TSTP Solution File: LCL835-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL835-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 13:50:40 EDT 2022
% Result : Unsatisfiable 29.64s 29.95s
% Output : Refutation 29.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL835-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n016.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 : Sun Jul 3 03:55:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.88/1.18 ============================== Prover9 ===============================
% 0.88/1.18 Prover9 (32) version 2009-11A, November 2009.
% 0.88/1.18 Process 23490 was started by sandbox on n016.cluster.edu,
% 0.88/1.18 Sun Jul 3 03:55:15 2022
% 0.88/1.18 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23336_n016.cluster.edu".
% 0.88/1.18 ============================== end of head ===========================
% 0.88/1.18
% 0.88/1.18 ============================== INPUT =================================
% 0.88/1.18
% 0.88/1.18 % Reading from file /tmp/Prover9_23336_n016.cluster.edu
% 0.88/1.18
% 0.88/1.18 set(prolog_style_variables).
% 0.88/1.18 set(auto2).
% 0.88/1.18 % set(auto2) -> set(auto).
% 0.88/1.18 % set(auto) -> set(auto_inference).
% 0.88/1.18 % set(auto) -> set(auto_setup).
% 0.88/1.18 % set(auto_setup) -> set(predicate_elim).
% 0.88/1.18 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.88/1.18 % set(auto) -> set(auto_limits).
% 0.88/1.18 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.88/1.18 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.88/1.18 % set(auto) -> set(auto_denials).
% 0.88/1.18 % set(auto) -> set(auto_process).
% 0.88/1.18 % set(auto2) -> assign(new_constants, 1).
% 0.88/1.18 % set(auto2) -> assign(fold_denial_max, 3).
% 0.88/1.18 % set(auto2) -> assign(max_weight, "200.000").
% 0.88/1.18 % set(auto2) -> assign(max_hours, 1).
% 0.88/1.18 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.88/1.18 % set(auto2) -> assign(max_seconds, 0).
% 0.88/1.18 % set(auto2) -> assign(max_minutes, 5).
% 0.88/1.18 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.88/1.18 % set(auto2) -> set(sort_initial_sos).
% 0.88/1.18 % set(auto2) -> assign(sos_limit, -1).
% 0.88/1.18 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.88/1.18 % set(auto2) -> assign(max_megs, 400).
% 0.88/1.18 % set(auto2) -> assign(stats, some).
% 0.88/1.18 % set(auto2) -> clear(echo_input).
% 0.88/1.18 % set(auto2) -> set(quiet).
% 0.88/1.18 % set(auto2) -> clear(print_initial_clauses).
% 0.88/1.18 % set(auto2) -> clear(print_given).
% 0.88/1.18 assign(lrs_ticks,-1).
% 0.88/1.18 assign(sos_limit,10000).
% 0.88/1.18 assign(order,kbo).
% 0.88/1.18 set(lex_order_vars).
% 0.88/1.18 clear(print_given).
% 0.88/1.18
% 0.88/1.18 % formulas(sos). % not echoed (494 formulas)
% 0.88/1.18
% 0.88/1.18 ============================== end of input ==========================
% 0.88/1.18
% 0.88/1.18 % From the command line: assign(max_seconds, 300).
% 0.88/1.18
% 0.88/1.18 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.88/1.18
% 0.88/1.18 % Formulas that are not ordinary clauses:
% 0.88/1.18
% 0.88/1.18 ============================== end of process non-clausal formulas ===
% 0.88/1.18
% 0.88/1.18 ============================== PROCESS INITIAL CLAUSES ===============
% 0.88/1.18
% 0.88/1.18 ============================== PREDICATE ELIMINATION =================
% 0.88/1.18 1 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.88/1.18 2 -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].
% 0.88/1.18 3 -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].
% 0.88/1.18 4 -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].
% 0.88/1.18 5 -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].
% 0.88/1.18 6 -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].
% 0.88/1.18 7 -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].
% 0.88/1.21 8 -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].
% 0.88/1.21 9 -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].
% 0.88/1.21 10 -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].
% 0.88/1.21 11 -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].
% 0.88/1.21 12 -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].
% 0.88/1.21 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(1,a,2,a)].
% 0.88/1.21 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(1,a,3,a)].
% 0.88/1.21 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(1,a,4,a)].
% 0.88/1.21 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(1,a,5,a)].
% 0.88/1.21 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(1,a,7,a)].
% 0.88/1.21 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(1,a,9,a)].
% 0.88/1.21 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(1,a,10,a)].
% 0.88/1.21 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(1,a,11,a)].
% 0.88/1.21 13 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.88/1.21 14 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__max_Oless__supI1_0) # label(axiom). [assumption].
