TSTP Solution File: SCT031-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT031-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 22:03:31 EDT 2022
% Result : Unsatisfiable 41.86s 42.14s
% Output : Refutation 41.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT031-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 21:05:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.00/1.37 ============================== Prover9 ===============================
% 1.00/1.37 Prover9 (32) version 2009-11A, November 2009.
% 1.00/1.37 Process 18694 was started by sandbox on n020.cluster.edu,
% 1.00/1.37 Fri Jul 1 21:05:46 2022
% 1.00/1.37 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18478_n020.cluster.edu".
% 1.00/1.37 ============================== end of head ===========================
% 1.00/1.37
% 1.00/1.37 ============================== INPUT =================================
% 1.00/1.37
% 1.00/1.37 % Reading from file /tmp/Prover9_18478_n020.cluster.edu
% 1.00/1.37
% 1.00/1.37 set(prolog_style_variables).
% 1.00/1.37 set(auto2).
% 1.00/1.37 % set(auto2) -> set(auto).
% 1.00/1.37 % set(auto) -> set(auto_inference).
% 1.00/1.37 % set(auto) -> set(auto_setup).
% 1.00/1.37 % set(auto_setup) -> set(predicate_elim).
% 1.00/1.37 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.00/1.37 % set(auto) -> set(auto_limits).
% 1.00/1.37 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.00/1.37 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.00/1.37 % set(auto) -> set(auto_denials).
% 1.00/1.37 % set(auto) -> set(auto_process).
% 1.00/1.37 % set(auto2) -> assign(new_constants, 1).
% 1.00/1.37 % set(auto2) -> assign(fold_denial_max, 3).
% 1.00/1.37 % set(auto2) -> assign(max_weight, "200.000").
% 1.00/1.37 % set(auto2) -> assign(max_hours, 1).
% 1.00/1.37 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.00/1.37 % set(auto2) -> assign(max_seconds, 0).
% 1.00/1.37 % set(auto2) -> assign(max_minutes, 5).
% 1.00/1.37 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.00/1.37 % set(auto2) -> set(sort_initial_sos).
% 1.00/1.37 % set(auto2) -> assign(sos_limit, -1).
% 1.00/1.37 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.00/1.37 % set(auto2) -> assign(max_megs, 400).
% 1.00/1.37 % set(auto2) -> assign(stats, some).
% 1.00/1.37 % set(auto2) -> clear(echo_input).
% 1.00/1.37 % set(auto2) -> set(quiet).
% 1.00/1.37 % set(auto2) -> clear(print_initial_clauses).
% 1.00/1.37 % set(auto2) -> clear(print_given).
% 1.00/1.37 assign(lrs_ticks,-1).
% 1.00/1.37 assign(sos_limit,10000).
% 1.00/1.37 assign(order,kbo).
% 1.00/1.37 set(lex_order_vars).
% 1.00/1.37 clear(print_given).
% 1.00/1.37
% 1.00/1.37 % formulas(sos). % not echoed (696 formulas)
% 1.00/1.37
% 1.00/1.37 ============================== end of input ==========================
% 1.00/1.37
% 1.00/1.37 % From the command line: assign(max_seconds, 300).
% 1.00/1.37
% 1.00/1.37 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.00/1.37
% 1.00/1.37 % Formulas that are not ordinary clauses:
% 1.00/1.37
% 1.00/1.37 ============================== end of process non-clausal formulas ===
% 1.00/1.37
% 1.00/1.37 ============================== PROCESS INITIAL CLAUSES ===============
% 1.00/1.37
% 1.00/1.37 ============================== PREDICATE ELIMINATION =================
% 1.00/1.37 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.37 2 -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].
% 1.00/1.37 3 -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].
% 1.00/1.37 4 -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].
% 1.00/1.37 5 -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].
% 1.00/1.37 6 -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].
% 1.00/1.37 7 -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].
% 1.00/1.37 8 -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].
% 1.00/1.37 9 -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].
% 1.00/1.37 10 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.00/1.37 11 -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].
% 1.00/1.37 12 -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].
% 1.00/1.37 13 -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].
% 1.00/1.37 14 -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].
% 1.00/1.37 15 -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].
% 1.00/1.37 16 -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].
