TSTP Solution File: SWV854-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV854-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 21:15:02 EDT 2022
% Result : Unsatisfiable 22.98s 23.26s
% Output : Refutation 22.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV854-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n003.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 : Thu Jun 16 05:17:41 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.97/1.35 ============================== Prover9 ===============================
% 0.97/1.35 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.35 Process 20920 was started by sandbox on n003.cluster.edu,
% 0.97/1.35 Thu Jun 16 05:17:42 2022
% 0.97/1.35 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20767_n003.cluster.edu".
% 0.97/1.35 ============================== end of head ===========================
% 0.97/1.35
% 0.97/1.35 ============================== INPUT =================================
% 0.97/1.35
% 0.97/1.35 % Reading from file /tmp/Prover9_20767_n003.cluster.edu
% 0.97/1.35
% 0.97/1.35 set(prolog_style_variables).
% 0.97/1.35 set(auto2).
% 0.97/1.35 % set(auto2) -> set(auto).
% 0.97/1.35 % set(auto) -> set(auto_inference).
% 0.97/1.35 % set(auto) -> set(auto_setup).
% 0.97/1.35 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.35 % set(auto) -> set(auto_limits).
% 0.97/1.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.35 % set(auto) -> set(auto_denials).
% 0.97/1.35 % set(auto) -> set(auto_process).
% 0.97/1.35 % set(auto2) -> assign(new_constants, 1).
% 0.97/1.35 % set(auto2) -> assign(fold_denial_max, 3).
% 0.97/1.35 % set(auto2) -> assign(max_weight, "200.000").
% 0.97/1.35 % set(auto2) -> assign(max_hours, 1).
% 0.97/1.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.97/1.35 % set(auto2) -> assign(max_seconds, 0).
% 0.97/1.35 % set(auto2) -> assign(max_minutes, 5).
% 0.97/1.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.97/1.35 % set(auto2) -> set(sort_initial_sos).
% 0.97/1.35 % set(auto2) -> assign(sos_limit, -1).
% 0.97/1.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.97/1.35 % set(auto2) -> assign(max_megs, 400).
% 0.97/1.35 % set(auto2) -> assign(stats, some).
% 0.97/1.35 % set(auto2) -> clear(echo_input).
% 0.97/1.35 % set(auto2) -> set(quiet).
% 0.97/1.35 % set(auto2) -> clear(print_initial_clauses).
% 0.97/1.35 % set(auto2) -> clear(print_given).
% 0.97/1.35 assign(lrs_ticks,-1).
% 0.97/1.35 assign(sos_limit,10000).
% 0.97/1.35 assign(order,kbo).
% 0.97/1.35 set(lex_order_vars).
% 0.97/1.35 clear(print_given).
% 0.97/1.35
% 0.97/1.35 % formulas(sos). % not echoed (763 formulas)
% 0.97/1.35
% 0.97/1.35 ============================== end of input ==========================
% 0.97/1.35
% 0.97/1.35 % From the command line: assign(max_seconds, 300).
% 0.97/1.35
% 0.97/1.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.97/1.35
% 0.97/1.35 % Formulas that are not ordinary clauses:
% 0.97/1.35
% 0.97/1.35 ============================== end of process non-clausal formulas ===
% 0.97/1.35
% 0.97/1.35 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.35
% 0.97/1.35 ============================== PREDICATE ELIMINATION =================
% 0.97/1.35 1 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.97/1.35 2 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 0.97/1.35 3 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),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].
% 0.97/1.35 4 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 0.97/1.35 5 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),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].
% 0.97/1.35 6 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Orderings_Oord__class_Omin(B,C,A)),D) = c_Orderings_Oord__class_Omin(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_min__add__distrib__left_0) # label(axiom). [assumption].
% 0.97/1.35 7 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 0.97/1.35 8 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 0.97/1.35 9 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 0.97/1.35 10 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 0.97/1.35 11 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Orderings_Oord__class_Omax(B,C,A)),D) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 0.97/1.35 12 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 0.97/1.35 13 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 0.97/1.35 14 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 0.97/1.35 15 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 0.97/1.35 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(1,a,2,a)].
% 0.97/1.35 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(1,a,3,a)].
% 0.97/1.35 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(1,a,4,a)].
% 0.97/1.35 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(1,a,5,a)].
% 0.97/1.35 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Oord__class_Omin(A,B,tc_nat)),C) = c_Orderings_Oord__class_Omin(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(1,a,6,a)].
% 0.97/1.35 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,7,a)].
% 0.97/1.35 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(1,a,8,a)].
% 0.97/1.37 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(1,a,9,a)].
% 0.97/1.37 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(1,a,10,a)].
% 0.97/1.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Oord__class_Omax(A,B,tc_nat)),C) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(1,a,11,a)].
