TSTP Solution File: LCL789-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL789-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 13:50:12 EDT 2022
% Result : Unsatisfiable 0.78s 1.14s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL789-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 20:05:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.78/1.07 ============================== Prover9 ===============================
% 0.78/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.07 Process 22069 was started by sandbox2 on n021.cluster.edu,
% 0.78/1.07 Mon Jul 4 20:05:32 2022
% 0.78/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21913_n021.cluster.edu".
% 0.78/1.07 ============================== end of head ===========================
% 0.78/1.07
% 0.78/1.07 ============================== INPUT =================================
% 0.78/1.07
% 0.78/1.07 % Reading from file /tmp/Prover9_21913_n021.cluster.edu
% 0.78/1.07
% 0.78/1.07 set(prolog_style_variables).
% 0.78/1.07 set(auto2).
% 0.78/1.07 % set(auto2) -> set(auto).
% 0.78/1.07 % set(auto) -> set(auto_inference).
% 0.78/1.07 % set(auto) -> set(auto_setup).
% 0.78/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.07 % set(auto) -> set(auto_limits).
% 0.78/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.07 % set(auto) -> set(auto_denials).
% 0.78/1.07 % set(auto) -> set(auto_process).
% 0.78/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.07 % set(auto2) -> assign(stats, some).
% 0.78/1.07 % set(auto2) -> clear(echo_input).
% 0.78/1.07 % set(auto2) -> set(quiet).
% 0.78/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.07 % set(auto2) -> clear(print_given).
% 0.78/1.07 assign(lrs_ticks,-1).
% 0.78/1.07 assign(sos_limit,10000).
% 0.78/1.07 assign(order,kbo).
% 0.78/1.07 set(lex_order_vars).
% 0.78/1.07 clear(print_given).
% 0.78/1.07
% 0.78/1.07 % formulas(sos). % not echoed (321 formulas)
% 0.78/1.07
% 0.78/1.07 ============================== end of input ==========================
% 0.78/1.07
% 0.78/1.07 % From the command line: assign(max_seconds, 300).
% 0.78/1.07
% 0.78/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.07
% 0.78/1.07 % Formulas that are not ordinary clauses:
% 0.78/1.07
% 0.78/1.07 ============================== end of process non-clausal formulas ===
% 0.78/1.07
% 0.78/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.78/1.07
% 0.78/1.07 ============================== PREDICATE ELIMINATION =================
% 0.78/1.07 1 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 0.78/1.07 2 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 0.78/1.07 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(1,a,2,a)].
% 0.78/1.07 3 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.78/1.07 4 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),B,D,A)),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),C,D,A)) # label(cls_comm__monoid__add_Opower__mult__distrib_0) # label(axiom). [assumption].
% 0.78/1.07 5 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_comm__monoid__add_Opower__one_0) # label(axiom). [assumption].
% 0.78/1.07 6 -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].
% 0.78/1.07 7 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),B,C,A)),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),B,C,A)) # label(cls_comm__monoid__add_Opower__commutes_0) # label(axiom). [assumption].
% 0.78/1.08 8 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_comm__monoid__add_Opower__0_0) # label(axiom). [assumption].
% 0.78/1.08 9 -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].
% 0.78/1.08 10 -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].
% 0.78/1.08 11 -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].
% 0.78/1.08 12 -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].
% 0.78/1.08 13 -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].
% 0.78/1.08 Derived: c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),A,C,tc_nat)),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat)). [resolve(3,a,4,a)].
% 0.78/1.08 Derived: c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(3,a,5,a)].
% 0.78/1.08 Derived: c_List_Olistsum(c_List_Orev(A,tc_nat),tc_nat) = c_List_Olistsum(A,tc_nat). [resolve(3,a,6,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat)). [resolve(3,a,7,a)].
% 0.78/1.08 Derived: c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(3,a,8,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(3,a,9,a)].
% 0.78/1.08 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(3,a,10,a)].
% 0.78/1.08 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(3,a,11,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(3,a,12,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(3,a,13,a)].
% 0.78/1.08 14 class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.78/1.08 Derived: c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,C,tc_Int_Oint)),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),B,C,tc_Int_Oint)). [resolve(14,a,4,a)].
% 0.78/1.08 Derived: c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(14,a,5,a)].