% 1.00/1.37 17 -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].
% 1.00/1.37 18 -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].
% 1.00/1.37 19 -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].
% 1.00/1.37 20 -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].
% 1.00/1.37 21 -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].
% 1.00/1.37 22 -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].
% 1.00/1.37 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(1,a,2,a)].
% 1.00/1.37 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(1,a,3,a)].
% 1.00/1.37 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(1,a,4,a)].
% 1.00/1.37 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(1,a,5,a)].
% 1.00/1.37 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(1,a,7,a)].
% 1.00/1.37 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(1,a,8,a)].
% 1.00/1.37 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(1,a,9,a)].
% 1.00/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,10,a)].
% 1.00/1.37 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(1,a,12,a)].
% 1.00/1.38 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(1,a,13,a)].
% 1.00/1.38 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(1,a,14,a)].
% 1.00/1.38 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(1,a,15,a)].
% 1.00/1.38 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(1,a,16,a)].
% 1.00/1.38 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(1,a,19,a)].
% 1.00/1.38 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(1,a,20,a)].
% 1.00/1.38 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(1,a,21,a)].
% 1.00/1.38 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(1,a,22,a)].
% 1.00/1.38 23 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.38 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(23,a,2,a)].
% 1.00/1.38 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,3,a)].
% 1.00/1.38 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,4,a)].
% 1.00/1.38 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(23,a,5,a)].
% 1.00/1.38 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(23,a,7,a)].
% 1.00/1.38 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(23,a,8,a)].
% 1.00/1.38 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(23,a,9,a)].
% 1.00/1.38 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(23,a,10,a)].
% 1.00/1.38 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(23,a,12,a)].
% 1.00/1.38 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(23,a,13,a)].
% 1.00/1.38 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(23,a,14,a)].
% 1.00/1.38 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(23,a,15,a)].
% 1.00/1.38 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(23,a,16,a)].
% 1.00/1.38 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(23,a,19,a)].
% 1.00/1.38 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(23,a,20,a)].
% 1.00/1.41 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(23,a,21,a)].
% 1.00/1.41 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(23,a,22,a)].
% 1.00/1.41 24 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.41 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(24,a,2,a)].
% 1.00/1.41 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(24,a,3,a)].
% 1.00/1.41 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(24,a,4,a)].
% 1.00/1.41 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(24,a,5,a)].
% 1.00/1.41 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(24,a,7,a)].
% 1.00/1.41 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(24,a,8,a)].
% 1.00/1.41 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(24,a,9,a)].
% 1.00/1.41 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(24,a,10,a)].
% 1.00/1.41 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(24,a,12,a)].
% 1.00/1.41 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(24,a,13,a)].
% 1.00/1.41 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(24,a,14,a)].
% 1.00/1.41 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(24,a,15,a)].
% 1.00/1.41 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(24,a,16,a)].
% 1.00/1.41 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(24,a,19,a)].
% 1.00/1.41 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(24,a,20,a)].
% 1.00/1.41 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(24,a,21,a)].
% 1.00/1.41 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(24,a,22,a)].
% 1.00/1.41 25 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.00/1.41 26 -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].
% 1.00/1.41 27 -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].
% 1.00/1.41 28 -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].
% 1.00/1.41 29 -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].
% 1.00/1.41 30 -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].
% 1.00/1.41 31 -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].
% 1.00/1.41 32 -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].
% 1.00/1.41 33 -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].
% 1.00/1.41 34 -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].
% 1.00/1.41 35 -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].
% 1.00/1.41 36 -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].
% 1.00/1.41 37 -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].
% 1.00/1.41 38 -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].
% 1.00/1.41 39 -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].
% 1.00/1.41 40 -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].
% 1.00/1.41 41 -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].
% 1.00/1.41 42 -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].
% 1.00/1.41 43 -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].
% 1.00/1.41 44 -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].
% 1.00/1.41 45 -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].
% 1.00/1.41 46 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.00/1.41 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(25,a,26,a)].
% 1.00/1.41 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(25,a,27,a)].
% 1.00/1.41 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(25,a,28,a)].
% 1.00/1.41 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(25,a,31,a)].
% 1.00/1.41 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(25,a,32,a)].
% 1.00/1.41 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(25,a,33,a)].