% 0.88/1.21 15 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__supI2_0) # label(axiom). [assumption].
% 0.88/1.21 16 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__max__iff__disj_1) # label(axiom). [assumption].
% 0.88/1.21 17 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__max__iff__disj_2) # label(axiom). [assumption].
% 0.88/1.21 18 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_max__less__iff__conj_0) # label(axiom). [assumption].
% 0.88/1.21 19 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_max__less__iff__conj_1) # label(axiom). [assumption].
% 0.88/1.21 20 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_max__less__iff__conj_2) # label(axiom). [assumption].
% 0.88/1.21 21 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_less__max__iff__disj_0) # label(axiom). [assumption].
% 0.88/1.21 22 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.88/1.21 23 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = c_Orderings_Oord__class_Omax(C,B,A) # label(cls_min__max_Osup__commute_0) # label(axiom). [assumption].
% 0.88/1.21 24 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) # label(cls_min__max_Osup__assoc_0) # label(axiom). [assumption].
% 0.88/1.21 25 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) = c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,A),A) # label(cls_min__max_Osup__left__commute_0) # label(axiom). [assumption].
% 0.88/1.21 26 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,A),A) = c_Orderings_Oord__class_Omax(B,C,A) # label(cls_min__max_Osup__left__idem_0) # label(axiom). [assumption].
% 0.88/1.21 27 -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].
% 0.88/1.21 28 -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].
% 0.88/1.21 29 -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].
% 0.88/1.21 30 -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].
% 0.88/1.21 31 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,B,A) = B # label(cls_min__max_Osup__idem_0) # label(axiom). [assumption].
% 0.88/1.21 32 -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].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(13,a,14,a)].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(13,a,15,a)].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,C,tc_nat),B,tc_nat). [resolve(13,a,18,a)].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(C,A,tc_nat),B,tc_nat). [resolve(13,a,19,a)].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(13,a,20,a)].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(C,B,tc_nat),tc_nat). [resolve(13,a,21,a)].
% 0.88/1.21 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(13,a,22,a)].
% 0.88/1.21 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = c_Orderings_Oord__class_Omax(B,A,tc_nat). [resolve(13,a,23,a)].
% 0.88/1.21 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat). [resolve(13,a,24,a)].
% 0.88/1.21 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(A,C,tc_nat),tc_nat). [resolve(13,a,25,a)].
% 0.88/1.22 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(A,B,tc_nat). [resolve(13,a,26,a)].
% 0.88/1.22 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(13,a,27,a)].
% 0.88/1.22 Derived: c_Orderings_Oord__class_Omax(A,A,tc_nat) = A. [resolve(13,a,31,a)].
% 0.88/1.22 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(13,a,32,a)].
% 0.88/1.22 33 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.88/1.22 34 -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].
% 0.88/1.22 35 -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].
% 0.88/1.22 36 -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].
% 0.88/1.22 37 -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].
% 0.88/1.22 38 -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].
% 0.88/1.22 39 -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].
% 0.88/1.22 40 -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].
% 0.88/1.22 41 -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].
% 0.88/1.22 42 -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].
% 0.88/1.22 43 -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].
% 0.88/1.22 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(33,a,34,a)].
% 0.88/1.22 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(33,a,37,a)].
% 0.88/1.22 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(33,a,38,a)].
% 0.88/1.22 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(33,a,39,a)].
% 0.88/1.22 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(33,a,40,a)].
% 0.88/1.22 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(33,a,41,a)].
% 0.88/1.22 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(33,a,42,a)].
% 0.88/1.26 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(33,a,43,a)].
% 0.88/1.26 44 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.88/1.26 45 -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].
% 0.88/1.26 46 -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].
% 0.88/1.26 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(44,a,45,a)].
% 0.88/1.26 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(44,a,46,a)].
% 0.88/1.26 47 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.26 48 -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].
% 0.88/1.26 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(47,a,48,a)].
% 0.88/1.26 49 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.88/1.26 50 -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].
% 0.88/1.26 51 -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].
% 0.88/1.26 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(49,a,51,a)].
% 0.88/1.26 52 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.26 53 -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].
% 0.88/1.26 54 -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].
% 0.88/1.26 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(52,a,54,a)].
% 0.88/1.26 55 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.88/1.26 56 -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].
% 0.88/1.29 57 -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].
% 0.88/1.29 58 -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].
% 0.88/1.29 59 -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].
% 0.88/1.29 60 -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].
% 0.88/1.29 61 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 0.88/1.29 62 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 0.88/1.29 63 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 0.88/1.29 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(61,a,62,a)].
% 0.88/1.29 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(61,a,63,a)].
% 0.88/1.29 64 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 0.88/1.29 65 -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].
