TSTP Solution File: LCL818-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL818-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 13:50:30 EDT 2022
% Result : Unsatisfiable 6.88s 7.15s
% Output : Refutation 6.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL818-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jul 4 22:58:59 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.92/1.21 ============================== Prover9 ===============================
% 0.92/1.21 Prover9 (32) version 2009-11A, November 2009.
% 0.92/1.21 Process 2501 was started by sandbox2 on n013.cluster.edu,
% 0.92/1.21 Mon Jul 4 22:59:00 2022
% 0.92/1.21 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2348_n013.cluster.edu".
% 0.92/1.21 ============================== end of head ===========================
% 0.92/1.21
% 0.92/1.21 ============================== INPUT =================================
% 0.92/1.21
% 0.92/1.21 % Reading from file /tmp/Prover9_2348_n013.cluster.edu
% 0.92/1.21
% 0.92/1.21 set(prolog_style_variables).
% 0.92/1.21 set(auto2).
% 0.92/1.21 % set(auto2) -> set(auto).
% 0.92/1.21 % set(auto) -> set(auto_inference).
% 0.92/1.21 % set(auto) -> set(auto_setup).
% 0.92/1.21 % set(auto_setup) -> set(predicate_elim).
% 0.92/1.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.92/1.21 % set(auto) -> set(auto_limits).
% 0.92/1.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.92/1.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.92/1.21 % set(auto) -> set(auto_denials).
% 0.92/1.21 % set(auto) -> set(auto_process).
% 0.92/1.21 % set(auto2) -> assign(new_constants, 1).
% 0.92/1.21 % set(auto2) -> assign(fold_denial_max, 3).
% 0.92/1.21 % set(auto2) -> assign(max_weight, "200.000").
% 0.92/1.21 % set(auto2) -> assign(max_hours, 1).
% 0.92/1.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.92/1.21 % set(auto2) -> assign(max_seconds, 0).
% 0.92/1.21 % set(auto2) -> assign(max_minutes, 5).
% 0.92/1.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.92/1.21 % set(auto2) -> set(sort_initial_sos).
% 0.92/1.21 % set(auto2) -> assign(sos_limit, -1).
% 0.92/1.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.92/1.21 % set(auto2) -> assign(max_megs, 400).
% 0.92/1.21 % set(auto2) -> assign(stats, some).
% 0.92/1.21 % set(auto2) -> clear(echo_input).
% 0.92/1.21 % set(auto2) -> set(quiet).
% 0.92/1.21 % set(auto2) -> clear(print_initial_clauses).
% 0.92/1.21 % set(auto2) -> clear(print_given).
% 0.92/1.21 assign(lrs_ticks,-1).
% 0.92/1.21 assign(sos_limit,10000).
% 0.92/1.21 assign(order,kbo).
% 0.92/1.21 set(lex_order_vars).
% 0.92/1.21 clear(print_given).
% 0.92/1.21
% 0.92/1.21 % formulas(sos). % not echoed (398 formulas)
% 0.92/1.21
% 0.92/1.21 ============================== end of input ==========================
% 0.92/1.21
% 0.92/1.21 % From the command line: assign(max_seconds, 300).
% 0.92/1.21
% 0.92/1.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.92/1.21
% 0.92/1.21 % Formulas that are not ordinary clauses:
% 0.92/1.21
% 0.92/1.21 ============================== end of process non-clausal formulas ===
% 0.92/1.21
% 0.92/1.21 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.21
% 0.92/1.21 ============================== PREDICATE ELIMINATION =================
% 0.92/1.21 1 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.92/1.21 2 -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].
% 0.92/1.21 3 -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].
% 0.92/1.21 4 -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].
% 0.92/1.21 5 -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].
% 0.92/1.21 6 -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].
% 0.92/1.21 7 -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].
% 0.92/1.21 8 -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].
% 0.92/1.21 9 -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].
% 0.92/1.22 10 -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].
% 0.92/1.22 11 -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].
% 0.92/1.22 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(1,a,2,a)].
% 0.92/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(1,a,3,a)].
% 0.92/1.22 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,4,a)].
% 0.92/1.22 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(1,a,5,a)].
% 0.92/1.22 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(1,a,6,a)].
% 0.92/1.22 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(1,a,7,a)].
% 0.92/1.22 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(1,a,8,a)].
% 0.92/1.22 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(1,a,9,a)].