% 1.00/1.41 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(25,a,34,a)].
% 1.00/1.41 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(25,a,35,a)].
% 1.00/1.41 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(25,a,36,a)].
% 1.00/1.41 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(25,a,37,a)].
% 1.00/1.41 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(25,a,40,a)].
% 1.00/1.41 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(25,a,41,a)].
% 1.00/1.41 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(25,a,42,a)].
% 1.00/1.41 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(25,a,43,a)].
% 1.00/1.41 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(25,a,44,a)].
% 1.00/1.41 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(25,a,45,a)].
% 1.00/1.41 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(25,a,46,a)].
% 1.00/1.41 47 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.00/1.41 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(47,a,26,a)].
% 1.00/1.41 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(47,a,27,a)].
% 1.00/1.41 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(47,a,28,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(47,a,31,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(47,a,32,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(47,a,33,a)].
% 1.00/1.41 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(47,a,34,a)].
% 1.00/1.41 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(47,a,35,a)].
% 1.00/1.41 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(47,a,36,a)].
% 1.00/1.41 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(47,a,37,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(47,a,40,a)].
% 1.00/1.41 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(47,a,41,a)].
% 1.00/1.41 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(47,a,42,a)].
% 1.00/1.41 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(47,a,43,a)].
% 1.00/1.41 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(47,a,44,a)].
% 1.00/1.41 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(47,a,45,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(47,a,46,a)].
% 1.00/1.41 48 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.00/1.41 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(48,a,26,a)].
% 1.00/1.41 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(48,a,27,a)].
% 1.00/1.41 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(48,a,28,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(48,a,31,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(48,a,32,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(48,a,33,a)].
% 1.00/1.41 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(48,a,34,a)].
% 1.00/1.41 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(48,a,35,a)].
% 1.00/1.41 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(48,a,36,a)].
% 1.00/1.41 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(48,a,37,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(48,a,40,a)].
% 1.00/1.41 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(48,a,41,a)].
% 1.00/1.41 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(48,a,42,a)].
% 1.00/1.41 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(48,a,43,a)].
% 1.00/1.41 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(48,a,44,a)].
% 1.00/1.41 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(48,a,45,a)].
% 1.00/1.41 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(48,a,46,a)].
% 1.40/1.67 49 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.40/1.67 50 -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].
% 1.40/1.67 51 -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].
% 1.40/1.67 52 -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].
% 1.40/1.67 53 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.40/1.67 54 -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].
% 1.40/1.67 55 -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].
% 1.40/1.67 56 -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].
% 1.40/1.67 57 -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].
% 1.40/1.67 58 -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].
% 1.40/1.67 59 -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].
% 1.40/1.67 60 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.40/1.67 61 -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].
% 1.40/1.67 62 -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].
% 1.40/1.67 63 -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].
% 1.40/1.67 64 -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].
% 1.40/1.67 65 -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].
% 1.40/1.67 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(49,a,50,a)].
% 1.40/1.67 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(49,a,51,a)].
% 1.40/1.67 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(49,a,53,a)].
% 1.40/1.67 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(49,a,54,a)].
% 1.40/1.67 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(49,a,56,a)].
% 1.40/1.67 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(49,a,60,a)].
% 1.40/1.67 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(49,a,61,a)].
