TSTP Solution File: SCT095-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT095-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : Mon Jul 18 22:03:52 EDT 2022
% Result : Timeout 300.04s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT095-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 2 04:19:09 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.94/1.28 ============================== Prover9 ===============================
% 0.94/1.28 Prover9 (32) version 2009-11A, November 2009.
% 0.94/1.28 Process 4345 was started by sandbox2 on n029.cluster.edu,
% 0.94/1.28 Sat Jul 2 04:19:10 2022
% 0.94/1.28 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4192_n029.cluster.edu".
% 0.94/1.28 ============================== end of head ===========================
% 0.94/1.28
% 0.94/1.28 ============================== INPUT =================================
% 0.94/1.28
% 0.94/1.28 % Reading from file /tmp/Prover9_4192_n029.cluster.edu
% 0.94/1.28
% 0.94/1.28 set(prolog_style_variables).
% 0.94/1.28 set(auto2).
% 0.94/1.28 % set(auto2) -> set(auto).
% 0.94/1.28 % set(auto) -> set(auto_inference).
% 0.94/1.28 % set(auto) -> set(auto_setup).
% 0.94/1.28 % set(auto_setup) -> set(predicate_elim).
% 0.94/1.28 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.94/1.28 % set(auto) -> set(auto_limits).
% 0.94/1.28 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.94/1.28 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.94/1.28 % set(auto) -> set(auto_denials).
% 0.94/1.28 % set(auto) -> set(auto_process).
% 0.94/1.28 % set(auto2) -> assign(new_constants, 1).
% 0.94/1.28 % set(auto2) -> assign(fold_denial_max, 3).
% 0.94/1.28 % set(auto2) -> assign(max_weight, "200.000").
% 0.94/1.28 % set(auto2) -> assign(max_hours, 1).
% 0.94/1.28 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.94/1.28 % set(auto2) -> assign(max_seconds, 0).
% 0.94/1.28 % set(auto2) -> assign(max_minutes, 5).
% 0.94/1.28 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.94/1.28 % set(auto2) -> set(sort_initial_sos).
% 0.94/1.28 % set(auto2) -> assign(sos_limit, -1).
% 0.94/1.28 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.94/1.28 % set(auto2) -> assign(max_megs, 400).
% 0.94/1.28 % set(auto2) -> assign(stats, some).
% 0.94/1.28 % set(auto2) -> clear(echo_input).
% 0.94/1.28 % set(auto2) -> set(quiet).
% 0.94/1.28 % set(auto2) -> clear(print_initial_clauses).
% 0.94/1.28 % set(auto2) -> clear(print_given).
% 0.94/1.28 assign(lrs_ticks,-1).
% 0.94/1.28 assign(sos_limit,10000).
% 0.94/1.28 assign(order,kbo).
% 0.94/1.28 set(lex_order_vars).
% 0.94/1.28 clear(print_given).
% 0.94/1.28
% 0.94/1.28 % formulas(sos). % not echoed (692 formulas)
% 0.94/1.28
% 0.94/1.28 ============================== end of input ==========================
% 0.94/1.28
% 0.94/1.28 % From the command line: assign(max_seconds, 300).
% 0.94/1.28
% 0.94/1.28 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.94/1.28
% 0.94/1.28 % Formulas that are not ordinary clauses:
% 0.94/1.28
% 0.94/1.28 ============================== end of process non-clausal formulas ===
% 0.94/1.28
% 0.94/1.28 ============================== PROCESS INITIAL CLAUSES ===============
% 0.94/1.28
% 0.94/1.28 ============================== PREDICATE ELIMINATION =================
% 0.94/1.28 1 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.94/1.28 2 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.94/1.28 3 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.94/1.28 4 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.94/1.28 5 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.94/1.28 6 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.94/1.28 7 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.94/1.28 8 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.94/1.28 9 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.94/1.28 10 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.94/1.28 11 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.94/1.28 12 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.94/1.28 13 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.94/1.28 14 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.94/1.28 15 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 0.94/1.28 16 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 0.94/1.28 17 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.94/1.28 18 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.94/1.28 19 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.94/1.28 20 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.94/1.28 21 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.94/1.28 22 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,2,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,3,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(1,a,4,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(1,a,5,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(1,a,6,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,7,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(1,a,8,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,9,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,10,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(1,a,11,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(1,a,12,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(D,A)). [resolve(1,a,15,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(C,E,tc_fun(D,A)). [resolve(1,a,16,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(1,a,19,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(1,a,20,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(1,a,21,a)].
