TSTP Solution File: LCL806-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL806-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 : Sun Jul 17 13:50:22 EDT 2022
% Result : Unsatisfiable 12.37s 12.68s
% Output : Refutation 12.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL806-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 11:47:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.89/1.23 ============================== Prover9 ===============================
% 0.89/1.23 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.23 Process 17804 was started by sandbox on n020.cluster.edu,
% 0.89/1.23 Mon Jul 4 11:47:15 2022
% 0.89/1.23 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17427_n020.cluster.edu".
% 0.89/1.23 ============================== end of head ===========================
% 0.89/1.23
% 0.89/1.23 ============================== INPUT =================================
% 0.89/1.23
% 0.89/1.23 % Reading from file /tmp/Prover9_17427_n020.cluster.edu
% 0.89/1.23
% 0.89/1.23 set(prolog_style_variables).
% 0.89/1.23 set(auto2).
% 0.89/1.23 % set(auto2) -> set(auto).
% 0.89/1.23 % set(auto) -> set(auto_inference).
% 0.89/1.23 % set(auto) -> set(auto_setup).
% 0.89/1.23 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.23 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.23 % set(auto) -> set(auto_limits).
% 0.89/1.23 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.23 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.23 % set(auto) -> set(auto_denials).
% 0.89/1.23 % set(auto) -> set(auto_process).
% 0.89/1.23 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.23 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.23 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.23 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.23 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.23 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.23 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.23 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.23 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.23 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.23 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.23 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.23 % set(auto2) -> assign(stats, some).
% 0.89/1.23 % set(auto2) -> clear(echo_input).
% 0.89/1.23 % set(auto2) -> set(quiet).
% 0.89/1.23 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.23 % set(auto2) -> clear(print_given).
% 0.89/1.23 assign(lrs_ticks,-1).
% 0.89/1.23 assign(sos_limit,10000).
% 0.89/1.23 assign(order,kbo).
% 0.89/1.23 set(lex_order_vars).
% 0.89/1.23 clear(print_given).
% 0.89/1.23
% 0.89/1.23 % formulas(sos). % not echoed (411 formulas)
% 0.89/1.23
% 0.89/1.23 ============================== end of input ==========================
% 0.89/1.23
% 0.89/1.23 % From the command line: assign(max_seconds, 300).
% 0.89/1.23
% 0.89/1.23 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.23
% 0.89/1.23 % Formulas that are not ordinary clauses:
% 0.89/1.23
% 0.89/1.23 ============================== end of process non-clausal formulas ===
% 0.89/1.23
% 0.89/1.23 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.23
% 0.89/1.23 ============================== PREDICATE ELIMINATION =================
% 0.89/1.23 1 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 0.89/1.23 2 -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].
% 0.89/1.23 3 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(B,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].
% 0.89/1.23 4 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Oplus__class_Oplus(A)),c_HOL_Oone__class_Oone(A)),B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_semiring__1__class_Oof__nat__code_0) # label(axiom). [assumption].
% 0.89/1.23 5 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 0.89/1.23 6 -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].
% 0.89/1.23 7 -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].
% 0.89/1.23 8 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 0.89/1.27 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(A,c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) = B. [resolve(1,a,2,a)].
% 0.89/1.27 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(A,c_Suc(B),C,tc_nat) = c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,hAPP(A,C),tc_nat). [resolve(1,a,3,a)].
% 0.89/1.27 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,4,a)].
% 0.89/1.27 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(1,a,5,a)].
% 0.89/1.27 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(1,a,6,a)].
% 0.89/1.27 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(1,a,7,a)].
% 0.89/1.27 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(1,a,8,a)].
% 0.89/1.27 9 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.89/1.27 10 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 0.89/1.27 11 -class_OrderedGroup_Omonoid__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A) # label(cls_foldl__foldr1_0) # label(axiom). [assumption].
% 0.89/1.27 12 -class_OrderedGroup_Omonoid__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),C,c_HOL_Ozero__class_Ozero(A),A,A)) # label(cls_foldl__foldr1__lemma_0) # label(axiom). [assumption].