% 0.92/1.22 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(1,a,10,a)].
% 0.92/1.22 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(1,a,11,a)].
% 0.92/1.22 12 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.92/1.22 13 -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].
% 0.92/1.22 14 -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].
% 0.92/1.22 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(12,a,13,a)].
% 0.92/1.22 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(12,a,14,a)].
% 0.92/1.22 15 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 0.92/1.22 16 -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].
% 0.92/1.22 17 -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].
% 0.92/1.22 18 -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].
% 0.92/1.23 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(15,a,16,a)].
% 0.92/1.23 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(15,a,17,a)].
% 0.92/1.23 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(15,a,18,a)].
% 0.92/1.23 19 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.92/1.23 20 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(B,A) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A) # label(cls_listsum_0) # label(axiom). [assumption].
% 0.92/1.23 21 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Olist_OCons(B,C,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Olistsum(C,A)) # label(cls_listsum_Osimps_I2_J_0) # label(axiom). [assumption].
% 0.92/1.23 22 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Oappend(B,C,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Olistsum(B,A)),c_List_Olistsum(C,A)) # label(cls_listsum__append_0) # label(axiom). [assumption].
% 0.92/1.23 23 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Olist_ONil(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_listsum_Osimps_I1_J_0) # label(axiom). [assumption].
% 0.92/1.23 24 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(B,A) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A) # label(cls_listsum__foldr_0) # label(axiom). [assumption].
% 0.92/1.23 25 -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].
% 0.92/1.23 26 -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].
% 0.92/1.23 27 -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].
% 0.92/1.23 28 -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].
% 0.92/1.23 29 -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].
% 0.92/1.23 Derived: c_List_Olistsum(A,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat). [resolve(19,a,20,a)].
% 0.92/1.23 Derived: c_List_Olistsum(c_List_Olist_OCons(A,B,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Olistsum(B,tc_nat)). [resolve(19,a,21,a)].
% 0.92/1.23 Derived: c_List_Olistsum(c_List_Oappend(A,B,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olistsum(A,tc_nat)),c_List_Olistsum(B,tc_nat)). [resolve(19,a,22,a)].
% 0.92/1.23 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(19,a,23,a)].
% 0.92/1.23 Derived: c_List_Olistsum(A,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(19,a,24,a)].
% 0.92/1.23 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(19,a,25,a)].
% 0.92/1.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(19,a,26,a)].
% 0.92/1.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(19,a,27,a)].
% 0.92/1.26 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(19,a,28,a)].
% 0.92/1.26 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(19,a,29,a)].
% 0.92/1.26 30 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 0.92/1.26 31 -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].
% 0.92/1.26 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(30,a,31,a)].
% 0.92/1.26 32 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.92/1.26 33 -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].
% 0.92/1.26 34 -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].
% 0.92/1.26 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(32,a,33,a)].
% 0.92/1.26 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(32,a,34,a)].
% 0.92/1.26 35 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.92/1.26 36 -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].
% 0.92/1.26 37 -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].
% 0.92/1.26 38 -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].
% 0.92/1.26 39 -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].
% 0.92/1.26 40 -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].
% 0.92/1.26 41 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.92/1.26 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(35,a,36,a)].
% 0.92/1.26 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(35,a,37,a)].
% 0.92/1.26 42 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.92/1.26 43 -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].
% 0.92/1.26 44 -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].
% 0.92/1.30 45 -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].
% 0.92/1.30 46 -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].
% 0.92/1.30 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(42,a,43,a)].
% 0.92/1.30 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(42,a,44,a)].
% 0.92/1.30 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(42,a,45,a)].
% 0.92/1.30 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(42,a,46,a)].
% 0.92/1.30 47 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.92/1.30 48 -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].
% 0.92/1.30 49 -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].
% 0.92/1.30 50 -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].
% 0.92/1.30 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(47,a,50,a)].
% 0.92/1.30 51 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.92/1.30 52 -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].
% 0.92/1.30 53 -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].
% 0.92/1.30 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(51,a,53,a)].
% 0.92/1.30 54 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.92/1.30 55 -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].
% 0.92/1.30 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(54,a,55,a)].
% 0.92/1.30 56 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.92/1.30 57 -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].
% 0.92/1.30 58 -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].
% 0.92/1.30 59 -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].
% 0.92/1.30 60 -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].
% 0.92/1.30 61 -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].