% 1.40/1.67 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(49,a,65,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. c_Arrow__Order__Mirabelle_OLin=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OProf=1. c_Not=1. v_F=1. v_Q____=1. v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1=1. hAPP=1. tc_fun=1. tc_prod=1. c_Collect=1. c_Complete__Lattice_OSup__class_OSup=1. c_Complete__Lattice_OInf__class_OInf=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Set_OPow=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1=1. c_in=1. c_Orderings_Obot__class_Obot=1. c_HOL_Ouminus__class_Ouminus=1. c_fequal=1. c_HOL_Oundefined=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Arrow__Order__Mirabelle_Obelow=1. c_COMBK=1. c_Relation_Oconverse=1. c_FuncSet_Oextensional=1. c_ATP__Linkup_Osko__Set__XbexCI__1__1=1. c_Equiv__Relations_Oquotient=1. c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1=1. c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1=1. c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1=1. c_ATP__Linkup_Osko__Set__XballE__1__1=1. c_ATP__Linkup_Osko__Set__XbexE__1__1=1. c_ATP__Linkup_Osko__Set__XbexI__1__1=1. c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1=1. c_SetInterval_Oord_OatMost=1. c_SetInterval_Oord_OgreaterThan=1. c_SetInterval_Oord_OlessThan=1. c_Pair=1. c_Set_Oimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Set_Ovimage=1. c_Relation_OImage=1. c_COMBC=1. c_FuncSet_OPi=1. c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1=1. c_ATP__Linkup_Osko__Set__Xbex__Un__1__3=1. c_SetInterval_Oord_OatLeastAtMost=1. c_SetInterval_Oord_OgreaterThanLessThan=1. c_Finite__Set_Osetsum=1. c_List_Osko__Equiv__Relations__XquotientE__1__1=1. c_Fun_Ofun__upd=1. c_COMBB=1. c_FuncSet_Osko__FuncSet__XPi__I_H__1__1=1. c_FuncSet_Osko__FuncSet__XPi__I__1__1=1. c_FuncSet_Osko__FuncSet__XextensionalityI__1__1=1. c_SetInterval_Oord_OatLeastLessThan=1. c_SetInterval_Oord_OgreaterThanAtMost=1. c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3=1. c_FuncSet_Osko__FuncSet__XfuncsetI__1__1=1.
% 3.00/3.28
% 3.00/3.28 ============================== end of process initial clauses ========
% 3.00/3.28
% 3.00/3.28 ============================== CLAUSES FOR SEARCH ====================
% 3.00/3.28
% 3.00/3.28 ============================== end of clauses for search =============
% 3.00/3.28
% 3.00/3.28 ============================== SEARCH ================================
% 3.00/3.28
% 3.00/3.28 % Starting search at 0.41 seconds.
% 3.00/3.28
% 3.00/3.28 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 0.94 sec).
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=58.000, iters=3603
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=55.000, iters=3576
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=47.000, iters=3402
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=46.000, iters=3439
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=45.000, iters=3466
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=44.000, iters=3504
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=41.000, iters=3379
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=39.000, iters=3353
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=38.000, iters=3571
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=37.000, iters=3426
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=34.000, iters=3493
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=33.000, iters=3432
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=32.000, iters=3366
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=31.000, iters=3498
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=29.000, iters=3456
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=28.000, iters=3359
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=27.000, iters=3409
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=25.000, iters=3481
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=24.000, iters=3432
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=23.000, iters=3466
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=22.000, iters=3358
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=21.000, iters=3345
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=20.000, iters=3407
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=19.000, iters=3342
% 3.00/3.28
% 3.00/3.28 Low Water (keep): wt=18.000, iters=3343
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=2768, wt=188.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3104, wt=147.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3103, wt=146.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3124, wt=125.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3098, wt=123.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3132, wt=117.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3133, wt=113.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3038, wt=107.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3134, wt=101.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3052, wt=95.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3141, wt=91.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3116, wt=89.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=2773, wt=87.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3091, wt=85.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3581, wt=75.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=3118, wt=73.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=2774, wt=69.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=8327, wt=63.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=6915, wt=60.000
% 3.00/3.28
% 3.00/3.28 Low Water (displace): id=8361, wt=54.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=6914, wt=51.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=8557, wt=48.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=12109, wt=46.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=8554, wt=45.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=12107, wt=43.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=9022, wt=40.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=13333, wt=38.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=13335, wt=37.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=11526, wt=36.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=13331, wt=35.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=13334, wt=34.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=11527, wt=33.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=7075, wt=32.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=4382, wt=31.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=8352, wt=30.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=8324, wt=29.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=8377, wt=28.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=9342, wt=27.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=13861, wt=26.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=13889, wt=17.000
% 41.86/42.14
% 41.86/42.14 Low Water (keep): wt=17.000, iters=3334
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=14813, wt=16.000
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=16286, wt=15.000
% 41.86/42.14
% 41.86/42.14 Low Water (keep): wt=16.000, iters=3381
% 41.86/42.14
% 41.86/42.14 Low Water (keep): wt=15.000, iters=3333
% 41.86/42.14
% 41.86/42.14 Low Water (displace): id=20280, wt=14.000
% 41.86/42.14
% 41.86/42.14 ============================== PROOF =================================
% 41.86/42.14 % SZS status Unsatisfiable
% 41.86/42.14 % SZS output start Refutation
% 41.86/42.14
% 41.86/42.14 % Proof 1 at 40.13 (+ 0.76) seconds.
