78/1.03 Derived: class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(13,a,14,a)].
% 0.78/1.03 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b). [resolve(13,a,15,a)].
% 0.78/1.03 Derived: c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b). [resolve(13,a,16,a)].
% 0.78/1.03 Derived: c_HOL_Oabs(c_uminus(A,t_b),t_b) = c_HOL_Oabs(A,t_b). [resolve(13,a,17,a)].
% 0.78/1.03 Derived: -c_lessequals(A,c_0,t_b) | c_HOL_Oabs(A,t_b) = c_uminus(A,t_b). [resolve(13,a,18,a)].
% 0.78/1.03 19 class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 0.78/1.03 20 -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].
% 0.78/1.03 Derived: c_plus(c_0,A,t_b) = A. [resolve(19,a,20,a)].
% 0.78/1.03 21 class_OrderedGroup_Oab__group__add(t_b). [resolve(5,a,2,a)].
% 0.78/1.03 22 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,B,A) = c_0 # label(cls_OrderedGroup_Odiff__self_0) # label(axiom). [assumption].
% 0.78/1.03 23 -class_OrderedGroup_Oab__group__add(A) | c_minus(c_plus(B,C,A),C,A) = B # label(cls_OrderedGroup_Ocompare__rls__10_1) # label(axiom). [assumption].
% 0.78/1.03 24 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,C,A) = c_plus(B,c_uminus(C,A),A) # label(cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) # label(axiom). [assumption].
% 0.78/1.03 25 -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].
% 0.78/1.03 26 -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].
% 0.78/1.03 27 -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].
% 0.78/1.03 28 -class_OrderedGroup_Oab__group__add(A) | c_minus(c_minus(B,C,A),D,A) = c_minus(B,c_plus(C,D,A),A) # label(cls_OrderedGroup_Ocompare__rls__4_0) # label(axiom). [assumption].
% 0.78/1.03 Derived: c_minus(A,A,t_b) = c_0. [resolve(21,a,22,a)].
% 0.78/1.03 Derived: c_minus(c_plus(A,B,t_b),B,t_b) = A. [resolve(21,a,23,a)].
% 0.78/1.03 Derived: c_minus(A,B,t_b) = c_plus(A,c_uminus(B,t_b),t_b). [resolve(21,a,24,a)].
% 0.78/1.03 Derived: c_uminus(c_minus(A,B,t_b),t_b) = c_minus(B,A,t_b). [resolve(21,a,25,a)].
% 0.78/1.03 Derived: c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,B,t_b),C,t_b). [resolve(21,a,26,a)].
% 0.78/1.03 Derived: c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(c_plus(A,C,t_b),B,t_b). [resolve(21,a,27,a)].
% 0.78/1.03 Derived: c_minus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_plus(B,C,t_b),t_b). [resolve(21,a,28,a)].
% 1.13/1.40 29 class_Orderings_Oorder(t_b). [resolve(11,a,12,a)].
% 1.13/1.40 30 -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].
% 1.13/1.40 31 -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].
% 1.13/1.40 Derived: -c_less(A,B,t_b) | c_lessequals(A,B,t_b). [resolve(29,a,30,a)].
% 1.13/1.40 Derived: -c_lessequals(A,B,t_b) | -c_lessequals(C,A,t_b) | c_lessequals(C,B,t_b). [resolve(29,a,31,a)].
% 1.13/1.40 32 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b). [resolve(13,a,15,a)].
% 1.13/1.40 33 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A) # label(cls_OrderedGroup_Oadd__le__cancel__left_1) # label(axiom). [assumption].
% 1.13/1.40 34 -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].
% 1.13/1.40 Derived: -c_lessequals(A,B,t_b) | c_lessequals(c_plus(C,A,t_b),c_plus(C,B,t_b),t_b). [resolve(32,a,33,a)].
% 1.13/1.40 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,34,a)].
% 1.13/1.40 35 class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(13,a,14,a)].
% 1.13/1.40 36 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_minus(B,C,A),D,A) | c_less(B,c_plus(D,C,A),A) # label(cls_OrderedGroup_Ocompare__rls__6_0) # label(axiom). [assumption].
% 1.13/1.40 37 -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].