% 0.89/1.27 13 -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].
% 0.89/1.27 14 -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].
% 0.89/1.27 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(9,a,10,a)].
% 0.89/1.27 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat). [resolve(9,a,11,a)].
% 0.89/1.27 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat)). [resolve(9,a,12,a)].
% 0.89/1.27 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(9,a,13,a)].
% 0.89/1.27 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(9,a,14,a)].
% 0.89/1.27 15 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.89/1.27 16 -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].
% 0.89/1.27 17 -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].
% 0.89/1.28 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(15,a,16,a)].
% 0.89/1.28 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(15,a,17,a)].
% 0.89/1.28 18 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.89/1.28 19 -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].
% 0.89/1.28 20 -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].
% 0.89/1.28 21 -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].
% 0.89/1.28 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(18,a,19,a)].
% 0.89/1.28 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(18,a,20,a)].
% 0.89/1.28 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(18,a,21,a)].
% 0.89/1.28 22 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.89/1.28 23 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 0.89/1.28 24 -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].
% 0.89/1.28 25 -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].
% 0.89/1.28 26 -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].
% 0.89/1.28 27 -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].
% 0.89/1.28 28 -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].
% 0.89/1.28 29 -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].
% 0.89/1.28 30 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 0.89/1.28 31 -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].
% 0.89/1.30 32 -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].
% 0.89/1.30 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(22,a,23,a)].
% 0.89/1.30 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(22,a,24,a)].
% 0.89/1.30 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(22,a,25,a)].
% 0.89/1.30 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(22,a,26,a)].
% 0.89/1.30 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(22,a,27,a)].
% 0.89/1.30 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(22,a,28,a)].
% 0.89/1.30 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(22,a,29,a)].
% 0.89/1.30 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(22,a,30,a)].
% 0.89/1.30 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(22,a,31,a)].
% 0.89/1.30 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(22,a,32,a)].
% 0.89/1.30 33 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.89/1.30 34 -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].
% 0.89/1.30 35 -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].
% 0.89/1.30 36 -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].
% 0.89/1.30 37 -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].
% 0.89/1.30 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(33,a,35,a)].
% 0.89/1.30 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(33,a,37,a)].
% 0.89/1.30 38 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.89/1.30 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_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].
% 0.89/1.32 40 -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].
% 0.89/1.32 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(38,a,39,a)].
% 0.89/1.32 41 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.89/1.32 42 -class_OrderedGroup_Oab__semigroup__add(A) | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,C,A,A) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,B,A,A) # label(cls_foldr__conv__foldl_0) # label(axiom). [assumption].
% 0.89/1.32 43 -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].
% 0.89/1.32 Derived: c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,A,tc_nat,tc_nat). [resolve(41,a,42,a)].
% 0.89/1.32 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(41,a,43,a)].
% 0.89/1.32 44 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 0.89/1.32 45 -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].
% 0.89/1.32 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(44,a,45,a)].
% 0.89/1.32 46 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.89/1.32 47 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 0.89/1.32 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(46,a,47,a)].
% 0.89/1.32 48 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.89/1.32 49 -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].
% 0.89/1.32 50 -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].
% 0.89/1.32 51 -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].
% 0.89/1.32 52 -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].
% 0.89/1.32 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)),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].
% 0.89/1.32 54 -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].
% 0.89/1.32 55 -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].
% 0.89/1.32 56 -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].
% 0.89/1.32 57 -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].
% 0.89/1.32 58 -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].
% 0.89/1.32 59 -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].
% 0.89/1.32 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(48,a,49,a)].
% 0.89/1.32 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(48,a,51,a)].
% 0.89/1.32 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(48,a,53,a)].
% 0.89/1.32 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(48,a,54,a)].
% 0.89/1.32 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(48,a,56,a)].
% 0.89/1.32 60 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.89/1.32 61 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 0.89/1.32 62 -class_OrderedGroup_Ocomm__monoid__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_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 0.89/1.32 63 -class_OrderedGroup_Ocomm__monoid__add(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_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 0.89/1.37 64 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 0.89/1.37 65 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 0.89/1.37 66 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.89/1.37 67 -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].