% 0.94/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(1,a,22,a)].
% 0.94/1.28 23 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.94/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(23,a,2,a)].
% 0.94/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(23,a,3,a)].
% 0.94/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(23,a,4,a)].
% 0.94/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(23,a,5,a)].
% 0.94/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(23,a,6,a)].
% 0.94/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(23,a,7,a)].
% 0.94/1.28 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,8,a)].
% 0.94/1.28 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(23,a,9,a)].
% 0.94/1.28 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(23,a,10,a)].
% 0.94/1.28 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,11,a)].
% 0.94/1.28 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(23,a,12,a)].
% 0.94/1.28 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(23,a,15,a)].
% 0.94/1.28 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(23,a,16,a)].
% 0.94/1.28 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(23,a,19,a)].
% 0.94/1.31 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(23,a,20,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(23,a,21,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(23,a,22,a)].
% 0.94/1.31 24 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(24,a,2,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(24,a,3,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(24,a,4,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(24,a,5,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(24,a,6,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(24,a,7,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(24,a,8,a)].
% 0.94/1.31 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(24,a,9,a)].
% 0.94/1.31 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(24,a,10,a)].
% 0.94/1.31 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(24,a,11,a)].
% 0.94/1.31 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(24,a,12,a)].
% 0.94/1.31 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(24,a,15,a)].
% 0.94/1.31 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(24,a,16,a)].
% 0.94/1.31 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(24,a,19,a)].
% 0.94/1.31 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(24,a,20,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(24,a,21,a)].
% 0.94/1.31 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(24,a,22,a)].
% 0.94/1.31 25 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.94/1.31 26 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.94/1.31 27 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.94/1.31 28 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.94/1.31 29 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.94/1.31 30 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.94/1.31 31 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.94/1.31 32 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.94/1.31 33 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.94/1.31 34 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.94/1.31 35 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.94/1.31 36 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.94/1.31 37 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.94/1.31 38 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.94/1.31 39 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 0.94/1.31 40 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 0.94/1.31 41 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.94/1.31 42 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.94/1.31 43 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.94/1.31 44 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.94/1.31 45 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.94/1.31 46 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(25,a,26,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(25,a,27,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)),tc_fun(D,A)). [resolve(25,a,28,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(25,a,31,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(25,a,32,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(25,a,33,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)). [resolve(25,a,34,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | c_lessequals(B,C,tc_fun(D,A)). [resolve(25,a,35,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -c_lessequals(B,C,tc_fun(D,A)). [resolve(25,a,36,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(25,a,37,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(25,a,38,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,C,tc_fun(E,A)). [resolve(25,a,39,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,D,tc_fun(E,A)). [resolve(25,a,40,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(25,a,41,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(25,a,42,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)). [resolve(25,a,43,a)].
% 0.94/1.31 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(25,a,44,a)].
% 0.94/1.31 47 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.94/1.31 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(47,a,26,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(47,a,27,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(47,a,28,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(47,a,31,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(47,a,32,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(47,a,33,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(47,a,34,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(47,a,35,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(47,a,36,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(47,a,37,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat). [resolve(47,a,38,a)].
% 0.94/1.31 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(47,a,39,a)].
% 0.94/1.31 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(47,a,40,a)].
% 0.94/1.31 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(47,a,41,a)].
% 0.94/1.31 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(47,a,42,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(47,a,43,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(47,a,44,a)].
% 0.94/1.31 48 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.94/1.31 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(48,a,26,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(48,a,27,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(48,a,28,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(48,a,31,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(48,a,32,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(48,a,33,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(48,a,34,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(48,a,35,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(48,a,36,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(48,a,37,a)].
% 0.94/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(48,a,38,a)].
% 0.94/1.31 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(48,a,39,a)].
