TSTP Solution File: SWV882-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV882-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 : Wed Jul 20 21:15:08 EDT 2022
% Result : Unsatisfiable 18.73s 19.04s
% Output : Refutation 18.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV882-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n022.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
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 16:50:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.90/1.25 ============================== Prover9 ===============================
% 0.90/1.25 Prover9 (32) version 2009-11A, November 2009.
% 0.90/1.25 Process 26244 was started by sandbox2 on n022.cluster.edu,
% 0.90/1.25 Tue Jun 14 16:50:18 2022
% 0.90/1.25 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26090_n022.cluster.edu".
% 0.90/1.25 ============================== end of head ===========================
% 0.90/1.25
% 0.90/1.25 ============================== INPUT =================================
% 0.90/1.25
% 0.90/1.25 % Reading from file /tmp/Prover9_26090_n022.cluster.edu
% 0.90/1.25
% 0.90/1.25 set(prolog_style_variables).
% 0.90/1.25 set(auto2).
% 0.90/1.25 % set(auto2) -> set(auto).
% 0.90/1.25 % set(auto) -> set(auto_inference).
% 0.90/1.25 % set(auto) -> set(auto_setup).
% 0.90/1.25 % set(auto_setup) -> set(predicate_elim).
% 0.90/1.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.90/1.25 % set(auto) -> set(auto_limits).
% 0.90/1.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.90/1.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.90/1.25 % set(auto) -> set(auto_denials).
% 0.90/1.25 % set(auto) -> set(auto_process).
% 0.90/1.25 % set(auto2) -> assign(new_constants, 1).
% 0.90/1.25 % set(auto2) -> assign(fold_denial_max, 3).
% 0.90/1.25 % set(auto2) -> assign(max_weight, "200.000").
% 0.90/1.25 % set(auto2) -> assign(max_hours, 1).
% 0.90/1.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.90/1.25 % set(auto2) -> assign(max_seconds, 0).
% 0.90/1.25 % set(auto2) -> assign(max_minutes, 5).
% 0.90/1.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.90/1.25 % set(auto2) -> set(sort_initial_sos).
% 0.90/1.25 % set(auto2) -> assign(sos_limit, -1).
% 0.90/1.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.90/1.25 % set(auto2) -> assign(max_megs, 400).
% 0.90/1.25 % set(auto2) -> assign(stats, some).
% 0.90/1.25 % set(auto2) -> clear(echo_input).
% 0.90/1.25 % set(auto2) -> set(quiet).
% 0.90/1.25 % set(auto2) -> clear(print_initial_clauses).
% 0.90/1.25 % set(auto2) -> clear(print_given).
% 0.90/1.25 assign(lrs_ticks,-1).
% 0.90/1.25 assign(sos_limit,10000).
% 0.90/1.25 assign(order,kbo).
% 0.90/1.25 set(lex_order_vars).
% 0.90/1.25 clear(print_given).
% 0.90/1.25
% 0.90/1.25 % formulas(sos). % not echoed (627 formulas)
% 0.90/1.25
% 0.90/1.25 ============================== end of input ==========================
% 0.90/1.25
% 0.90/1.25 % From the command line: assign(max_seconds, 300).
% 0.90/1.25
% 0.90/1.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.90/1.25
% 0.90/1.25 % Formulas that are not ordinary clauses:
% 0.90/1.25
% 0.90/1.25 ============================== end of process non-clausal formulas ===
% 0.90/1.25
% 0.90/1.25 ============================== PROCESS INITIAL CLAUSES ===============
% 0.90/1.25
% 0.90/1.25 ============================== PREDICATE ELIMINATION =================
% 0.90/1.25 1 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.90/1.25 2 -class_OrderedGroup_Oab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 0.90/1.25 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(1,a,2,a)].
% 0.90/1.25 3 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.90/1.25 4 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 0.90/1.25 5 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 0.90/1.25 6 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 0.90/1.25 7 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(A),A,B),C,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__0_0) # label(axiom). [assumption].
% 0.90/1.25 8 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 0.90/1.25 9 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 0.90/1.25 10 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 0.90/1.25 11 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setsum__def_1) # label(axiom). [assumption].
% 0.90/1.25 12 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(C,D) # label(cls_setsum__infinite_0) # label(axiom). [assumption].
% 0.90/1.25 13 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom). [assumption].
% 0.90/1.25 14 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 0.90/1.25 15 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 0.90/1.25 16 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 0.90/1.25 17 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Set_Oinsert(C,D,E),E,A) = c_HOL_Oplus__class_Oplus(hAPP(B,C),c_Finite__Set_Osetsum(B,D,E,A),A) | c_in(C,D,E) | -c_Finite__Set_Ofinite(D,E) # label(cls_setsum__insert_0) # label(axiom). [assumption].
