TSTP Solution File: LCL785-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL785-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 13:50:10 EDT 2022
% Result : Unsatisfiable 0.96s 1.51s
% Output : Refutation 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL785-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n011.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 05:50:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.96/1.25 ============================== Prover9 ===============================
% 0.96/1.25 Prover9 (32) version 2009-11A, November 2009.
% 0.96/1.25 Process 32580 was started by sandbox2 on n011.cluster.edu,
% 0.96/1.25 Mon Jul 4 05:50:37 2022
% 0.96/1.25 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32183_n011.cluster.edu".
% 0.96/1.25 ============================== end of head ===========================
% 0.96/1.25
% 0.96/1.25 ============================== INPUT =================================
% 0.96/1.25
% 0.96/1.25 % Reading from file /tmp/Prover9_32183_n011.cluster.edu
% 0.96/1.25
% 0.96/1.25 set(prolog_style_variables).
% 0.96/1.25 set(auto2).
% 0.96/1.25 % set(auto2) -> set(auto).
% 0.96/1.25 % set(auto) -> set(auto_inference).
% 0.96/1.25 % set(auto) -> set(auto_setup).
% 0.96/1.25 % set(auto_setup) -> set(predicate_elim).
% 0.96/1.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.96/1.25 % set(auto) -> set(auto_limits).
% 0.96/1.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.96/1.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.96/1.25 % set(auto) -> set(auto_denials).
% 0.96/1.25 % set(auto) -> set(auto_process).
% 0.96/1.25 % set(auto2) -> assign(new_constants, 1).
% 0.96/1.25 % set(auto2) -> assign(fold_denial_max, 3).
% 0.96/1.25 % set(auto2) -> assign(max_weight, "200.000").
% 0.96/1.25 % set(auto2) -> assign(max_hours, 1).
% 0.96/1.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.96/1.25 % set(auto2) -> assign(max_seconds, 0).
% 0.96/1.25 % set(auto2) -> assign(max_minutes, 5).
% 0.96/1.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.96/1.25 % set(auto2) -> set(sort_initial_sos).
% 0.96/1.25 % set(auto2) -> assign(sos_limit, -1).
% 0.96/1.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.96/1.25 % set(auto2) -> assign(max_megs, 400).
% 0.96/1.25 % set(auto2) -> assign(stats, some).
% 0.96/1.25 % set(auto2) -> clear(echo_input).
% 0.96/1.25 % set(auto2) -> set(quiet).
% 0.96/1.25 % set(auto2) -> clear(print_initial_clauses).
% 0.96/1.25 % set(auto2) -> clear(print_given).
% 0.96/1.25 assign(lrs_ticks,-1).
% 0.96/1.25 assign(sos_limit,10000).
% 0.96/1.25 assign(order,kbo).
% 0.96/1.25 set(lex_order_vars).
% 0.96/1.25 clear(print_given).
% 0.96/1.25
% 0.96/1.25 % formulas(sos). % not echoed (418 formulas)
% 0.96/1.25
% 0.96/1.25 ============================== end of input ==========================
% 0.96/1.25
% 0.96/1.25 % From the command line: assign(max_seconds, 300).
% 0.96/1.25
% 0.96/1.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.96/1.25
% 0.96/1.25 % Formulas that are not ordinary clauses:
% 0.96/1.25
% 0.96/1.25 ============================== end of process non-clausal formulas ===
% 0.96/1.25
% 0.96/1.25 ============================== PROCESS INITIAL CLAUSES ===============
% 0.96/1.25
% 0.96/1.25 ============================== PREDICATE ELIMINATION =================
% 0.96/1.25 1 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.96/1.25 2 -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].
% 0.96/1.25 3 -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].
% 0.96/1.25 4 -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].
% 0.96/1.25 5 -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].
% 0.96/1.25 6 -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].
% 0.96/1.25 7 -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].
% 0.96/1.25 8 -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].
% 0.96/1.25 9 -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].
% 0.96/1.27 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].
% 0.96/1.27 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].
% 0.96/1.27 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(1,a,2,a)].
% 0.96/1.27 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,3,a)].
% 0.96/1.27 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(1,a,4,a)].
% 0.96/1.27 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(1,a,5,a)].
% 0.96/1.27 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(1,a,6,a)].
% 0.96/1.27 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(1,a,7,a)].
% 0.96/1.27 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(1,a,8,a)].
% 0.96/1.27 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(1,a,9,a)].
% 0.96/1.27 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(1,a,10,a)].
% 0.96/1.27 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(1,a,11,a)].
% 0.96/1.27 12 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 0.96/1.27 13 -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].
% 0.96/1.27 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(12,a,13,a)].
% 0.96/1.27 14 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.96/1.27 15 -class_OrderedGroup_Ocomm__monoid__add(A) | c_List_Olistsum(c_List_Orev(B,A),A) = c_List_Olistsum(B,A) # label(cls_listsum__rev_0) # label(axiom). [assumption].
% 0.96/1.27 16 -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].
% 0.96/1.27 17 -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].