% 0.97/1.37 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,12,a)].
% 0.97/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(1,a,13,a)].
% 0.97/1.37 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(1,a,14,a)].
% 0.97/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(1,a,15,a)].
% 0.97/1.37 16 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 0.97/1.37 17 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 0.97/1.37 18 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 0.97/1.37 19 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__eq_0) # label(axiom). [assumption].
% 0.97/1.37 20 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__add__left__eq_0) # label(axiom). [assumption].
% 0.97/1.37 21 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__right__eq_0) # label(axiom). [assumption].
% 0.97/1.37 22 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 0.97/1.37 23 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 0.97/1.37 24 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A) # label(cls_mod__add__cong_0) # label(axiom). [assumption].
% 0.97/1.37 25 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom). [assumption].
% 0.97/1.37 26 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom). [assumption].
% 0.97/1.37 27 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom). [assumption].
% 0.97/1.42 28 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom). [assumption].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(16,a,17,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(16,a,18,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(16,a,19,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat). [resolve(16,a,20,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(16,a,21,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(16,a,22,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(16,a,23,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),C),B,tc_nat). [resolve(16,a,24,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(16,a,25,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat). [resolve(16,a,26,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat). [resolve(16,a,27,a)].
% 0.97/1.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat). [resolve(16,a,28,a)].
% 0.97/1.42 29 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 0.97/1.42 30 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 0.97/1.42 31 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 0.97/1.42 32 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 0.97/1.42 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(29,a,30,a)].
% 0.97/1.43 33 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.97/1.43 34 -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) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 0.97/1.43 35 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.43 36 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != 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].
% 0.97/1.43 37 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != 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].
% 0.97/1.43 38 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.43 39 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.43 40 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.43 41 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.43 42 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.43 43 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.43 44 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.43 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(33,a,34,a)].
% 0.97/1.45 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(33,a,35,a)].
% 0.97/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != 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(33,a,36,a)].
% 0.97/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != 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(33,a,37,a)].
% 0.97/1.45 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(33,a,38,a)].
% 0.97/1.45 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(33,a,39,a)].
% 0.97/1.45 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(33,a,40,a)].
% 0.97/1.45 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(33,a,41,a)].
% 0.97/1.45 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(33,a,42,a)].
% 0.97/1.45 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(33,a,43,a)].
% 0.97/1.45 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(33,a,44,a)].
% 0.97/1.45 45 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.97/1.45 46 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 0.97/1.45 47 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 0.97/1.45 48 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 0.97/1.45 49 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 0.97/1.56 50 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 0.97/1.56 51 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 0.97/1.56 52 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 0.97/1.56 53 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 0.97/1.56 54 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 0.97/1.56 55 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 0.97/1.56 56 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 0.97/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(45,a,46,a)].
% 0.97/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(45,a,48,a)].
% 0.97/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(45,a,49,a)].
% 0.97/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(45,a,50,a)].
% 0.97/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(45,a,51,a)].
% 0.97/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(45,a,53,a)].
% 0.97/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(45,a,54,a)].
% 0.97/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(45,a,55,a)].
% 0.97/1.56 57 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.97/1.56 58 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 0.97/1.56 59 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.97/1.56 60 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 0.97/1.61 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(59,a,60,a)].
% 0.97/1.61 61 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.97/1.61 62 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 0.97/1.61 63 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 0.97/1.61 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(61,a,63,a)].
% 0.97/1.61 64 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.97/1.61 65 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),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].
% 0.97/1.61 66 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 0.97/1.61 67 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 0.97/1.61 68 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 0.97/1.61 69 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 0.97/1.61 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(64,a,65,a)].
% 0.97/1.61 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(64,a,66,a)].
% 0.97/1.61 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(64,a,67,a)].
% 0.97/1.61 70 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.97/1.61 71 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 0.97/1.61 72 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 0.97/1.61 73 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.97/1.61 74 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),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].
% 2.15/2.49 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),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(73,a,74,a)].
% 2.15/2.49 75 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.15/2.49 76 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(B,c_HOL_Ozero__class_Ozero(tc_nat),C,A) = C # label(cls_of__nat__aux_Osimps_I1_J_0) # label(axiom). [assumption].
% 2.15/2.49 77 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(B,hAPP(c_Suc,C),D,A) = c_Nat_Osemiring__1__class_Oof__nat__aux(B,C,hAPP(B,D),A) # label(cls_of__nat__aux_Osimps_I2_J_0) # label(axiom). [assumption].
% 2.15/2.49 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(A,c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) = B. [resolve(75,a,76,a)].
% 2.15/2.49 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(A,hAPP(c_Suc,B),C,tc_nat) = c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,hAPP(A,C),tc_nat). [resolve(75,a,77,a)].