% 0.90/1.25 18 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_HOL_Oplus__class_Oplus(hAPP(B,E),c_Finite__Set_Osetsum(B,c_HOL_Ominus__class_Ominus(C,c_Set_Oinsert(E,c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)),D),tc_fun(D,tc_bool)),D,A),A) | -c_in(E,C,D) | -c_Finite__Set_Ofinite(C,D) # label(cls_setsum__diff1_H_0) # label(axiom). [assumption].
% 0.90/1.25 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat). [resolve(3,a,4,a)].
% 0.90/1.25 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(3,a,6,b)].
% 0.90/1.25 Derived: c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,A),B,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(3,a,7,a)].
% 0.90/1.25 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(3,a,8,b)].
% 0.90/1.25 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(3,a,9,b)].
% 0.90/1.25 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) = c_HOL_Oplus__class_Oplus(B,A,tc_nat). [resolve(3,a,10,a)].
% 0.90/1.25 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(B,C). [resolve(3,a,11,a)].
% 0.90/1.25 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(3,a,13,a)].
% 0.90/1.28 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(3,a,14,b)].
% 0.90/1.28 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(3,a,15,a)].
% 0.90/1.28 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(3,a,16,a)].
% 0.90/1.28 Derived: c_Finite__Set_Osetsum(A,c_Set_Oinsert(B,C,D),D,tc_nat) = c_HOL_Oplus__class_Oplus(hAPP(A,B),c_Finite__Set_Osetsum(A,C,D,tc_nat),tc_nat) | c_in(B,C,D) | -c_Finite__Set_Ofinite(C,D). [resolve(3,a,17,a)].
% 0.90/1.28 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = c_HOL_Oplus__class_Oplus(hAPP(A,D),c_Finite__Set_Osetsum(A,c_HOL_Ominus__class_Ominus(B,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C,tc_nat),tc_nat) | -c_in(D,B,C) | -c_Finite__Set_Ofinite(B,C). [resolve(3,a,18,a)].
% 0.90/1.28 19 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.90/1.28 20 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 0.90/1.28 21 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 0.90/1.28 22 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 0.90/1.28 23 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 0.90/1.28 24 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 0.90/1.28 25 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 0.90/1.28 26 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 0.90/1.28 27 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 0.90/1.28 28 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 0.90/1.28 29 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 0.90/1.28 30 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 0.90/1.28 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat). [resolve(19,a,20,a)].
% 0.90/1.28 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). [resolve(19,a,24,a)].
% 0.90/1.30 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,D,tc_nat),tc_nat). [resolve(19,a,27,a)].
% 0.90/1.30 31 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.90/1.30 32 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 0.90/1.30 33 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 0.90/1.30 34 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 0.90/1.30 35 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 0.90/1.30 36 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 0.90/1.30 37 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 0.90/1.30 38 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 0.90/1.30 39 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 0.90/1.30 40 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 0.90/1.30 41 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 0.90/1.30 42 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 0.90/1.30 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(31,a,32,a)].
% 0.90/1.38 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(31,a,34,a)].
% 0.90/1.38 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(31,a,35,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(31,a,36,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(31,a,37,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(31,a,38,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(31,a,39,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(31,a,40,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(31,a,41,a)].
% 0.90/1.38 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(31,a,42,a)].
% 0.90/1.38 43 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 0.90/1.38 44 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 0.90/1.38 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(43,a,44,a)].
% 0.90/1.38 45 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.90/1.38 46 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 0.90/1.38 47 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 0.90/1.38 48 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 0.90/1.38 49 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 0.90/1.38 50 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 0.90/1.38 51 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 0.90/1.38 52 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 0.90/1.38 53 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 0.90/1.38 54 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 0.90/1.38 55 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 0.90/1.38 56 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 0.90/1.38 57 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 0.90/1.38 58 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 0.90/1.38 59 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 0.90/1.38 60 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_lessequals(B,C,tc_nat) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 0.90/1.38 61 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 0.90/1.38 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(45,a,46,a)].
% 0.90/1.38 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(45,a,47,a)].
% 0.90/1.38 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(45,a,48,a)].
% 0.90/1.38 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(45,a,49,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(45,a,50,a)].
% 0.90/1.38 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(45,a,51,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(45,a,53,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(45,a,54,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(45,a,55,a)].
% 0.90/1.38 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(45,a,56,a)].