% 0.89/1.37 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(66,a,67,a)].
% 0.89/1.37 68 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.89/1.37 69 -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].
% 0.89/1.37 70 -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].
% 0.89/1.37 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(68,a,70,a)].
% 0.89/1.37 71 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.89/1.37 72 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.89/1.37 73 -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].
% 0.89/1.37 74 -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].
% 0.89/1.37 75 -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].
% 0.89/1.37 76 -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].
% 0.89/1.37 77 -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].
% 0.89/1.37 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(71,a,72,a)].
% 0.89/1.37 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(71,a,73,a)].
% 0.89/1.37 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(71,a,77,a)].
% 0.89/1.37 78 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 0.89/1.37 79 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 0.89/1.37 Derived: A = A. [resolve(78,b,79,a)].
% 0.89/1.37
% 0.89/1.37 ============================== end predicate elimination =============
% 0.89/1.37
% 0.89/1.37 Auto_denials: (non-Horn, no changes).
% 0.89/1.37
% 0.89/1.37 Term ordering decisions:
% 0.89/1.37 Function symbol KB weights: tc_nat=1. tc_Lambda_OdB=1. tc_Type_Otype=1. tc_bool=1. c_Lambda_OdB_OApp=1. c_Type_Otyping=1. c_Lambda_Osubst=1. c_Lambda_Obeta=1. c_Lambda_Olift=1. c_InductTermi_OIT=1. v_T____=1. c_Type_Otype_OFun=1. v_i____=1. v_e____=1. v_b____=1. v_x=1. v_T_H____=1. v_Ts____=1. v_n____=1. v_u____=1. t_a=1. v_T_H_H____=1. c_implies=1. v_bs____=1. v_a____=1. v_ea______=1. v_rs____=1. v_ua______=1. v_xb=1. c_and=1. v_T_Ha______=1. v_as____=1. v_ia______=1. v_xa=1. v_xc=1. hAPP=1. tc_fun=1. c_Transitive__Closure_Ortranclp=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Nat_Osize__class_Osize=1. c_Type_Osko__Type__Xabs__typeE__1__1=1. c_Type_Osko__Type__Xabs__typeE__1__2=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. c_Suc=1. c_Lambda_OdB_OVar=1. c_HOL_Oone__class_Oone=1. c_Type_Oshift=1. c_Lambda_OdB_OAbs=1. c_Fun_Oid=1. c_All=1. c_Type_Otype_Otype__size=1. c_Ex=1. c_HOL_Ominus__class_Ominus=1. c_COMBB=1. c_COMBC=1. c_Lambda_Oliftn=1. c_Lambda_Osubstn=1. c_COMBS=1. c_COMBK=1. c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1=1. c_Type_Osko__Type__Xtyping__elims__3__1=1. c_Type_Osko__Type__Xtyping__elims__3__2=1. c_List_Omap=1. c_Nat_Ocompow=1. c_Nat_Osemiring__1__class_Oof__nat__aux=1. c_Type_Osko__Type__Xlist__app__typeD__1__1=1. c_Type_Osko__Type__Xlist__app__typeE__1__1=1. c_Type_Osko__Type__Xtyping__elims__2__1=1. c_Type_Osko__Type__Xvar__app__typesE__1__1=1. c_Type_Osko__Type__Xvar__app__types__1__1=1. v_sko__CHAINED__1=1. v_sko__local__XCons__1__1=1. v_sko__local__XCons__Xhyps__1__1=1. c_List_Ofoldl=1. c_Fun_Ocomp=1. c_List_Ofoldr=1. c_Fun_Ofcomp=1.
% 12.37/12.68
% 12.37/12.68 ============================== end of process initial clauses ========
% 12.37/12.68
% 12.37/12.68 ============================== CLAUSES FOR SEARCH ====================
% 12.37/12.68
% 12.37/12.68 ============================== end of clauses for search =============
% 12.37/12.68
% 12.37/12.68 ============================== SEARCH ================================
% 12.37/12.68
% 12.37/12.68 % Starting search at 0.21 seconds.