% 41.86/42.14 % Length of proof is 16.
% 41.86/42.14 % Level of proof is 5.
% 41.86/42.14 % Maximum clause weight is 48.000.
% 41.86/42.14 % Given clauses 13286.
% 41.86/42.14
% 41.86/42.14 299 hAPP(c_COMBK(A,B,C),D) = A # label(cls_COMBK__def_0) # label(axiom). [assumption].
% 41.86/42.14 300 hAPP(hAPP(c_COMBC(A,B,C,D),E),F) = hAPP(hAPP(A,F),E) # label(cls_COMBC__def_0) # label(axiom). [assumption].
% 41.86/42.14 339 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 41.86/42.14 602 c_Collect(hAPP(c_COMBC(c_in(A),A,tc_fun(A,tc_bool),tc_bool),B),A) = B # label(cls_Collect__mem__eq_0) # label(axiom). [assumption].
% 41.86/42.14 603 hAPP(c_COMBC(c_in(A),A,tc_fun(A,tc_bool),tc_bool),B) = B. [copy(602),rewrite([339(7)])].
% 41.86/42.14 686 hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),hAPP(D,C))) | -hBOOL(hAPP(hAPP(c_in(E),C),F)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(E,A)),B),c_FuncSet_OPi(F,D,E,A))) # label(cls_Pi__mem_0) # label(axiom). [assumption].
% 41.86/42.14 697 hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) # label(cls_CHAINED_0) # label(axiom). [assumption].
% 41.86/42.14 698 hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)) # label(cls_CHAINED_0_01) # label(axiom). [assumption].
% 41.86/42.14 699 -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 41.86/42.14 2613 hAPP(hAPP(c_in(A),B),C) = hAPP(C,B). [para(603(a,1),300(a,1,1)),flip(a)].
% 41.86/42.14 3362 -hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,v_Q____))). [back_rewrite(699),rewrite([2613(12)])].
% 41.86/42.14 3363 hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)). [back_rewrite(698),rewrite([2613(12)])].
% 41.86/42.14 3364 hBOOL(hAPP(c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F)). [back_rewrite(697),rewrite([2613(47)])].
% 41.86/42.14 3375 hBOOL(hAPP(hAPP(A,B),hAPP(C,B))) | -hBOOL(hAPP(D,B)) | -hBOOL(hAPP(c_FuncSet_OPi(D,A,E,F),C)). [back_rewrite(686),rewrite([2613(5),2613(7),2613(11)])].
% 41.86/42.14 138932 hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,A))) | -hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,A)). [resolve(3375,c,3364,a),rewrite([299(17)])].
% 41.86/42.14 138946 $F. [resolve(138932,b,3363,a),unit_del(a,3362)].
% 41.86/42.14
% 41.86/42.14 % SZS output end Refutation
% 41.86/42.14 ============================== end of proof ==========================
% 41.86/42.14
% 41.86/42.14 ============================== STATISTICS ============================
% 41.86/42.14
% 41.86/42.14 Given=13286. Generated=1249882. Kept=138710. proofs=1.
% 41.86/42.14 Usable=13006. Sos=9998. Demods=1653. Limbo=10, Disabled=116502. Hints=0.
% 41.86/42.14 Megabytes=127.53.
% 41.86/42.14 User_CPU=40.13, System_CPU=0.76, Wall_clock=41.
% 41.86/42.14
% 41.86/42.14 ============================== end of statistics =====================
% 41.86/42.14
% 41.86/42.14 ============================== end of search =========================
% 41.86/42.14
% 41.86/42.14 THEOREM PROVED
% 41.86/42.14 % SZS status Unsatisfiable
% 41.86/42.14
% 41.86/42.14 Exiting with 1 proof.
% 41.86/42.14
% 41.86/42.14 Process 18694 exit (max_proofs) Fri Jul 1 21:06:27 2022
% 41.86/42.14 Prover9 interrupted
%------------------------------------------------------------------------------