% 0.90/1.40 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(45,a,57,a)].
% 0.90/1.40 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(45,a,58,a)].
% 0.90/1.40 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(45,a,59,a)].
% 0.90/1.40 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(45,a,60,a)].
% 0.90/1.40 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(45,a,61,a)].
% 0.90/1.40 62 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.90/1.40 63 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 0.90/1.40 64 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 0.90/1.40 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(62,a,63,a)].
% 0.90/1.40 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(62,a,64,a)].
% 0.90/1.40 65 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.90/1.40 66 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.90/1.40 67 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.90/1.40 68 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.90/1.40 69 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.90/1.40 70 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.90/1.40 71 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 0.90/1.40 72 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 0.90/1.40 73 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 0.90/1.40 74 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 0.90/1.40 75 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 0.90/1.40 76 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 0.90/1.40 77 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 0.90/1.40 78 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 0.90/1.40 79 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 0.90/1.40 80 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.90/1.40 81 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Max__singleton_0) # label(axiom). [assumption].
% 0.90/1.40 82 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Min__singleton_0) # label(axiom). [assumption].
% 0.90/1.40 83 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),C,A) | -c_in(C,B,A) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 0.90/1.40 84 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Finite__Set_Olinorder__class_OMax(C,A),A) | -c_in(B,C,A) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 0.90/1.40 85 -class_Orderings_Olinorder(A) | c_in(c_Finite__Set_Olinorder__class_OMax(B,A),B,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom). [assumption].
% 0.90/1.40 86 -class_Orderings_Olinorder(A) | c_in(c_Finite__Set_Olinorder__class_OMin(B,A),B,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom). [assumption].
% 0.90/1.40 87 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMax(B,A),c_Finite__Set_Olinorder__class_OMax(C,A),A) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(B,C,tc_fun(A,tc_bool)) # label(cls_Max__mono_0) # label(axiom). [assumption].
% 0.90/1.40 88 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),c_Finite__Set_Olinorder__class_OMin(C,A),A) | -c_Finite__Set_Ofinite(B,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(C,B,tc_fun(A,tc_bool)) # label(cls_Min__antimono_0) # label(axiom). [assumption].
% 0.90/1.40 89 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.90/1.40 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(65,a,66,a)].
% 0.90/1.40 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(65,a,67,a)].
% 0.90/1.40 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(65,a,71,a)].
% 0.90/1.40 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(65,a,73,a)].
% 0.90/1.40 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(65,a,76,a)].
% 0.90/1.40 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(65,a,80,a)].
% 0.90/1.40 Derived: c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = A. [resolve(65,a,81,a)].
% 0.90/1.40 Derived: c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = A. [resolve(65,a,82,a)].
% 0.90/1.40 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),B,tc_nat) | -c_in(B,A,tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(65,a,83,a)].
% 0.90/1.40 Derived: c_lessequals(A,c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -c_in(A,B,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(65,a,84,a)].
% 0.90/1.40 Derived: c_in(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),A,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(65,a,85,a)].
% 0.90/1.40 Derived: c_in(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),A,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(65,a,86,a)].
% 0.90/1.40 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(A,B,tc_fun(tc_nat,tc_bool)). [resolve(65,a,87,a)].
% 0.90/1.40 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),c_Finite__Set_Olinorder__class_OMin(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(B,A,tc_fun(tc_nat,tc_bool)). [resolve(65,a,88,a)].
% 0.90/1.46 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(65,a,89,a)].
% 0.90/1.46 90 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 0.90/1.46 91 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 0.90/1.46 92 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 0.90/1.46 93 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 0.90/1.46 94 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),A) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 0.90/1.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(90,a,91,a)].
% 0.90/1.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(90,a,92,a)].
% 0.90/1.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(90,a,93,a)].
% 0.90/1.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(90,a,94,a)].
% 0.90/1.46 95 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.90/1.46 96 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 0.90/1.46 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(95,a,96,a)].
% 0.90/1.46 97 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.90/1.46 98 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 0.90/1.46 99 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 0.90/1.46 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(97,a,99,a)].
% 0.90/1.46 100 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.90/1.46 101 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 0.90/1.46 102 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 0.90/1.46 103 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.90/1.46 104 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 0.90/1.51 105 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 0.90/1.51 106 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 0.90/1.51 107 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 0.90/1.51 108 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 0.90/1.51 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(103,a,104,a)].
% 0.90/1.51 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(103,a,105,a)].
% 0.90/1.51 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(103,a,106,a)].
% 0.90/1.51 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(103,a,107,a)].