% 1.13/1.40 Derived: -c_less(c_minus(A,B,t_b),C,t_b) | c_less(A,c_plus(C,B,t_b),t_b). [resolve(35,a,36,a)].
% 1.13/1.40 Derived: -c_lessequals(A,c_plus(B,C,t_b),t_b) | c_lessequals(c_minus(A,C,t_b),B,t_b). [resolve(35,a,37,a)].
% 1.13/1.40
% 1.13/1.40 ============================== end predicate elimination =============
% 1.13/1.40
% 1.13/1.40 Auto_denials: (non-Horn, no changes).
% 1.13/1.40
% 1.13/1.40 Term ordering decisions:
% 1.13/1.40 Function symbol KB weights: t_b=1. c_0=1. v_x=1. c_HOL_Oabs=1. c_uminus=1. v_g=1. v_k=1. v_f=1. c_minus=1. c_plus=1. c_Orderings_Omax=1.
% 1.13/1.40
% 1.13/1.40 ============================== end of process initial clauses ========
% 1.13/1.40
% 1.13/1.40 ============================== CLAUSES FOR SEARCH ====================
% 1.13/1.40
% 1.13/1.40 ============================== end of clauses for search =============
% 1.13/1.40
% 1.13/1.40 ============================== SEARCH ================================
% 1.13/1.40
% 1.13/1.40 % Starting search at 0.01 seconds.
% 1.13/1.40
% 1.13/1.40 ============================== PROOF =================================
% 1.13/1.40 % SZS status Unsatisfiable
% 1.13/1.40 % SZS output start Refutation
% 1.13/1.40
% 1.13/1.40 % Proof 1 at 0.37 (+ 0.01) seconds.
% 1.13/1.40 % Length of proof is 102.
% 1.13/1.40 % Level of proof is 14.
% 1.13/1.40 % Maximum clause weight is 19.000.
% 1.13/1.40 % Given clauses 384.
% 1.13/1.40
% 1.13/1.40 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].
% 1.13/1.40 2 class_Ring__and__Field_Oordered__idom(t_b) # label(tfree_tcs) # label(negated_conjecture). [assumption].
% 1.13/1.40 3 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 1.13/1.40 4 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 1.13/1.40 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].
% 1.13/1.40 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].
% 1.13/1.40 7 class_Orderings_Olinorder(t_b). [resolve(3,a,2,a)].
% 1.13/1.40 8 -class_Orderings_Olinorder(A) | -c_less(B,C,A) | -c_lessequals(C,B,A) # label(cls_Orderings_Olinorder__not__le_1) # label(axiom). [assumption].
% 1.13/1.40 9 -class_Orderings_Olinorder(A) | c_less(B,C,A) | c_lessequals(C,B,A) # label(cls_Orderings_Olinorder__not__le_0) # label(axiom). [assumption].
% 1.13/1.40 10 -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].
% 1.13/1.40 11 class_LOrder_Ojoin__semilorder(t_b). [resolve(4,a,2,a)].
% 1.13/1.40 12 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 1.13/1.40 13 class_OrderedGroup_Olordered__ab__group__abs(t_b). [resolve(6,a,2,a)].
% 1.13/1.40 14 -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].
% 1.13/1.40 15 -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].
% 1.13/1.40 16 -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].
% 1.13/1.40 17 -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].
% 1.13/1.40 18 -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].
% 1.13/1.40 19 class_OrderedGroup_Ocomm__monoid__add(t_b). [resolve(1,a,2,a)].
% 1.13/1.40 20 -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].
% 1.13/1.40 21 class_OrderedGroup_Oab__group__add(t_b). [resolve(5,a,2,a)].
% 1.13/1.40 22 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,B,A) = c_0 # label(cls_OrderedGroup_Odiff__self_0) # label(axiom). [assumption].
% 1.13/1.40 23 -class_OrderedGroup_Oab__group__add(A) | c_minus(c_plus(B,C,A),C,A) = B # label(cls_OrderedGroup_Ocompare__rls__10_1) # label(axiom). [assumption].
% 1.13/1.40 24 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,C,A) = c_plus(B,c_uminus(C,A),A) # label(cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) # label(axiom). [assumption].
% 1.13/1.40 25 -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].
% 1.13/1.40 26 -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].
% 1.13/1.40 27 -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].