% 0.88/1.29 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(64,a,65,a)].
% 0.88/1.29 66 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.88/1.29 67 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 0.88/1.29 68 -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].
% 0.88/1.29 69 -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].
% 0.88/1.29 70 -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].
% 0.88/1.29 71 -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].
% 0.88/1.29 72 -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].
% 0.88/1.29 73 -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].
% 0.88/1.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(66,a,67,a)].
% 0.88/1.29 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(66,a,68,a)].
% 0.88/1.29 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(66,a,69,a)].
% 0.88/1.29 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(66,a,70,a)].
% 0.88/1.29 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(66,a,71,a)].
% 0.88/1.29 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(66,a,72,a)].
% 0.88/1.29 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(66,a,73,a)].
% 0.88/1.29 74 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.88/1.29 75 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Orderings_Oord__class_Omax(B,C,A)),D) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 0.88/1.29 76 -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].
% 0.88/1.29 77 -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].
% 0.88/1.29 78 -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].
% 0.88/1.29 79 -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].
% 0.88/1.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Oord__class_Omax(A,B,tc_nat)),C) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(74,a,75,a)].
% 0.88/1.29 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(74,a,76,a)].
% 0.88/1.29 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(74,a,77,a)].
% 0.88/1.29 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(74,a,78,a)].
% 0.88/1.32 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(74,a,79,a)].
% 0.88/1.32 80 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.88/1.32 81 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 0.88/1.32 82 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 0.88/1.32 83 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 0.88/1.32 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(80,a,81,a)].
% 0.88/1.32 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(80,a,83,a)].
% 0.88/1.32 84 -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].
% 0.88/1.32 85 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].
% 0.88/1.32 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(84,b,85,b)].
% 0.88/1.32 86 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].
% 0.88/1.32 87 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.32 88 -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].
% 0.88/1.32 89 -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].
% 0.88/1.32 90 -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].
% 0.88/1.32 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(87,a,88,a)].
% 0.88/1.35 91 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 0.88/1.35 92 -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].
% 0.88/1.35 93 -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].
% 0.88/1.35 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(91,a,92,a)].
% 0.88/1.35 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(91,a,93,a)].
% 0.88/1.35 94 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.88/1.35 95 -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].
% 0.88/1.35 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(94,a,95,a)].
% 0.88/1.35 96 -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(84,b,85,b)].
% 0.88/1.35 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(96,a,94,a)].
% 0.88/1.35
% 0.88/1.35 ============================== end predicate elimination =============
% 0.88/1.35
% 0.88/1.35 Auto_denials: (non-Horn, no changes).
% 0.88/1.35
% 0.88/1.35 Term ordering decisions:
% 0.88/1.35 Function symbol KB weights: tc_nat=1. tc_Lambda_OdB=1. c_Lambda_OdB_OApp=1. c_Lambda_Obeta=1. c_Lambda_Osubst=1. c_InductTermi_OIT=1. tc_Type_Otype=1. c_Lambda_Olift=1. c_Type_Otype_OFun=1. v_T____=1. v_a____=1. v_as____=1. v_r____=1. t_a=1. v_e____=1. tc_bool=1. v_T_H____=1. v_ea______=1. v_i____=1. v_u____=1. v_ua______=1. v_T_Ha______=1. v_ia______=1. hAPP=1. c_Transitive__Closure_Ortranclp=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_List_Olistsum=1. tc_fun=1. c_Type_Osko__Type__Xabs__typeE__1__1=1. c_Type_Osko__Type__Xabs__typeE__1__2=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. c_Suc=1. c_List_Olist_ONil=1. c_Lambda_OdB_OVar=1. c_Lambda_OdB_OAbs=1. c_fequal=1. c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1=1. c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2=1. c_List_Oappend=1. c_List_Olist_OCons=1. c_Orderings_Oord__class_Omax=1. c_List_Oreplicate=1. c_Predicate_Oconversep=1. c_Lambda_Oliftn=1. c_Lambda_Osubstn=1. c_Power_Opower__class_Opower=1. c_Type_Osko__Type__Xtyping__elims__3__1=1. c_Type_Osko__Type__Xtyping__elims__3__2=1. c_Type_Oshift=1. c_List_Omap=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_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1=1. c_List_Ofoldl=1. c_List_Ofoldr=1. c_Lambda_OdB_OdB__case=1. c_COMBC=1. c_Lambda_OdB_OdB__rec=1.
% 0.88/1.35
% 0.88/1.35 ============================== end of process initial clauses ========
% 0.88/1.35
% 0.88/1.35 ============================== CLAUSES FOR SEARCH ====================
% 29.64/29.95
% 29.64/29.95 ============================== end of clauses for search =============
% 29.64/29.95
% 29.64/29.95 ============================== SEARCH ================================
% 29.64/29.95
% 29.64/29.95 % Starting search at 0.23 seconds.