% 0.92/1.30 62 -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].
% 0.92/1.30 63 -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].
% 0.92/1.30 64 -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].
% 0.92/1.30 65 -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].
% 0.92/1.30 66 -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].
% 0.92/1.30 67 -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].
% 0.92/1.30 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(56,a,57,a)].
% 0.92/1.30 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(56,a,59,a)].
% 0.92/1.30 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(56,a,61,a)].
% 0.92/1.34 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(56,a,62,a)].
% 0.92/1.34 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(56,a,64,a)].
% 0.92/1.34 68 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.92/1.34 69 -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].
% 0.92/1.34 70 -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].
% 0.92/1.34 71 -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].
% 0.92/1.34 72 -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].
% 0.92/1.34 73 -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].
% 0.92/1.34 74 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.92/1.34 75 -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].
% 0.92/1.34 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(74,a,75,a)].
% 0.92/1.34 76 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.92/1.34 77 -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].
% 0.92/1.34 78 -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].
% 0.92/1.34 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(76,a,78,a)].
% 0.92/1.34
% 0.92/1.34 ============================== end predicate elimination =============
% 0.92/1.34
% 0.92/1.34 Auto_denials: (non-Horn, no changes).
% 0.92/1.34
% 0.92/1.34 Term ordering decisions:
% 0.92/1.34 Function symbol KB weights: tc_nat=1. tc_Lambda_OdB=1. c_Lambda_OdB_OApp=1. c_Lambda_Obeta=1. tc_Type_Otype=1. c_Type_Otype_OFun=1. c_InductTermi_OIT=1. v_T____=1. t_a=1. v_e____=1. v_i____=1. v_T_H_H____=1. v_T_H____=1. v_Ts____=1. v_n____=1. v_u____=1. v_a____=1. v_rs____=1. tc_bool=1. v_as____=1. v_ea______=1. v_ua______=1. v_T_Ha______=1. v_ia______=1. hAPP=1. c_Transitive__Closure_Ortranclp=1. c_Lambda_Olift=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_List_Olistsum=1. c_List_Orotate1=1. tc_fun=1. c_HOL_Oplus__class_Oplus=1. c_List_Olist_ONil=1. c_HOL_Ozero__class_Ozero=1. c_Lambda_OdB_OVar=1. c_Lambda_OdB_OAbs=1. c_HOL_Oone__class_Oone=1. c_Type_Otype_OAtom=1. c_fequal=1. c_Type_Osko__Type__Xtype__induct__1__1=1. c_List_Oappend=1. c_List_Olist_OCons=1. c_Lambda_Osubst=1. c_List_Oreplicate=1. c_Predicate_Oconversep=1. c_Lambda_Oliftn=1. c_Lambda_Osubstn=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_Type_Oshift=1. c_Type_Otype_Otype__case=1. c_Type_Otype_Otype__rec=1. c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1=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. c_Type_Osko__Type__Xtypes__snocE__1__1=1. c_Type_Osko__Type__Xtypes__snocE__1__2=1. c_List_Ofoldl=1. c_List_Ofoldr=1. c_Lambda_OdB_OdB__case=1. c_Lambda_OdB_OdB__rec=1.
% 6.88/7.15
% 6.88/7.15 ============================== end of process initial clauses ========
% 6.88/7.15
% 6.88/7.15 ============================== CLAUSES FOR SEARCH ====================
% 6.88/7.15
% 6.88/7.15 ============================== end of clauses for search =============
% 6.88/7.15
% 6.88/7.15 ============================== SEARCH ================================
% 6.88/7.15
% 6.88/7.15 % Starting search at 0.18 seconds.
% 6.88/7.15
% 6.88/7.15 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 130 (0.00 of 0.47 sec).