% 1.13/1.40 28 -class_OrderedGroup_Oab__group__add(A) | c_minus(c_minus(B,C,A),D,A) = c_minus(B,c_plus(C,D,A),A) # label(cls_OrderedGroup_Ocompare__rls__4_0) # label(axiom). [assumption].
% 1.13/1.40 29 class_Orderings_Oorder(t_b). [resolve(11,a,12,a)].
% 1.13/1.40 30 -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].
% 1.13/1.40 31 -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].
% 1.13/1.40 32 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b). [resolve(13,a,15,a)].
% 1.13/1.40 33 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A) # label(cls_OrderedGroup_Oadd__le__cancel__left_1) # label(axiom). [assumption].
% 1.13/1.40 34 -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].
% 1.13/1.40 35 class_OrderedGroup_Opordered__ab__group__add(t_b). [resolve(13,a,14,a)].
% 1.13/1.40 36 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_minus(B,C,A),D,A) | c_less(B,c_plus(D,C,A),A) # label(cls_OrderedGroup_Ocompare__rls__6_0) # label(axiom). [assumption].
% 1.13/1.40 37 -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].
% 1.13/1.40 38 c_lessequals(v_g(A),v_k(A),t_b) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 1.13/1.40 39 -c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(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].
% 1.13/1.40 40 -c_less(A,B,t_b) | -c_lessequals(B,A,t_b). [resolve(7,a,8,a)].
% 1.13/1.40 41 c_less(A,B,t_b) | c_lessequals(B,A,t_b). [resolve(7,a,9,a)].
% 1.13/1.40 42 -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(7,a,10,a)].
% 1.13/1.40 43 c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b). [resolve(13,a,16,a)].
% 1.13/1.40 44 c_HOL_Oabs(c_uminus(A,t_b),t_b) = c_HOL_Oabs(A,t_b). [resolve(13,a,17,a)].
% 1.13/1.40 45 -c_lessequals(A,c_0,t_b) | c_HOL_Oabs(A,t_b) = c_uminus(A,t_b). [resolve(13,a,18,a)].
% 1.13/1.40 46 -c_lessequals(A,c_0,t_b) | c_uminus(A,t_b) = c_HOL_Oabs(A,t_b). [copy(45),flip(b)].
% 1.13/1.40 47 c_plus(c_0,A,t_b) = A. [resolve(19,a,20,a)].
% 1.13/1.40 48 c_minus(A,A,t_b) = c_0. [resolve(21,a,22,a)].
% 1.13/1.40 49 c_minus(c_plus(A,B,t_b),B,t_b) = A. [resolve(21,a,23,a)].
% 1.13/1.40 50 c_minus(A,B,t_b) = c_plus(A,c_uminus(B,t_b),t_b). [resolve(21,a,24,a)].
% 1.13/1.40 51 c_plus(A,c_uminus(B,t_b),t_b) = c_minus(A,B,t_b). [copy(50),flip(a)].
% 1.13/1.40 52 c_uminus(c_minus(A,B,t_b),t_b) = c_minus(B,A,t_b). [resolve(21,a,25,a)].
% 1.13/1.40 53 c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,B,t_b),C,t_b). [resolve(21,a,26,a)].
% 1.13/1.40 54 c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(c_plus(A,C,t_b),B,t_b). [resolve(21,a,27,a)].
% 1.13/1.40 55 c_minus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_plus(B,C,t_b),t_b). [resolve(21,a,28,a)].
% 1.13/1.40 56 -c_less(A,B,t_b) | c_lessequals(A,B,t_b). [resolve(29,a,30,a)].
% 1.13/1.40 57 -c_lessequals(A,B,t_b) | -c_lessequals(C,A,t_b) | c_lessequals(C,B,t_b). [resolve(29,a,31,a)].
% 1.13/1.40 58 -c_lessequals(A,B,t_b) | c_lessequals(c_plus(C,A,t_b),c_plus(C,B,t_b),t_b). [resolve(32,a,33,a)].
% 1.13/1.40 59 -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,34,a)].
% 1.13/1.40 60 -c_less(c_minus(A,B,t_b),C,t_b) | c_less(A,c_plus(C,B,t_b),t_b). [resolve(35,a,36,a)].