% 0.94/1.31 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(48,a,40,a)].
% 0.94/1.31 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(48,a,41,a)].
% 0.94/1.31 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(48,a,42,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(48,a,43,a)].
% 0.94/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(48,a,44,a)].
% 0.94/1.38 49 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.94/1.38 50 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_lessequals(B,C,tc_nat) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 0.94/1.38 51 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 0.94/1.38 52 -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].
% 0.94/1.38 53 -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].
% 0.94/1.38 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(49,a,50,a)].
% 0.94/1.38 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(49,a,51,a)].
% 0.94/1.38 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(49,a,52,a)].
% 0.94/1.38 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(49,a,53,a)].
% 0.94/1.38 54 c_Order__Relation_Ostrict__linear__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C) | -c_Relation_Oirrefl(B,C) | -c_Relation_Otrans(B,C) # label(cls_strict__linear__order__on__def_3) # label(axiom). [assumption].
% 0.94/1.38 55 c_Relation_Ototal__on(A,B,C) | -c_Order__Relation_Ostrict__linear__order__on(A,B,C) # label(cls_strict__linear__order__on__def_2) # label(axiom). [assumption].
% 0.94/1.38 56 c_Relation_Otrans(A,B) | -c_Order__Relation_Ostrict__linear__order__on(C,A,B) # label(cls_strict__linear__order__on__def_0) # label(axiom). [assumption].
% 0.94/1.38 57 c_Relation_Oirrefl(A,B) | -c_Order__Relation_Ostrict__linear__order__on(C,A,B) # label(cls_strict__linear__order__on__def_1) # label(axiom). [assumption].
% 0.94/1.38 58 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.94/1.38 59 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 0.94/1.38 60 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 0.94/1.38 61 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 0.94/1.38 62 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 0.94/1.38 63 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 0.94/1.38 64 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 0.94/1.38 65 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 0.94/1.38 66 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 0.94/1.38 67 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 0.94/1.47 68 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.94/1.47 69 -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].
% 0.94/1.47 70 -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].
% 0.94/1.47 71 -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].
% 0.94/1.47 72 -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].
% 0.94/1.47 73 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.94/1.47 74 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.94/1.47 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(58,a,59,a)].
% 0.94/1.47 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(58,a,61,a)].
% 0.94/1.47 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(58,a,62,a)].
% 0.94/1.47 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(58,a,64,a)].
% 0.94/1.47 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(58,a,68,a)].
% 0.94/1.47 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(58,a,69,a)].
% 0.94/1.47 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(58,a,70,a)].
% 0.94/1.47 75 -hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -c_Relation_Oirrefl(C,B) # label(cls_irrefl__def_0) # label(axiom). [assumption].
% 0.94/1.47 76 c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(A,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),B) # label(cls_irrefl__diff__Id_0) # label(axiom). [assumption].
% 0.94/1.47 77 c_Relation_Oirrefl(A,B) | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),B,B),A,tc_prod(B,B))) # label(cls_irrefl__def_1) # label(axiom). [assumption].
% 0.94/1.47 Derived: -hBOOL(c_in(c_Pair(A,A,B,B),c_HOL_Ominus__class_Ominus(C,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),tc_prod(B,B))). [resolve(75,b,76,a)].
% 0.94/1.47 Derived: -hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),B,B),C,tc_prod(B,B))). [resolve(75,b,77,a)].
% 0.94/1.47 78 hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -c_Nitpick_Orefl_H(C,B) # label(cls_Nitpick_Orefl_H__def_0) # label(axiom). [assumption].
% 0.94/1.47 79 c_Nitpick_Orefl_H(A,B) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),B,B),A,tc_prod(B,B))) # label(cls_Nitpick_Orefl_H__def_1) # label(axiom). [assumption].
% 0.94/1.47 Derived: hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),B,B),C,tc_prod(B,B))). [resolve(78,b,79,a)].
% 0.94/1.47 80 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oequiv(c_Relation_ODomain(A,B,B),A,B) # label(cls_comp__equivI_0) # label(axiom). [assumption].