% 0.78/1.08 Derived: c_List_Olistsum(c_List_Orev(A,tc_Int_Oint),tc_Int_Oint) = c_List_Olistsum(A,tc_Int_Oint). [resolve(14,a,6,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,B,tc_Int_Oint)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,B,tc_Int_Oint)). [resolve(14,a,7,a)].
% 0.78/1.08 Derived: c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(14,a,8,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(14,a,9,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(14,a,10,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(14,a,11,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(14,a,12,a)].
% 0.78/1.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(14,a,13,a)].
% 0.78/1.08 15 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.78/1.08 16 -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].
% 0.78/1.08 17 -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].
% 0.78/1.08 18 -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].
% 0.78/1.08 19 -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].
% 0.78/1.08 20 -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].
% 0.78/1.08 21 -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].
% 0.78/1.08 22 -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].
% 0.78/1.08 23 -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].
% 0.78/1.08 24 -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].
% 0.78/1.09 25 -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].
% 0.78/1.09 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(15,a,16,a)].
% 0.78/1.09 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(15,a,17,a)].
% 0.78/1.09 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(15,a,18,a)].
% 0.78/1.09 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(15,a,19,a)].
% 0.78/1.09 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(15,a,20,a)].
% 0.78/1.09 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(15,a,21,a)].
% 0.78/1.09 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(15,a,24,a)].
% 0.78/1.09 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(15,a,25,a)].
% 0.78/1.09 26 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.78/1.09 Derived: c_List_Olistsum(c_List_Olist_OCons(A,B,tc_Int_Oint),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_List_Olistsum(B,tc_Int_Oint)). [resolve(26,a,16,a)].
% 0.78/1.09 Derived: c_List_Olistsum(c_List_Oappend(A,B,tc_Int_Oint),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_List_Olistsum(A,tc_Int_Oint)),c_List_Olistsum(B,tc_Int_Oint)). [resolve(26,a,17,a)].
% 0.78/1.09 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(26,a,18,a)].
% 0.78/1.09 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint,tc_Int_Oint)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,B,tc_Int_Oint,tc_Int_Oint). [resolve(26,a,19,a)].
% 0.78/1.09 Derived: c_List_Olistsum(A,tc_Int_Oint) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,tc_Int_Oint). [resolve(26,a,20,a)].
% 0.78/1.09 Derived: c_List_Olistsum(A,tc_Int_Oint) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint). [resolve(26,a,21,a)].
% 0.78/1.09 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,B,tc_Int_Oint,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,tc_Int_Oint)). [resolve(26,a,24,a)].
% 0.78/1.09 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,tc_Int_Oint). [resolve(26,a,25,a)].
% 0.78/1.09 27 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.78/1.09 28 -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].
% 0.78/1.09 29 -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].
% 0.78/1.11 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(27,a,28,a)].
% 0.78/1.11 30 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.78/1.11 Derived: c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,B,tc_Int_Oint,tc_Int_Oint) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B,A,tc_Int_Oint,tc_Int_Oint). [resolve(30,a,28,a)].
% 0.78/1.11 31 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 0.78/1.11 32 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 0.78/1.11 33 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 0.78/1.11 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(31,a,32,a)].
% 0.78/1.11 34 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 0.78/1.11 35 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 0.78/1.11 36 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(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_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 0.78/1.11 37 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 0.78/1.11 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(34,a,35,a)].
% 0.78/1.11 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(34,a,36,a)].
% 0.78/1.11 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)). [resolve(34,a,37,a)].
% 0.78/1.11 38 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.78/1.11 39 -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].
% 0.78/1.11 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(38,a,39,a)].
% 0.78/1.11 40 class_OrderedGroup_Osemigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.78/1.11 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B,C,tc_Int_Oint,tc_Int_Oint)). [resolve(40,a,39,a)].
% 0.78/1.11 41 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.78/1.11 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].
% 0.78/1.11 43 -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].
% 0.78/1.11 44 -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].
% 0.78/1.11 45 -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].
% 0.78/1.11 46 -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].
% 0.78/1.11 47 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 0.78/1.11 48 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 0.78/1.11 49 -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].
% 0.78/1.11 50 -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].
% 0.78/1.11 51 -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].
% 0.78/1.11 52 -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].
% 0.78/1.11 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(41,a,44,a)].
% 0.78/1.11 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(41,a,46,a)].
% 0.78/1.11 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(41,a,49,a)].