% 1.13/1.40 61 -c_lessequals(A,c_plus(B,C,t_b),t_b) | c_lessequals(c_minus(A,C,t_b),B,t_b). [resolve(35,a,37,a)].
% 1.13/1.40 68 -c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b). [ur(42,a,43,a,c,39,a)].
% 1.13/1.40 70 c_minus(c_0,A,t_b) = c_uminus(A,t_b). [para(51(a,1),47(a,1))].
% 1.13/1.40 74 c_minus(A,c_plus(B,A,t_b),t_b) = c_uminus(B,t_b). [para(49(a,1),52(a,1,1)),flip(a)].
% 1.13/1.40 75 c_uminus(c_uminus(A,t_b),t_b) = A. [para(49(a,1),52(a,2)),rewrite([74(4)])].
% 1.13/1.40 76 c_minus(c_plus(A,B,t_b),C,t_b) = c_minus(A,c_minus(C,B,t_b),t_b). [para(52(a,1),51(a,1,2)),rewrite([53(4)])].
% 1.13/1.40 77 c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_minus(B,C,t_b),t_b). [back_rewrite(54),rewrite([76(8)])].
% 1.13/1.40 78 c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(A,c_minus(C,B,t_b),t_b). [back_rewrite(53),rewrite([76(8)])].
% 1.13/1.40 80 c_minus(A,c_plus(A,B,t_b),t_b) = c_uminus(B,t_b). [para(48(a,1),55(a,1,1)),rewrite([70(3)]),flip(a)].
% 1.13/1.40 81 c_minus(A,c_minus(B,C,t_b),t_b) = c_minus(C,c_minus(B,A,t_b),t_b). [para(55(a,1),52(a,1,1)),rewrite([52(6),76(4)])].
% 1.13/1.40 83 c_lessequals(A,B,t_b) | c_lessequals(B,A,t_b). [resolve(56,a,41,a)].
% 1.13/1.40 85 c_lessequals(A,A,t_b). [factor(83,a,b)].
% 1.13/1.40 90 -c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_0,t_b). [ur(57,a,43,a,c,39,a)].
% 1.13/1.40 92 c_lessequals(c_plus(A,v_g(B),t_b),c_plus(A,v_k(B),t_b),t_b). [resolve(58,a,38,a)].
% 1.13/1.40 95 -c_lessequals(c_plus(A,B,t_b),B,t_b) | c_lessequals(A,c_0,t_b). [para(47(a,1),59(a,2))].
% 1.13/1.40 97 c_less(A,c_plus(B,C,t_b),t_b) | c_lessequals(B,c_minus(A,C,t_b),t_b). [resolve(60,a,41,a)].
% 1.13/1.40 100 -c_lessequals(A,B,t_b) | c_lessequals(c_minus(A,B,t_b),c_0,t_b). [para(47(a,1),61(a,2))].
% 1.13/1.40 116 -c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b). [ur(42,a,85,a,c,90,a)].
% 1.13/1.40 121 -c_lessequals(v_f(v_x),v_k(v_x),t_b). [ur(61,b,116,a),rewrite([47(7)])].
% 1.13/1.40 125 -c_lessequals(v_f(v_x),v_g(v_x),t_b). [ur(57,a,38,a,c,121,a)].
% 1.13/1.40 127 -c_lessequals(c_plus(v_f(v_x),A,t_b),c_plus(v_g(v_x),A,t_b),t_b). [ur(59,b,125,a)].
% 1.13/1.40 129 c_minus(A,c_uminus(B,t_b),t_b) = c_plus(A,B,t_b). [para(75(a,1),51(a,1,2)),flip(a)].
% 1.13/1.40 259 -c_lessequals(v_f(v_x),c_plus(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),v_k(v_x),t_b),t_b). [ur(61,b,68,a)].
% 1.13/1.40 350 c_minus(A,c_minus(B,c_minus(C,A,t_b),t_b),t_b) = c_minus(C,B,t_b). [para(52(a,1),74(a,2)),rewrite([77(4)])].
% 1.13/1.40 436 c_minus(A,c_minus(A,B,t_b),t_b) = B. [para(48(a,1),77(a,1,1)),rewrite([47(3)]),flip(a)].