% 29.64/29.95
% 29.64/29.95 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 128 (0.00 of 0.57 sec).
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=57.000, iters=3443
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=51.000, iters=3357
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=50.000, iters=3333
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=45.000, iters=3339
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=42.000, iters=3367
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=41.000, iters=3336
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=40.000, iters=3380
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=39.000, iters=3398
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=38.000, iters=3351
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=37.000, iters=3361
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=36.000, iters=3340
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=35.000, iters=3396
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=33.000, iters=3352
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=32.000, iters=3335
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=31.000, iters=3336
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=29.000, iters=3385
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=28.000, iters=3476
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=27.000, iters=3361
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=26.000, iters=3369
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=24.000, iters=3357
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=23.000, iters=3461
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=22.000, iters=3339
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=21.000, iters=3346
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=20.000, iters=3366
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=19.000, iters=3334
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=18.000, iters=3337
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=17.000, iters=3333
% 29.64/29.95
% 29.64/29.95 Low Water (keep): wt=16.000, iters=3406
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=6011, wt=48.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=4805, wt=46.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=9730, wt=45.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=7394, wt=44.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=6012, wt=43.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=7120, wt=41.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=9731, wt=40.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=6484, wt=39.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=10337, wt=38.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=9734, wt=37.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=12199, wt=36.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=10722, wt=35.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=12042, wt=34.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=11503, wt=33.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=11395, wt=32.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=12491, wt=31.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=12584, wt=30.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=12489, wt=29.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=12609, wt=28.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=12733, wt=27.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=12789, wt=26.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=13163, wt=25.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=13364, wt=24.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=14001, wt=23.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=14651, wt=22.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=15314, wt=21.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=19267, wt=20.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=21891, wt=19.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=30186, wt=18.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=30197, wt=17.000
% 29.64/29.95
% 29.64/29.95 Low Water (displace): id=30285, wt=16.000
% 29.64/29.95
% 29.64/29.95 ============================== PROOF =================================
% 29.64/29.95 % SZS status Unsatisfiable
% 29.64/29.95 % SZS output start Refutation
% 29.64/29.95
% 29.64/29.95 % Proof 1 at 27.92 (+ 0.91) seconds.
% 29.64/29.95 % Length of proof is 8.
% 29.64/29.95 % Level of proof is 2.
% 29.64/29.95 % Maximum clause weight is 28.000.
% 29.64/29.95 % Given clauses 8153.
% 29.64/29.95
% 29.64/29.95 406 c_Type_Otyping(A,B,C) | -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B)) | -c_Type_Otyping(A,D,C) # label(cls_subject__reduction_0) # label(axiom). [assumption].
% 29.64/29.95 414 hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)))) # label(cls_beta_0) # label(axiom). [assumption].
% 29.64/29.95 428 hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB))) | -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)) # label(cls_apps__preserves__beta_0) # label(axiom). [assumption].
% 29.64/29.95 446 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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) # label(cls_T_0) # label(axiom). [assumption].
% 29.64/29.95 455 -c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 29.64/29.95 1511 hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),C,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB))). [resolve(428,b,414,a)].
% 29.64/29.95 1595 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),A,v_T_H____) | -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),A)). [resolve(446,a,406,c)].
% 29.64/29.95 32102 $F. [resolve(1595,b,1511,a),unit_del(a,455)].
% 29.64/29.95
% 29.64/29.95 % SZS output end Refutation
% 29.64/29.95 ============================== end of proof ==========================
% 29.64/29.95
% 29.64/29.95 ============================== STATISTICS ============================
% 29.64/29.95
% 29.64/29.95 Given=8153. Generated=1726855. Kept=31872. proofs=1.
% 29.64/29.95 Usable=8134. Sos=9440. Demods=752. Limbo=0, Disabled=14850. Hints=0.
% 29.64/29.95 Megabytes=38.73.
% 29.64/29.95 User_CPU=27.92, System_CPU=0.91, Wall_clock=29.
% 29.64/29.95
% 29.64/29.95 ============================== end of statistics =====================
% 29.64/29.95
% 29.64/29.95 ============================== end of search =========================
% 29.64/29.95
% 29.64/29.95 THEOREM PROVED
% 29.64/29.95 % SZS status Unsatisfiable
% 29.64/29.95
% 29.64/29.95 Exiting with 1 proof.
% 29.64/29.95
% 29.64/29.95 Process 23490 exit (max_proofs) Sun Jul 3 03:55:44 2022
% 29.64/29.95 Prover9 interrupted
%------------------------------------------------------------------------------