% 0.78/1.11 53 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.78/1.11 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C). [resolve(53,a,44,a)].
% 0.78/1.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(53,a,46,a)].
% 0.78/1.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(53,a,49,a)].
% 0.78/1.14 54 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 0.78/1.14 55 -class_OrderedGroup_Oab__group__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_add__cancel__21_1) # label(axiom). [assumption].
% 0.78/1.14 56 -class_OrderedGroup_Oab__group__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),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 0.78/1.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) = D. [resolve(54,a,56,a)].
% 0.78/1.14 57 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.78/1.14 58 -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].
% 0.78/1.14 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(57,a,58,a)].
% 0.78/1.14 59 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.78/1.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(59,a,58,a)].
% 0.78/1.14 60 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.78/1.14 61 -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].
% 0.78/1.14 62 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 0.78/1.14 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(60,a,62,a)].
% 0.78/1.14 63 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.78/1.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B) | A = C. [resolve(63,a,62,a)].
% 0.78/1.14
% 0.78/1.14 ============================== end predicate elimination =============
% 0.78/1.14
% 0.78/1.14 Auto_denials: (non-Horn, no changes).
% 0.78/1.14
% 0.78/1.14 Term ordering decisions:
% 0.78/1.14 Function symbol KB weights: tc_Lambda_OdB=1. tc_nat=1. tc_Int_Oint=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. v_e____=1. v_i____=1. v_T_H____=1. v_Ts____=1. v_n____=1. t_a=1. v_T_H_H____=1. v_a____=1. v_rs____=1. v_u____=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_List_Orev=1. c_List_Olistsum=1. c_List_Obutlast=1. c_List_Olast=1. c_Int_Onumber__class_Onumber__of=1. c_List_Orotate1=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_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_List_Oreplicate=1. c_Lambda_Osubst=1. c_Predicate_Oconversep=1. c_List_Otake=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__2=1. c_List_Ofoldl=1. c_List_Ofoldr=1. c_Power_Opower_Opower=1. c_List_Osko__List__XCons__eq__append__conv__1__1=1. c_List_Osko__List__Xappend__eq__Cons__conv__1__1=1.
% 0.78/1.14
% 0.78/1.14 ============================== PROOF =================================
% 0.78/1.14 % SZS status Unsatisfiable
% 0.78/1.14 % SZS output start Refutation
% 0.78/1.14
% 0.78/1.14 % Proof 1 at 0.11 (+ 0.00) seconds.
% 0.78/1.14 % Length of proof is 5.
% 0.78/1.14 % Level of proof is 2.
% 0.78/1.14 % Maximum clause weight is 12.000.
% 0.78/1.14 % Given clauses 0.
% 0.78/1.14
% 0.78/1.14 339 c_Type_Otyping(v_e____,v_u____,v_T____) # label(cls_uT_0) # label(axiom). [assumption].
% 0.78/1.14 362 v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) # label(cls_T_0) # label(axiom). [assumption].
% 0.78/1.14 363 hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = v_T____. [copy(362),flip(a)].
% 0.78/1.14 374 -c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),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].
% 0.78/1.14 375 $F. [copy(374),rewrite([363(12)]),unit_del(a,339)].
% 0.78/1.14
% 0.78/1.14 % SZS output end Refutation
% 0.78/1.14 ============================== end of proof ==========================
% 0.78/1.14
% 0.78/1.14 ============================== STATISTICS ============================
% 0.78/1.14
% 0.78/1.14 Given=0. Generated=255. Kept=207. proofs=1.
% 0.78/1.14 Usable=0. Sos=0. Demods=48. Limbo=207, Disabled=318. Hints=0.
% 0.78/1.14 Megabytes=0.68.
% 0.78/1.14 User_CPU=0.11, System_CPU=0.00, Wall_clock=1.
% 0.78/1.14
% 0.78/1.14 ============================== end of statistics =====================
% 0.78/1.14
% 0.78/1.14 ============================== end of search =========================
% 0.78/1.14
% 0.78/1.14 THEOREM PROVED
% 0.78/1.14 % SZS status Unsatisfiable
% 0.78/1.14
% 0.78/1.14 Exiting with 1 proof.
% 0.78/1.14
% 0.78/1.14 Process 22069 exit (max_proofs) Mon Jul 4 20:05:33 2022
% 0.78/1.14 Prover9 interrupted
%------------------------------------------------------------------------------