% 2.15/2.49 78 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 2.15/2.49 79 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 2.15/2.49 Derived: A = A. [resolve(78,b,79,a)].
% 2.15/2.49
% 2.15/2.49 ============================== end predicate elimination =============
% 2.15/2.49
% 2.15/2.49 Auto_denials: (non-Horn, no changes).
% 2.15/2.49
% 2.15/2.49 Term ordering decisions:
% 2.15/2.49 Function symbol KB weights: tc_nat=1. c_Suc=1. t_a=1. tc_bool=1. v_P=1. v_x=1. tc_Com_Ocom=1. v_Q=1. c_Com_Ocom_OSKIP=1. t_b=1. v_R=1. t_c=1. tc_Com_Opname=1. v_Procs=1. v_na=1. v_G=1. hAPP=1. tc_fun=1. c_Com_Ocom_OWhile=1. c_Com_Ocom_OSemi=1. c_Option_Othe=1. c_Com_Ocom_OAss=1. c_Option_Ooption_OSome=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__1=1. v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__2=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. c_Orderings_Obot__class_Obot=1. tc_Hoare__Mirabelle_Otriple=1. c_Com_Ocom_OBODY=1. c_Com_Obody=1. c_Fun_Oid=1. c_COMBI=1. c_Option_Ooption_ONone=1. c_HOL_Ominus__class_Ominus=1. c_Orderings_Oord__class_Omin=1. c_Orderings_Oord__class_Omax=1. c_Set_Oinsert=1. c_Divides_Odiv__class_Omod=1. c_in=1. c_Com_Ocom_OCond=1. c_Com_Ocom_OCall=1. c_Com_Ocom_OLocal=1. c_COMBK=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Nat_Onat_Onat__case=1. c_Hoare__Mirabelle_Otriple_Otriple__case=1. c_Nat_Onat_Onat__rec=1. c_Nat_Osemiring__1__class_Oof__nat__aux=1. c_Natural_Osko__Natural__Xevaln__elim__cases__6__1=1. v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1=1. v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2=1. v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3=1. c_Hoare__Mirabelle_Otriple_Otriple__rec=1. c_Power_Opower_Opower=1. c_Fun_Ocomp=1. c_Fun_Ofcomp=1. c_COMBB=1. c_COMBC=1. c_COMBS=1. c_Com_Ocom_Ocom__rec=1. c_Com_Ocom_Ocom__case=1.
% 2.15/2.49
% 2.15/2.49 ============================== end of process initial clauses ========
% 2.15/2.49
% 2.15/2.49 ============================== CLAUSES FOR SEARCH ====================
% 2.15/2.49
% 2.15/2.49 ============================== end of clauses for search =============
% 2.15/2.49
% 2.15/2.49 ============================== SEARCH ================================
% 2.15/2.49
% 2.15/2.49 % Starting search at 0.49 seconds.
% 2.15/2.49
% 2.15/2.49 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 86 (0.00 of 0.76 sec).
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=48.000, iters=3377
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=45.000, iters=3334
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=43.000, iters=3418
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=39.000, iters=3352
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=37.000, iters=3454
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=35.000, iters=3443
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=31.000, iters=3467
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=30.000, iters=3422
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=29.000, iters=3418
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=27.000, iters=3336
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=25.000, iters=3354
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=24.000, iters=3379
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=22.000, iters=3342
% 2.15/2.49
% 2.15/2.49 Low Water (keep): wt=20.000, iters=3457
% 4.27/4.55
% 4.27/4.55 Low Water (keep): wt=19.000, iters=3342
% 4.27/4.55
% 4.27/4.55 Low Water (keep): wt=18.000, iters=3371
% 4.27/4.55
% 4.27/4.55 Low Water (keep): wt=17.000, iters=3672
% 4.27/4.55
% 4.27/4.55 Low Water (keep): wt=16.000, iters=3506
% 4.27/4.55
% 4.27/4.55 Low Water (keep): wt=14.000, iters=3345
% 4.27/4.55
% 4.27/4.55 Low Water (keep): wt=13.000, iters=3337
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=2530, wt=200.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4018, wt=199.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3728, wt=198.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3762, wt=197.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=2628, wt=196.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3575, wt=195.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3578, wt=194.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4020, wt=193.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=2769, wt=192.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4213, wt=191.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3881, wt=189.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3743, wt=188.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3763, wt=187.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3883, wt=186.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3756, wt=185.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3879, wt=184.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=2659, wt=183.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3456, wt=182.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3733, wt=181.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3279, wt=180.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3591, wt=179.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3887, wt=178.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4217, wt=177.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3873, wt=176.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3577, wt=175.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3461, wt=174.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3773, wt=173.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3889, wt=172.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3751, wt=171.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4224, wt=170.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3740, wt=169.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=2626, wt=168.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3750, wt=167.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3768, wt=166.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3780, wt=165.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3588, wt=164.