TSTP Solution File: SWV861-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV861-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 : Wed Jul 20 21:15:04 EDT 2022
% Result : Unsatisfiable 3.24s 3.56s
% Output : Refutation 3.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV861-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Tue Jun 14 18:25:13 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.72/1.07 ============================== Prover9 ===============================
% 0.72/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.07 Process 3367 was started by sandbox on n032.cluster.edu,
% 0.72/1.07 Tue Jun 14 18:25:13 2022
% 0.72/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3213_n032.cluster.edu".
% 0.72/1.07 ============================== end of head ===========================
% 0.72/1.07
% 0.72/1.07 ============================== INPUT =================================
% 0.72/1.07
% 0.72/1.07 % Reading from file /tmp/Prover9_3213_n032.cluster.edu
% 0.72/1.07
% 0.72/1.07 set(prolog_style_variables).
% 0.72/1.07 set(auto2).
% 0.72/1.07 % set(auto2) -> set(auto).
% 0.72/1.07 % set(auto) -> set(auto_inference).
% 0.72/1.07 % set(auto) -> set(auto_setup).
% 0.72/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.07 % set(auto) -> set(auto_limits).
% 0.72/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.07 % set(auto) -> set(auto_denials).
% 0.72/1.07 % set(auto) -> set(auto_process).
% 0.72/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.07 % set(auto2) -> assign(stats, some).
% 0.72/1.07 % set(auto2) -> clear(echo_input).
% 0.72/1.07 % set(auto2) -> set(quiet).
% 0.72/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.07 % set(auto2) -> clear(print_given).
% 0.72/1.07 assign(lrs_ticks,-1).
% 0.72/1.07 assign(sos_limit,10000).
% 0.72/1.07 assign(order,kbo).
% 0.72/1.07 set(lex_order_vars).
% 0.72/1.07 clear(print_given).
% 0.72/1.07
% 0.72/1.07 % formulas(sos). % not echoed (606 formulas)
% 0.72/1.07
% 0.72/1.07 ============================== end of input ==========================
% 0.72/1.07
% 0.72/1.07 % From the command line: assign(max_seconds, 300).
% 0.72/1.07
% 0.72/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.07
% 0.72/1.07 % Formulas that are not ordinary clauses:
% 0.72/1.07
% 0.72/1.07 ============================== end of process non-clausal formulas ===
% 0.72/1.07
% 0.72/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.07
% 0.72/1.07 ============================== PREDICATE ELIMINATION =================
% 0.72/1.07 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.72/1.07 2 -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].
% 0.72/1.07 3 -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].
% 0.72/1.07 4 -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].
% 0.72/1.07 5 -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].
% 0.72/1.07 6 -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].
% 0.72/1.07 7 -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].
% 0.72/1.07 8 -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].
% 0.72/1.07 9 -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].
% 0.72/1.07 10 -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].
% 0.72/1.07 11 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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].
% 0.72/1.07 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,2,a)].
% 0.72/1.07 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,3,a)].
% 0.72/1.07 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,4,a)].
% 0.72/1.07 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,5,a)].
% 0.72/1.07 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,6,a)].
% 0.72/1.07 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,7,a)].
% 0.72/1.07 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,8,a)].
% 0.72/1.07 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,11,a)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 23 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.72/1.07 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(23,a,2,a)].
% 0.72/1.07 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(23,a,3,a)].
% 0.72/1.07 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(23,a,4,a)].
% 0.72/1.07 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,5,a)].
% 0.72/1.07 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,6,a)].
% 0.72/1.07 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,7,a)].
% 0.72/1.07 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,8,a)].
% 0.72/1.07 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(23,a,11,a)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.72/1.07 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(23,a,15,a)].
% 0.72/1.07 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(23,a,16,a)].
% 0.72/1.07 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)].
% 0.72/1.07 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)].
% 0.75/1.10 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)].
% 0.75/1.10 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)].
% 0.75/1.10 24 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.75/1.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(24,a,2,a)].
% 0.75/1.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(24,a,3,a)].
% 0.75/1.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(24,a,4,a)].
% 0.75/1.10 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,5,a)].
% 0.75/1.10 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,6,a)].
% 0.75/1.10 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,7,a)].
% 0.75/1.10 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,8,a)].
% 0.75/1.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(24,a,11,a)].
% 0.75/1.10 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)].
% 0.75/1.10 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)].
% 0.75/1.10 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)].
% 0.75/1.10 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(24,a,15,a)].
% 0.75/1.10 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(24,a,16,a)].
% 0.75/1.10 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)].