% 0.96/1.27 18 -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].
% 0.96/1.27 19 -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].
% 0.96/1.27 20 -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].
% 0.96/1.29 Derived: c_List_Olistsum(c_List_Orev(A,tc_nat),tc_nat) = c_List_Olistsum(A,tc_nat). [resolve(14,a,15,a)].
% 0.96/1.29 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(14,a,16,a)].
% 0.96/1.29 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(14,a,17,a)].
% 0.96/1.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(14,a,20,a)].
% 0.96/1.29 21 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 0.96/1.29 22 -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].
% 0.96/1.29 23 -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].
% 0.96/1.29 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(21,a,22,a)].
% 0.96/1.29 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(21,a,23,a)].
% 0.96/1.29 24 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.96/1.29 25 -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].
% 0.96/1.29 26 -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].
% 0.96/1.29 27 -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].
% 0.96/1.29 28 -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].
% 0.96/1.29 29 -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].
% 0.96/1.29 30 -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].
% 0.96/1.29 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(24,a,25,a)].
% 0.96/1.29 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(24,a,26,a)].
% 0.96/1.29 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(24,a,27,a)].
% 0.96/1.31 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(24,a,28,a)].
% 0.96/1.31 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(24,a,29,a)].
% 0.96/1.31 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(24,a,30,a)].
% 0.96/1.31 31 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.96/1.31 32 -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].
% 0.96/1.31 33 -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].
% 0.96/1.31 34 -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].
% 0.96/1.31 35 -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].
% 0.96/1.31 36 -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].
% 0.96/1.31 37 -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].
% 0.96/1.31 38 -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].
% 0.96/1.31 39 -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].
% 0.96/1.31 40 -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].
% 0.96/1.31 41 -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].
% 0.96/1.31 42 -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].
% 0.96/1.31 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(31,a,32,a)].
% 0.96/1.31 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(31,a,34,a)].
% 0.96/1.35 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(31,a,37,a)].
% 0.96/1.35 43 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.96/1.35 44 -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].
% 0.96/1.35 45 -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].
% 0.96/1.35 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(43,a,45,a)].
% 0.96/1.35 46 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.96/1.35 47 -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].
% 0.96/1.35 48 -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].
% 0.96/1.35 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(46,a,47,a)].
% 0.96/1.35 49 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.96/1.35 50 -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].
% 0.96/1.35 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(49,a,50,a)].
% 0.96/1.35 51 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.96/1.35 52 -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].
% 0.96/1.35 53 -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].
% 0.96/1.35 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(51,a,53,a)].
% 0.96/1.35 54 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.96/1.35 55 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.96/1.35 56 -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].
% 0.96/1.36 57 -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].
% 0.96/1.36 58 -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].
% 0.96/1.36 59 -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].
% 0.96/1.36 60 -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].
% 0.96/1.36 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(54,a,55,a)].
% 0.96/1.36 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(54,a,56,a)].
% 0.96/1.36 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(54,a,60,a)].
% 0.96/1.36 61 -class_OrderedGroup_Osemigroup__add(A) | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(A),A) # label(cls_semigroup__add__class_Oaxioms_0) # label(axiom). [assumption].
% 0.96/1.36 62 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_OrderedGroup_Osemigroup__add(A,E) # label(cls_semigroup__add_Oadd__assoc_0) # label(axiom). [assumption].
% 0.96/1.36 Derived: -class_OrderedGroup_Osemigroup__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)). [resolve(61,b,62,b)].
% 0.96/1.36 63 c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,E,E) = hAPP(hAPP(A,B),c_List_Ofoldl(A,C,D,E,E)) | -c_OrderedGroup_Osemigroup__add(A,E) # label(cls_semigroup__add_Ofoldl__assoc_0) # label(axiom). [assumption].
% 0.96/1.36 64 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.96/1.36 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].
% 0.96/1.36 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),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 0.96/1.36 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),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 0.96/1.36 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)].
% 0.96/1.36 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(64,a,66,a)].
% 0.96/1.36 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(64,a,67,a)].
% 0.96/1.36 68 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.96/1.36 69 -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].
% 0.96/1.36 70 -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].
% 0.96/1.39 71 -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].
% 0.96/1.39 72 -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].
% 0.96/1.39 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(68,a,70,a)].
% 0.96/1.39 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(68,a,72,a)].
% 0.96/1.39 73 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.96/1.39 74 -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].
% 0.96/1.39 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(73,a,74,a)].
% 0.96/1.39 75 -class_OrderedGroup_Osemigroup__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)). [resolve(61,b,62,b)].
% 0.96/1.39 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(75,a,73,a)].
% 0.96/1.39
% 0.96/1.39 ============================== end predicate elimination =============
% 0.96/1.39
% 0.96/1.39 Auto_denials: (non-Horn, no changes).