% 0.90/1.51 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(103,a,108,a)].
% 0.90/1.51 109 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 0.90/1.51 110 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 0.90/1.51 111 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 0.90/1.51 112 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 0.90/1.51 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(109,a,110,a)].
% 0.90/1.51 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(109,a,111,a)].
% 0.90/1.51 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(109,a,112,a)].
% 0.90/1.51 113 hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(B),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -v_wt(B) # label(cls_assms_I3_J_1) # label(axiom). [assumption].
% 0.90/1.51 114 v_wt(c_Option_Othe(c_Com_Obody(A),tc_Com_Ocom)) | -c_in(A,v_U,tc_Com_Opname) # label(cls_assms_I4_J_0) # label(axiom). [assumption].
% 0.90/1.51 Derived: hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(B),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -c_in(B,v_U,tc_Com_Opname). [resolve(113,c,114,a)].
% 2.28/2.54 115 hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(B),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | c_in(v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname) | -v_wt(B) # label(cls_assms_I3_J_0) # label(axiom). [assumption].
% 2.28/2.54 Derived: hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(B),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | c_in(v_sko__local__Xassms__3__1(A,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname) | -c_in(B,v_U,tc_Com_Opname). [resolve(115,c,114,a)].
% 2.28/2.54 116 c_Finite__Set_Ocard(A,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) | -c_lessequals(A,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) | hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(B),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -v_wt(B) # label(cls_conjecture_7) # label(negated_conjecture). [assumption].
% 2.28/2.54 Derived: c_Finite__Set_Ocard(A,t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) | -c_lessequals(A,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) | hBOOL(hAPP(hAPP(v_P,A),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(B),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) | -c_in(B,v_U,tc_Com_Opname). [resolve(116,d,114,a)].
% 2.28/2.54 117 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 2.28/2.54 118 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 2.28/2.54 Derived: A = A. [resolve(117,b,118,a)].
% 2.28/2.54
% 2.28/2.54 ============================== end predicate elimination =============
% 2.28/2.54
% 2.28/2.54 Auto_denials: (non-Horn, no changes).
% 2.28/2.54
% 2.28/2.54 Term ordering decisions:
% 2.28/2.54 Function symbol KB weights: tc_nat=1. tc_bool=1. t_a=1. v_U=1. tc_Com_Opname=1. v_mgt__call=1. v_P=1. tc_Com_Ocom=1. v_G=1. v_na=1. v_pn=1. tc_fun=1. hAPP=1. c_Finite__Set_Ocard=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_Option_Othe=1. c_Inductive_Ocomplete__lattice__class_Ogfp=1. c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1=1. c_HOL_Ozero__class_Ozero=1. c_Suc=1. c_Orderings_Obot__class_Obot=1. c_HOL_Oone__class_Oone=1. c_Com_Obody=1. v_mgt=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ominus__class_Ominus=1. c_Set_Oinsert=1. c_COMBK=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_Finite__Set_Osetsum=1. v_sko__local__Xassms__3__1=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1=1. c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1=1. c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1=1.
% 2.28/2.54
% 2.28/2.54 ============================== end of process initial clauses ========
% 2.28/2.54
% 2.28/2.54 ============================== CLAUSES FOR SEARCH ====================
% 2.28/2.54
% 2.28/2.54 ============================== end of clauses for search =============
% 2.28/2.54
% 2.28/2.54 ============================== SEARCH ================================
% 2.28/2.54
% 2.28/2.54 % Starting search at 0.42 seconds.
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=49.000, iters=3357
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=45.000, iters=3351
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=40.000, iters=3462
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=35.000, iters=3341
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=33.000, iters=3409
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=32.000, iters=3377
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=31.000, iters=3400
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=30.000, iters=3359
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=29.000, iters=3394
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=28.000, iters=3359
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=27.000, iters=3333
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=26.000, iters=3348
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=25.000, iters=3354
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=24.000, iters=3391
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=23.000, iters=3336
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=22.000, iters=3367
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=21.000, iters=3368
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=20.000, iters=3351
% 18.73/19.04
% 18.73/19.04 Low Water (keep): wt=19.000, iters=3335
% 18.73/19.04
% 18.73/19.04 Low Water (keep): wt=18.000, iters=3346
% 18.73/19.04
% 18.73/19.04 Low Water (keep): wt=17.000, iters=3341
% 18.73/19.04
% 18.73/19.04 Low Water (keep): wt=16.000, iters=3336
% 18.73/19.04
% 18.73/19.04 Low Water (displace): id=11472, wt=43.000
% 18.73/19.04
% 18.73/19.04 Low Water (displace): id=14107, wt=31.000
% 18.73/19.04
% 18.73/19.04 Low Water (displace): id=14108, wt=25.000
% 18.73/19.04
% 18.73/19.04 Low Water (displace): id=14133, wt=23.000
% 18.73/19.04
% 18.73/19.04 Low Water (displace): id=21859, wt=15.000
% 18.73/19.04
% 18.73/19.04 ============================== PROOF =================================
% 18.73/19.04 % SZS status Unsatisfiable
% 18.73/19.04 % SZS output start Refutation
% 18.73/19.04
% 18.73/19.04 % Proof 1 at 17.41 (+ 0.49) seconds.