% 0.94/1.47 81 c_Equiv__Relations_Oquotient(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) | -hBOOL(c_in(c_Pair(A,D,B,B),C,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(A,E,B)) | -c_Equiv__Relations_Oequiv(E,C,B) # label(cls_eq__equiv__class__iff2_1) # label(axiom). [assumption].
% 0.94/1.47 82 c_Equiv__Relations_Oquotient(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(A,E,B)) | -c_Equiv__Relations_Oequiv(E,C,B) | hBOOL(c_in(c_Pair(A,D,B,B),C,tc_prod(B,B))) # label(cls_eq__equiv__class__iff2_0) # label(axiom). [assumption].
% 0.94/1.47 83 c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__subset_0) # label(axiom). [assumption].
% 0.94/1.47 84 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(B,E,C)) | -c_lessequals(c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,D,C) # label(cls_subset__equiv__class_0) # label(axiom). [assumption].
% 0.94/1.47 85 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)),C)) | -c_Equiv__Relations_Oequiv(F,D,C) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 0.94/1.47 86 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 0.94/1.47 87 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 0.94/1.47 88 hBOOL(c_in(A,c_Relation_OImage(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),C)) | -hBOOL(c_in(A,D,C)) | -c_Equiv__Relations_Oequiv(D,B,C) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 0.94/1.47 89 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 0.94/1.47 90 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 0.94/1.47 91 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 0.94/1.47 92 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oquotient(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(80,b,81,e)].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oquotient(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(80,b,82,d)].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(80,b,83,c)].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)). [resolve(80,b,84,d)].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)),B)). [resolve(80,b,85,c)].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(80,b,86,c)].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(C,c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(80,b,88,c)].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(80,b,89,d)].
% 0.94/1.47 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)). [resolve(80,b,92,d)].
% 0.94/1.47 93 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) = A | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv__comp__eq_0) # label(axiom). [assumption].
% 0.94/1.47 94 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 0.94/1.47 Derived: c_Relation_Orefl__on(c_Relation_ODomain(A,B,B),A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(94,b,80,b)].
% 0.94/1.47 95 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 0.94/1.47 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(95,b,80,b)].
% 0.94/1.47 96 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 0.94/1.47 Derived: c_Relation_Otrans(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(96,b,80,b)].
% 1.40/1.67 97 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(D,A,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_2) # label(axiom). [assumption].
% 1.40/1.67 Derived: hBOOL(c_in(A,c_Relation_ODomain(B,C,C),C)) | -hBOOL(c_in(c_Pair(D,A,C,C),B,tc_prod(C,C))) | c_Relation_Orel__comp(c_Relation_Oconverse(B,C,C),B,C,C,C) != B. [resolve(97,c,80,b)].
% 1.40/1.67 98 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(A,D,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_1) # label(axiom). [assumption].
% 1.40/1.67 99 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.40/1.67 100 -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].
% 1.40/1.67 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(99,a,100,a)].
% 1.40/1.67 101 hBOOL(c_in(c_Pair(A,B,C,D),E,tc_prod(C,D))) | -c_FunDef_Oin__rel(E,A,B,C,D) # label(cls_in__rel__def_0) # label(axiom). [assumption].
% 1.40/1.67 102 c_FunDef_Oin__rel(A,B,C,D,E) | -hBOOL(c_in(c_Pair(B,C,D,E),A,tc_prod(D,E))) # label(cls_in__rel__def_1) # label(axiom). [assumption].
% 1.40/1.67 103 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.40/1.67 104 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.40/1.67 Derived: A = A. [resolve(103,b,104,a)].
% 1.40/1.67
% 1.40/1.67 ============================== end predicate elimination =============
% 1.40/1.67
% 1.40/1.67 Auto_denials: (non-Horn, no changes).