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=53.000, iters=3387
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=49.000, iters=3399
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=41.000, iters=3350
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=40.000, iters=3399
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=39.000, iters=3521
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=37.000, iters=3425
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=36.000, iters=3413
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=33.000, iters=3422
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=31.000, iters=3398
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=30.000, iters=3475
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=28.000, iters=3363
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=27.000, iters=3489
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=26.000, iters=3435
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=23.000, iters=3427
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=22.000, iters=3522
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=20.000, iters=3334
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=19.000, iters=3405
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=18.000, iters=3335
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=17.000, iters=3336
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=1803, wt=84.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10504, wt=43.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10509, wt=42.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10366, wt=41.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=7639, wt=40.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10508, wt=39.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10365, wt=38.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10611, wt=37.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10364, wt=36.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10498, wt=35.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10457, wt=34.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10468, wt=33.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12460, wt=32.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10369, wt=31.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12400, wt=30.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10545, wt=29.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=10540, wt=28.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12286, wt=27.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12562, wt=26.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12673, wt=25.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12497, wt=24.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12507, wt=23.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12839, wt=22.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12801, wt=21.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=12489, wt=20.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=13413, wt=19.000
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=13708, wt=16.000
% 6.88/7.15
% 6.88/7.15 Low Water (keep): wt=16.000, iters=3334
% 6.88/7.15
% 6.88/7.15 Low Water (displace): id=15489, wt=15.000
% 6.88/7.15
% 6.88/7.15 ============================== PROOF =================================
% 6.88/7.15 % SZS status Unsatisfiable
% 6.88/7.15 % SZS output start Refutation
% 6.88/7.15
% 6.88/7.15 % Proof 1 at 5.84 (+ 0.15) seconds.
% 6.88/7.15 % Length of proof is 13.
% 6.88/7.15 % Level of proof is 4.
% 6.88/7.15 % Maximum clause weight is 20.000.
% 6.88/7.15 % Given clauses 5582.
% 6.88/7.15
% 6.88/7.15 351 c_Type_Otyping(v_e____,v_u____,v_T____) # label(cls_uT_0) # label(axiom). [assumption].
% 6.88/7.15 352 c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),C,D) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,C,D)),c_Lambda_Osubst(B,C,D)) # label(cls_subst__App_0) # label(axiom). [assumption].
% 6.88/7.15 353 hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C)) = c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C). [copy(352),flip(a)].
% 6.88/7.15 359 c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A) = B # label(cls_subst__eq_0) # label(axiom). [assumption].
% 6.88/7.15 380 v_n____ = v_i____ # label(cls_True_0) # label(axiom). [assumption].
% 6.88/7.15 388 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) # label(cls_headT_0) # label(axiom). [assumption].
% 6.88/7.15 389 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)). [copy(388),rewrite([380(7)])].
% 6.88/7.15 418 -c_Type_Otyping(A,B,C) | -c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F) | c_Type_Otyping(A,c_Lambda_Osubst(E,B,D),F) # label(cls_subst__lemma_0) # label(axiom). [assumption].
% 6.88/7.15 424 -c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 6.88/7.15 1094 hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_Osubst(B,A,C)) = c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C)),B),A,C). [para(359(a,1),353(a,1,1,2))].
% 6.88/7.15 1481 -c_Type_Otyping(c_Type_Oshift(v_e____,A,v_T____,tc_Type_Otype),B,C) | c_Type_Otyping(v_e____,c_Lambda_Osubst(B,v_u____,A),C). [resolve(418,a,351,a)].
% 6.88/7.15 23833 -c_Type_Otyping(v_e____,c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_u____,v_i____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)). [para(1094(a,1),424(a,2))].
% 6.88/7.15 29970 $F. [resolve(1481,a,389,a),unit_del(a,23833)].
% 6.88/7.15
% 6.88/7.15 % SZS output end Refutation
% 6.88/7.15 ============================== end of proof ==========================
% 6.88/7.15
% 6.88/7.15 ============================== STATISTICS ============================
% 6.88/7.15
% 6.88/7.15 Given=5582. Generated=224177. Kept=29770. proofs=1.
% 6.88/7.15 Usable=5572. Sos=9950. Demods=324. Limbo=3, Disabled=14687. Hints=0.
% 6.88/7.15 Megabytes=29.72.
% 6.88/7.15 User_CPU=5.84, System_CPU=0.15, Wall_clock=6.
% 6.88/7.15
% 6.88/7.15 ============================== end of statistics =====================
% 6.88/7.15
% 6.88/7.15 ============================== end of search =========================
% 6.88/7.15
% 6.88/7.15 THEOREM PROVED
% 6.88/7.15 % SZS status Unsatisfiable
% 6.88/7.15
% 6.88/7.15 Exiting with 1 proof.
% 6.88/7.15
% 6.88/7.15 Process 2501 exit (max_proofs) Mon Jul 4 22:59:06 2022
% 6.88/7.15 Prover9 interrupted
%------------------------------------------------------------------------------