% 1.13/1.40 478 -c_lessequals(c_minus(v_f(v_x),A,t_b),c_minus(v_g(v_x),A,t_b),t_b). [para(51(a,1),127(a,1)),rewrite([51(10)])].
% 1.13/1.40 485 c_plus(A,B,t_b) = c_plus(B,A,t_b). [para(74(a,1),436(a,1,2)),rewrite([129(4)])].
% 1.13/1.40 516 -c_lessequals(v_f(v_x),c_plus(v_k(v_x),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b). [back_rewrite(259),rewrite([485(14)])].
% 1.13/1.40 556 c_minus(A,c_plus(B,A,t_b),t_b) = c_uminus(B,t_b). [para(80(a,1),55(a,1)),rewrite([485(6),78(6),78(8),55(6),485(4),436(8)]),flip(a)].
% 1.13/1.40 587 c_lessequals(A,c_0,t_b) | c_lessequals(B,c_plus(A,B,t_b),t_b). [resolve(95,a,83,b)].
% 1.13/1.40 632 -c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b). [para(48(a,1),478(a,2))].
% 1.13/1.40 754 c_lessequals(c_minus(A,c_minus(v_k(B),v_g(B),t_b),t_b),A,t_b). [resolve(92,a,61,a),rewrite([76(6)])].
% 1.13/1.40 1185 c_lessequals(A,c_0,t_b) | c_lessequals(c_uminus(A,t_b),c_0,t_b). [resolve(587,b,100,a),rewrite([556(7)])].
% 1.13/1.40 1200 c_lessequals(A,c_0,t_b) | c_HOL_Oabs(A,t_b) = A. [resolve(1185,b,46,a),rewrite([75(7),44(7)]),flip(b)].
% 1.13/1.40 1205 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(1200,a,632,a)].
% 1.13/1.40 1232 -c_lessequals(v_f(v_x),c_minus(v_k(v_x),c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b). [back_rewrite(516),rewrite([1205(12),78(12)])].
% 1.13/1.40 3860 -c_less(A,c_minus(A,c_minus(v_k(B),v_g(B),t_b),t_b),t_b). [ur(40,b,754,a)].
% 1.13/1.40 3966 -c_less(A,c_minus(v_g(B),c_minus(v_k(B),A,t_b),t_b),t_b). [para(81(a,1),3860(a,2))].
% 1.13/1.40 3968 -c_less(c_minus(v_k(A),B,t_b),c_minus(v_g(A),B,t_b),t_b). [para(436(a,1),3966(a,2,2))].
% 1.13/1.40 4315 -c_less(c_minus(v_k(A),c_minus(v_g(A),B,t_b),t_b),B,t_b). [para(436(a,1),3968(a,2))].
% 1.13/1.40 4518 c_lessequals(A,c_minus(v_k(B),c_minus(v_g(B),A,t_b),t_b),t_b). [resolve(4315,a,97,a),rewrite([55(10),485(8),78(8),76(6),350(8)])].
% 1.13/1.40 4519 $F. [resolve(4518,a,1232,a)].
% 1.13/1.40
% 1.13/1.40 % SZS output end Refutation
% 1.13/1.40 ============================== end of proof ==========================
% 1.13/1.40
% 1.13/1.40 ============================== STATISTICS ============================
% 1.13/1.40
% 1.13/1.40 Given=384. Generated=8221. Kept=4479. proofs=1.
% 1.13/1.40 Usable=371. Sos=3997. Demods=68. Limbo=0, Disabled=169. Hints=0.
% 1.13/1.40 Megabytes=4.59.
% 1.13/1.40 User_CPU=0.37, System_CPU=0.01, Wall_clock=0.
% 1.13/1.40
% 1.13/1.40 ============================== end of statistics =====================
% 1.13/1.40
% 1.13/1.40 ============================== end of search =========================
% 1.13/1.40
% 1.13/1.40 THEOREM PROVED
% 1.13/1.40 % SZS status Unsatisfiable
% 1.13/1.40
% 1.13/1.40 Exiting with 1 proof.
% 1.13/1.40
% 1.13/1.40 Process 366 exit (max_proofs) Fri Jul 8 04:57:30 2022
% 1.13/1.40 Prover9 interrupted
%------------------------------------------------------------------------------