% 1.40/1.67
% 1.40/1.67 Term ordering decisions:
% 1.40/1.67 Function symbol KB weights: tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. tc_nat=1. t_a=1. v_x=1. v_e____=1. v_h____=1. v_n____=1. v_P____=1. v_d____=1. v_a____=1. v_b____=1. v_Lba____=1. v_c____=1. v_Lab____=1. v_r=1. t_b=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OProf=1. tc_fun=1. tc_prod=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=1. c_Relation_OField=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Wellfounded_Omeasure=1. v_sko__Wellfounded__Xacc__Xinduct__1=1. v_sko__Wellfounded__Xacc__Xinducts__1=1. c_ATP__Linkup_Osko__Relation__XIdE__1__1=1. c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1=1. c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1=1. c_Orderings_Obot__class_Obot=1. c_Relation_OId=1. c_Orderings_Otop__class_Otop=1. c_in=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_Relation_Oconverse=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Equiv__Relations_Oquotient=1. c_ATP__Linkup_Osko__Relation__XId__onE__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1=1. c_Wellfounded_Omlex__prod=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1=1. c_List_Osko__Recdef__Xtfl__wf__induct__1__1=1. v_sko__Transitive__Closure__Xrtrancl__Xcases__1=1. v_sko__Transitive__Closure__Xtrancl__Xcases__1=1. c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1=1. c_Pair=1. c_Relation_OImage=1. c_Product__Type_OSigma=1. c_Relation_Oinv__image=1. c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomainE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1=1. c_ATP__Linkup_Osko__Relation__XRangeE__1__1=1. c_ATP__Linkup_Osko__Relation__XRange__iff__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1=1. c_Relation_Orel__comp=1. c_Recdef_Ocut=1. c_ATP__Linkup_Osko__Relation__XImageE__1__1=1. c_ATP__Linkup_Osko__Relation__XImage__iff__1__1=1. c_Hilbert__Choice_Oinv__into=1. c_List_Osko__Recdef__Xcuts__eq__1__1=1. c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1=1.
% 3.26/3.51
% 3.26/3.51 ============================== end of process initial clauses ========
% 3.26/3.51
% 3.26/3.51 ============================== CLAUSES FOR SEARCH ====================
% 3.26/3.51
% 3.26/3.51 ============================== end of clauses for search =============
% 3.26/3.51
% 3.26/3.51 ============================== SEARCH ================================
% 3.26/3.51
% 3.26/3.51 % Starting search at 0.49 seconds.
% 3.26/3.51
% 3.26/3.51 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 66 (0.00 of 0.86 sec).
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=72.000, iters=3673
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=54.000, iters=3416
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=52.000, iters=3393
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=51.000, iters=3361
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=49.000, iters=3335
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=47.000, iters=3394
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=45.000, iters=3333
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=44.000, iters=3346
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=43.000, iters=3345
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=41.000, iters=3358
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=40.000, iters=3348
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=39.000, iters=3345
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=38.000, iters=3364
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=37.000, iters=3336
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=35.000, iters=3350
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=34.000, iters=3421
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=32.000, iters=3345
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=31.000, iters=3353
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=30.000, iters=3460
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=29.000, iters=3381
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=28.000, iters=3340
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=27.000, iters=3340
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=26.000, iters=3339
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=25.000, iters=3402
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=24.000, iters=3334
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=23.000, iters=3414
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=22.000, iters=3337
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=21.000, iters=3348
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=20.000, iters=3342
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=19.000, iters=3343
% 3.26/3.51
% 3.26/3.51 Low Water (keep): wt=18.000, iters=3349
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4029, wt=148.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4082, wt=140.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4053, wt=139.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4028, wt=129.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4081, wt=121.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4033, wt=119.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4086, wt=110.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4073, wt=107.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4160, wt=103.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4331, wt=101.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4011, wt=100.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4054, wt=91.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4052, wt=90.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4072, wt=88.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4040, wt=87.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4061, wt=84.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4018, wt=83.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4330, wt=82.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4120, wt=80.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=2367, wt=79.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4115, wt=78.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=3766, wt=77.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4030, wt=76.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=2315, wt=75.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4020, wt=74.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4077, wt=73.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4047, wt=72.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4036, wt=71.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4083, wt=70.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4068, wt=69.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4013, wt=68.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4085, wt=67.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=2307, wt=66.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=4089, wt=65.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=2238, wt=64.000
% 3.26/3.51
% 3.26/3.51 Low Water (displace): id=13131, wt=17.000
% 3.26/3.51
% 3.26/3.51 Low Water (displacCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------