% 0.96/1.39
% 0.96/1.39 Term ordering decisions:
% 0.96/1.39 Function symbol KB weights: tc_nat=1. tc_Lambda_OdB=1. c_Lambda_OdB_OApp=1. c_Lambda_Obeta=1. c_InductTermi_OIT=1. tc_Type_Otype=1. c_Type_Otype_OFun=1. v_T____=1. t_a=1. v_rs____=1. v_n____=1. v_e____=1. v_i____=1. tc_bool=1. v_T_H____=1. v_a____=1. v_as____=1. v_ea______=1. v_u____=1. v_ua______=1. v_T_Ha______=1. v_ia______=1. hAPP=1. c_Transitive__Closure_Ortranclp=1. c_List_Orev=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Lambda_Olift=1. c_Nat_Osize__class_Osize=1. c_List_Obutlast=1. c_List_Olast=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. tc_List_Olist=1. c_fequal=1. c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1=1. c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2=1. c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3=1. c_ListApplication_Osko__ListApplication__Xlem__1__1=1. c_ListApplication_Osko__ListApplication__Xlem__1__2=1. c_ListApplication_Osko__ListApplication__Xlem__1__3=1. c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4=1. c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1=1. c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2=1. c_ListApplication_Osko__ListApplication__Xlem__1__4=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_Oshift=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__2=1. c_List_Ofoldl=1. c_List_Ofoldr=1. c_Lambda_OdB_OdB__case=1. c_Lambda_OdB_OdB__rec=1. c_List_Osko__List__XCons__eq__append__conv__1__1=1. c_List_Osko__List__Xappend__eq__Cons__conv__1__1=1.
% 0.96/1.51
% 0.96/1.51 ============================== end of process initial clauses ========
% 0.96/1.51
% 0.96/1.51 ============================== CLAUSES FOR SEARCH ====================
% 0.96/1.51
% 0.96/1.51 ============================== end of clauses for search =============
% 0.96/1.51
% 0.96/1.51 ============================== SEARCH ================================
% 0.96/1.51
% 0.96/1.51 % Starting search at 0.19 seconds.
% 0.96/1.51
% 0.96/1.51 ============================== PROOF =================================
% 0.96/1.51 % SZS status Unsatisfiable
% 0.96/1.51 % SZS output start Refutation
% 0.96/1.51
% 0.96/1.51 % Proof 1 at 0.31 (+ 0.00) seconds.
% 0.96/1.51 % Length of proof is 12.
% 0.96/1.51 % Level of proof is 3.
% 0.96/1.51 % Maximum clause weight is 20.000.
% 0.96/1.51 % Given clauses 222.
% 0.96/1.51
% 0.96/1.51 395 v_n____ = v_i____ # label(cls_True_0) # label(axiom). [assumption].
% 0.96/1.51 396 v_i____ = v_n____. [copy(395),flip(a)].
% 0.96/1.51 405 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) # label(cls_nT_0) # label(axiom). [assumption].
% 0.96/1.51 406 c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____). [copy(405),rewrite([396(2)])].
% 0.96/1.51 415 c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,E),F,E) = c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,F,E) # label(cls_foldl__Cons_0) # label(axiom). [assumption].
% 0.96/1.51 416 c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,E,F) = c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,F),E,F). [copy(415),flip(a)].
% 0.96/1.51 432 v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) # label(cls_Cons_0) # label(axiom). [assumption].
% 0.96/1.51 433 c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) = v_rs____. [copy(432),flip(a)].
% 0.96/1.51 449 -c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 0.96/1.51 450 -c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____). [copy(449),rewrite([396(2)])].
% 0.96/1.51 1551 c_List_Ofoldl(A,hAPP(hAPP(A,B),v_a____),v_as____,C,tc_Lambda_OdB) = c_List_Ofoldl(A,B,v_rs____,C,tc_Lambda_OdB). [para(433(a,1),416(a,2,3))].
% 0.96/1.51 1552 $F. [back_rewrite(450),rewrite([1551(16)]),unit_del(a,406)].
% 0.96/1.51
% 0.96/1.51 % SZS output end Refutation
% 0.96/1.51 ============================== end of proof ==========================
% 0.96/1.51
% 0.96/1.51 ============================== STATISTICS ============================
% 0.96/1.51
% 0.96/1.51 Given=222. Generated=2105. Kept=1338. proofs=1.
% 0.96/1.51 Usable=220. Sos=1057. Demods=174. Limbo=1, Disabled=519. Hints=0.
% 0.96/1.51 Megabytes=4.44.
% 0.96/1.51 User_CPU=0.31, System_CPU=0.00, Wall_clock=0.
% 0.96/1.51
% 0.96/1.51 ============================== end of statistics =====================
% 0.96/1.51
% 0.96/1.51 ============================== end of search =========================
% 0.96/1.51
% 0.96/1.51 THEOREM PROVED
% 0.96/1.51 % SZS status Unsatisfiable
% 0.96/1.51
% 0.96/1.51 Exiting with 1 proof.
% 0.96/1.51
% 0.96/1.51 Process 32580 exit (max_proofs) Mon Jul 4 05:50:37 2022
% 0.96/1.51 Prover9 interrupted
%------------------------------------------------------------------------------