% 18.73/19.04 % Length of proof is 16.
% 18.73/19.04 % Level of proof is 5.
% 18.73/19.04 % Maximum clause weight is 20.000.
% 18.73/19.04 % Given clauses 7867.
% 18.73/19.04
% 18.73/19.04 262 c_Set_Oinsert(A,c_HOL_Ominus__class_Ominus(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C) = c_Set_Oinsert(A,B,C) # label(cls_insert__Diff__single_0) # label(axiom). [assumption].
% 18.73/19.04 420 c_Set_Oinsert(A,c_HOL_Ominus__class_Ominus(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C) = B | -c_in(A,B,C) # label(cls_insert__Diff_0) # label(axiom). [assumption].
% 18.73/19.04 421 c_Set_Oinsert(A,B,C) = B | -c_in(A,B,C). [copy(420),rewrite([262(8)])].
% 18.73/19.04 484 c_lessequals(c_Set_Oinsert(A,B,C),c_Set_Oinsert(A,D,C),tc_fun(C,tc_bool)) | -c_lessequals(B,D,tc_fun(C,tc_bool)) # label(cls_insert__mono_0) # label(axiom). [assumption].
% 18.73/19.04 532 c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)) # label(cls_empty__subsetI_0) # label(axiom). [assumption].
% 18.73/19.04 541 c_in(A,B,C) | -hBOOL(hAPP(B,A)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 18.73/19.04 542 hBOOL(hAPP(A,B)) | -c_in(B,A,C) # label(cls_mem__def_0) # label(axiom). [assumption].
% 18.73/19.04 568 hBOOL(hAPP(hAPP(v_P,A),B)) | -c_lessequals(B,A,tc_fun(t_a,tc_bool)) # label(cls_assms_I1_J_0) # label(axiom). [assumption].
% 18.73/19.04 586 c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 18.73/19.04 587 -hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) # label(cls_conjecture_6) # label(negated_conjecture). [assumption].
% 18.73/19.04 1543 c_lessequals(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),c_Set_Oinsert(A,C,B),tc_fun(B,tc_bool)). [resolve(532,a,484,b)].
% 18.73/19.04 1895 hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_pn))). [resolve(586,a,542,b)].
% 18.73/19.04 2738 c_in(hAPP(v_mgt__call,v_pn),v_G,A). [resolve(1895,a,541,b)].
% 18.73/19.04 2956 c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,A) = v_G. [resolve(2738,a,421,b)].
% 18.73/19.04 24779 c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),v_G,tc_fun(A,tc_bool)). [para(2956(a,1),1543(a,2))].
% 18.73/19.04 29274 $F. [resolve(24779,a,568,b),unit_del(a,587)].
% 18.73/19.04
% 18.73/19.04 % SZS output end Refutation
% 18.73/19.04 ============================== end of proof ==========================
% 18.73/19.04
% 18.73/19.04 ============================== STATISTICS ============================
% 18.73/19.04
% 18.73/19.04 Given=7867. Generated=930057. Kept=28992. proofs=1.
% 18.73/19.04 Usable=7442. Sos=9899. Demods=390. Limbo=1, Disabled=12355. Hints=0.
% 18.73/19.04 Megabytes=33.06.
% 18.73/19.04 User_CPU=17.41, System_CPU=0.49, Wall_clock=18.
% 18.73/19.04
% 18.73/19.04 ============================== end of statistics =====================
% 18.73/19.04
% 18.73/19.04 ============================== end of search =========================
% 18.73/19.04
% 18.73/19.04 THEOREM PROVED
% 18.73/19.04 % SZS status Unsatisfiable
% 18.73/19.04
% 18.73/19.04 Exiting with 1 proof.
% 18.73/19.04
% 18.73/19.04 Process 26244 exit (max_proofs) Tue Jun 14 16:50:36 2022
% 18.73/19.04 Prover9 interrupted
%------------------------------------------------------------------------------