% 12.37/12.68
% 12.37/12.68 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 0.75 sec).
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=61.000, iters=3344
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=52.000, iters=3625
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=41.000, iters=3373
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=39.000, iters=3351
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=37.000, iters=3335
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=36.000, iters=3373
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=35.000, iters=3370
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=34.000, iters=3409
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=33.000, iters=3350
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=31.000, iters=3403
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=30.000, iters=3382
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=29.000, iters=3344
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=28.000, iters=3390
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=27.000, iters=3391
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=26.000, iters=3345
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=25.000, iters=3368
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=24.000, iters=3366
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=23.000, iters=3381
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=22.000, iters=3346
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=21.000, iters=3423
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=20.000, iters=3351
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=19.000, iters=3334
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=18.000, iters=3342
% 12.37/12.68
% 12.37/12.68 Low Water (displace): id=1918, wt=107.000
% 12.37/12.68
% 12.37/12.68 Low Water (displace): id=1919, wt=105.000
% 12.37/12.68
% 12.37/12.68 Low Water (displace): id=11526, wt=44.000
% 12.37/12.68
% 12.37/12.68 Low Water (displace): id=12553, wt=40.000
% 12.37/12.68
% 12.37/12.68 Low Water (displace): id=12422, wt=39.000
% 12.37/12.68
% 12.37/12.68 Low Water (displace): id=12598, wt=17.000
% 12.37/12.68
% 12.37/12.68 Low Water (keep): wt=17.000, iters=3335
% 12.37/12.68
% 12.37/12.68 ============================== PROOF =================================
% 12.37/12.68 % SZS status Unsatisfiable
% 12.37/12.68 % SZS output start Refutation
% 12.37/12.68
% 12.37/12.68 % Proof 1 at 11.22 (+ 0.31) seconds.
% 12.37/12.68 % Length of proof is 7.
% 12.37/12.68 % Level of proof is 2.
% 12.37/12.68 % Maximum clause weight is 37.000.
% 12.37/12.68 % Given clauses 6411.
% 12.37/12.68
% 12.37/12.68 383 hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),A),B))) | -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,C),A),v_T____)) | -hBOOL(hAPP(c_InductTermi_OIT,A)) | -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),C),B),v_T____)),v_b____),D)) # label(cls_Cons_I1_J_0) # label(axiom). [assumption].
% 12.37/12.68 416 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 12.37/12.68 417 hBOOL(hAPP(c_InductTermi_OIT,v_xb)) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 12.37/12.68 418 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 12.37/12.68 419 -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 12.37/12.68 1362 hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),A),v_xc))) | -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),A),v_T____)) | -hBOOL(hAPP(c_InductTermi_OIT,A)). [resolve(416,a,383,d)].
% 12.37/12.68 32876 $F. [resolve(1362,b,418,a),unit_del(a,419),unit_del(b,417)].
% 12.37/12.68
% 12.37/12.68 % SZS output end Refutation
% 12.37/12.68 ============================== end of proof ==========================
% 12.37/12.68
% 12.37/12.68 ============================== STATISTICS ============================
% 12.37/12.68
% 12.37/12.68 Given=6411. Generated=549488. Kept=32692. proofs=1.
% 12.37/12.68 Usable=6372. Sos=9999. Demods=922. Limbo=0, Disabled=16777. Hints=0.
% 12.37/12.68 Megabytes=43.92.
% 12.37/12.68 User_CPU=11.22, System_CPU=0.31, Wall_clock=12.
% 12.37/12.68
% 12.37/12.68 ============================== end of statistics =====================
% 12.37/12.68
% 12.37/12.68 ============================== end of search =========================
% 12.37/12.68
% 12.37/12.68 THEOREM PROVED
% 12.37/12.68 % SZS status Unsatisfiable
% 12.37/12.68
% 12.37/12.68 Exiting with 1 proof.
% 12.37/12.68
% 12.37/12.68 Process 17804 exit (max_proofs) Mon Jul 4 11:47:27 2022
% 12.37/12.68 Prover9 interrupted
%------------------------------------------------------------------------------