% 0.75/1.10 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)].
% 0.75/1.10 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)].
% 0.75/1.10 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)].
% 0.75/1.10 25 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.75/1.10 26 -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].
% 0.75/1.10 27 -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].
% 0.75/1.10 28 -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].
% 0.75/1.10 29 -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].
% 0.75/1.10 30 -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].
% 0.75/1.10 31 -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].
% 0.75/1.10 32 -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].
% 0.75/1.10 33 -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].
% 0.75/1.10 34 -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].
% 0.75/1.10 35 -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].
% 0.75/1.10 36 -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].
% 0.75/1.10 37 -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].
% 0.75/1.10 38 -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].
% 0.75/1.10 39 -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].
% 0.75/1.10 40 -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].
% 0.75/1.10 41 -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].
% 0.75/1.10 42 -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].
% 0.75/1.10 43 -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].
% 0.75/1.10 44 -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].
% 0.75/1.10 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].
% 0.75/1.10 46 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.75/1.10 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,26,a)].
% 0.75/1.10 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,27,a)].
% 0.75/1.10 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,28,a)].
% 0.75/1.10 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,29,a)].
% 0.75/1.10 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,30,a)].
% 0.75/1.10 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,31,a)].
% 0.75/1.10 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,32,a)].
% 0.75/1.10 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,33,a)].
% 0.75/1.10 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,34,a)].
% 0.75/1.10 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,35,a)].
% 0.75/1.10 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,38,a)].
% 0.75/1.10 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,39,a)].
% 0.75/1.10 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,40,a)].
% 0.75/1.10 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,43,a)].
% 0.75/1.10 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,44,a)].
% 0.75/1.10 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)].
% 0.75/1.10 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(25,a,46,a)].
% 0.75/1.10 47 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.75/1.10 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,26,a)].
% 0.75/1.10 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,27,a)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(47,a,28,a)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(47,a,29,a)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(47,a,30,a)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(47,a,31,a)].
% 0.75/1.10 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,32,a)].
% 0.75/1.10 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,33,a)].
% 0.75/1.10 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,34,a)].
% 0.75/1.10 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,35,a)].
% 0.75/1.10 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,38,a)].
% 0.75/1.10 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,39,a)].
% 0.75/1.10 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,40,a)].
% 0.75/1.10 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(47,a,43,a)].
% 0.75/1.10 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(47,a,44,a)].
% 0.75/1.10 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)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(47,a,46,a)].
% 0.75/1.10 48 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.75/1.10 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,26,a)].
% 0.75/1.10 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,27,a)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(48,a,28,a)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(48,a,29,a)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(48,a,30,a)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(48,a,31,a)].
% 0.75/1.10 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,32,a)].
% 0.75/1.10 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,33,a)].
% 0.75/1.10 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,34,a)].
% 0.75/1.10 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,35,a)].
% 0.75/1.10 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,38,a)].
% 0.75/1.10 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,39,a)].
% 0.75/1.10 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,40,a)].
% 0.75/1.10 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(48,a,43,a)].
% 0.75/1.10 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(48,a,44,a)].
% 0.75/1.10 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)].
% 0.75/1.10 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(48,a,46,a)].
% 0.94/1.21 49 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.94/1.21 50 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.94/1.21 51 -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].
% 0.94/1.21 52 -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].
% 0.94/1.21 53 -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].
% 0.94/1.21 54 -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].
% 0.94/1.21 55 -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].
% 0.94/1.21 56 -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].
% 0.94/1.21 57 -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].
% 0.94/1.21 58 -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].
% 0.94/1.21 59 -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].
% 0.94/1.21 60 -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].
% 0.94/1.21 61 -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].
% 0.94/1.21 62 -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].
% 0.94/1.21 63 -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].
% 0.94/1.21 64 -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].
% 0.94/1.21 65 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.94/1.21 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(49,a,50,a)].
% 0.94/1.21 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(49,a,51,a)].
% 0.94/1.21 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(49,a,52,a)].
% 0.94/1.21 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(49,a,55,a)].
% 0.94/1.21 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(49,a,62,a)].
% 0.94/1.21 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(49,a,64,a)].
% 0.94/1.21 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(49,a,65,a)].
% 0.94/1.21
% 0.94/1.21 ============================== end predicate elimination =============
% 0.94/1.21
% 0.94/1.21 Auto_denials: (non-Horn, no changes).