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4220, wt=163.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4218, wt=162.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4019, wt=161.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4030, wt=160.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3786, wt=159.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4232, wt=158.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3781, wt=157.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3286, wt=156.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3884, wt=155.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4227, wt=154.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3754, wt=153.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3589, wt=152.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3863, wt=151.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4022, wt=150.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=2874, wt=149.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4225, wt=148.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3729, wt=147.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4024, wt=146.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4211, wt=145.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3880, wt=144.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3731, wt=143.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4032, wt=142.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3885, wt=141.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3554, wt=140.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3764, wt=139.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4228, wt=138.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3888, wt=137.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3706, wt=136.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3875, wt=135.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4233, wt=134.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4242, wt=133.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3303, wt=132.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=3738, wt=131.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4219, wt=130.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4300, wt=129.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=4033, wt=128.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=11874, wt=45.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=11816, wt=44.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=9249, wt=43.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=11115, wt=40.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=11682, wt=35.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=10821, wt=34.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=11898, wt=33.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=11890, wt=32.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=12362, wt=31.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=12344, wt=30.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=12538, wt=29.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=12521, wt=28.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=12633, wt=27.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=12602, wt=26.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=13090, wt=25.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=13515, wt=24.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=13985, wt=23.000
% 4.27/4.55
% 4.27/4.55 Low Water (displace): id=15803, wt=20.000
% 22.98/23.26
% 22.98/23.26 Low Water (displace): id=15813, wt=19.000
% 22.98/23.26
% 22.98/23.26 Low Water (displace): id=15822, wt=17.000
% 22.98/23.26
% 22.98/23.26 Low Water (displace): id=17160, wt=16.000
% 22.98/23.26
% 22.98/23.26 Low Water (displace): id=17367, wt=12.000
% 22.98/23.26
% 22.98/23.26 ============================== PROOF =================================
% 22.98/23.26 % SZS status Unsatisfiable
% 22.98/23.26 % SZS output start Refutation
% 22.98/23.26
% 22.98/23.26 % Proof 1 at 21.18 (+ 0.86) seconds.
% 22.98/23.26 % Length of proof is 6.
% 22.98/23.26 % Level of proof is 2.
% 22.98/23.26 % Maximum clause weight is 22.000.
% 22.98/23.26 % Given clauses 9383.
% 22.98/23.26
% 22.98/23.26 623 c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,A),c_Hoare__Mirabelle_Otriple_Otriple(B,c_Com_Ocom_OBODY(C),D,E),E) | -c_Hoare__Mirabelle_Otriple__valid(A,c_Hoare__Mirabelle_Otriple_Otriple(B,c_Option_Othe(c_Com_Obody(C),tc_Com_Ocom),D,E),E) # label(cls_Body__triple__valid__Suc_0) # label(axiom). [assumption].
% 22.98/23.26 626 hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 22.98/23.26 627 -c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 22.98/23.26 630 c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,A),c_Option_Othe(c_Com_Obody(A),tc_Com_Ocom),hAPP(v_Q,A),t_a),t_a) | -hBOOL(c_in(A,v_Procs,tc_Com_Opname)) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 22.98/23.26 2042 c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a). [resolve(630,b,626,a)].
% 22.98/23.26 23707 $F. [resolve(2042,a,623,b),unit_del(a,627)].
% 22.98/23.26
% 22.98/23.26 % SZS output end Refutation
% 22.98/23.26 ============================== end of proof ==========================
% 22.98/23.26
% 22.98/23.26 ============================== STATISTICS ============================
% 22.98/23.26
% 22.98/23.26 Given=9383. Generated=1695971. Kept=23498. proofs=1.
% 22.98/23.26 Usable=9213. Sos=9812. Demods=741. Limbo=0, Disabled=5291. Hints=0.
% 22.98/23.26 Megabytes=28.19.
% 22.98/23.26 User_CPU=21.18, System_CPU=0.86, Wall_clock=22.
% 22.98/23.26
% 22.98/23.26 ============================== end of statistics =====================
% 22.98/23.26
% 22.98/23.26 ============================== end of search =========================
% 22.98/23.26
% 22.98/23.26 THEOREM PROVED
% 22.98/23.26 % SZS status Unsatisfiable
% 22.98/23.26
% 22.98/23.26 Exiting with 1 proof.
% 22.98/23.26
% 22.98/23.26 Process 20920 exit (max_proofs) Thu Jun 16 05:18:04 2022
% 22.98/23.26 Prover9 interrupted
%------------------------------------------------------------------------------