% 0.94/1.21
% 0.94/1.21 Term ordering decisions:
% 0.94/1.21 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. v_P=1. v_Q=1. v_R=1. v_s=1. v_Z=1. v_n=1. c_Com_Ocom_OSKIP=1. t_b=1. t_c=1. v_c=1. v_d=1. v_p=1. v_s1=1. v_Ga=1. v_s_H=1. hAPP=1. tc_fun=1. c_Com_Ocom_OWhile=1. c_Collect=1. c_Com_Ocom_OSemi=1. c_Finite__Set_Ocard=1. c_and=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__1=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__2=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__3=1. v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1=1. c_in=1. c_Orderings_Obot__class_Obot=1. c_HOL_Ominus__class_Ominus=1. c_Suc=1. tc_Hoare__Mirabelle_Otriple=1. c_COMBI=1. c_fequal=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3=1. c_Com_Ocom_OCond=1. c_COMBK=1. c_ATP__Linkup_Osko__Set__XbexCI__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_Set_Oimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Set_Ovimage=1. c_COMBC=1. c_Hoare__Mirabelle_Otriple_Otriple=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_Fun_Ofun__upd=1. c_COMBB=1. c_SetInterval_Oord_OatLeastLessThan=1. c_SetInterval_Oord_OgreaterThanAtMost=1. c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3=1. c_COMBS=1. c_Hoare__Mirabelle_Opeek__and=1. c_Natural_Osko__Natural__Xevaln__max2__1__1=1.
% 3.24/3.56
% 3.24/3.56 ============================== end of process initial clauses ========
% 3.24/3.56
% 3.24/3.56 ============================== CLAUSES FOR SEARCH ====================
% 3.24/3.56
% 3.24/3.56 ============================== end of clauses for search =============
% 3.24/3.56
% 3.24/3.56 ============================== SEARCH ================================
% 3.24/3.56
% 3.24/3.56 % Starting search at 0.20 seconds.
% 3.24/3.56
% 3.24/3.56 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 49 (0.00 of 0.65 sec).
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=76.000, iters=3371
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=68.000, iters=3346
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=67.000, iters=3341
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=64.000, iters=3368
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=62.000, iters=3354
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=58.000, iters=3367
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=57.000, iters=3348
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=55.000, iters=3451
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=51.000, iters=3457
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=50.000, iters=3448
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=49.000, iters=3494
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=45.000, iters=3361
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=43.000, iters=3447
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=42.000, iters=3368
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=39.000, iters=3435
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=38.000, iters=3342
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=37.000, iters=3385
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=36.000, iters=3510
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=35.000, iters=3420
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=33.000, iters=3352
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=32.000, iters=3364
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=31.000, iters=3361
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=30.000, iters=3398
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=29.000, iters=3373
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=28.000, iters=3351
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=27.000, iters=3342
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=26.000, iters=3351
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=25.000, iters=3415
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=24.000, iters=3388
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=23.000, iters=3358
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=22.000, iters=3406
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=21.000, iters=3343
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=20.000, iters=3400
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=19.000, iters=3335
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=18.000, iters=3341
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=17.000, iters=3342
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=16.000, iters=3339
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=15.000, iters=3346
% 3.24/3.56
% 3.24/3.56 Low Water (keep): wt=14.000, iters=3341
% 3.24/3.56
% 3.24/3.56 ============================== PROOF =================================
% 3.24/3.56 % SZS status Unsatisfiable
% 3.24/3.56 % SZS output start Refutation
% 3.24/3.56
% 3.24/3.56 % Proof 1 at 2.48 (+ 0.07) seconds.
% 3.24/3.56 % Length of proof is 10.
% 3.24/3.56 % Level of proof is 3.
% 3.24/3.56 % Maximum clause weight is 17.000.
% 3.24/3.56 % Given clauses 2494.
% 3.24/3.56
% 3.24/3.56 630 hBOOL(hAPP(hAPP(v_P,v_Z),v_s)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 3.24/3.56 631 c_Natural_Oevaln(v_c,v_s,v_n,v_s1) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 3.24/3.56 632 c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 3.24/3.56 633 -hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 3.24/3.56 635 hBOOL(hAPP(hAPP(v_Q,A),B)) | -c_Natural_Oevaln(v_c,C,v_n,B) | -hBOOL(hAPP(hAPP(v_P,A),C)) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 3.24/3.56 636 hBOOL(hAPP(hAPP(v_R,A),B)) | -c_Natural_Oevaln(v_d,C,v_n,B) | -hBOOL(hAPP(hAPP(v_Q,A),C)) # label(cls_conjecture_6) # label(negated_conjecture). [assumption].
% 3.24/3.56 3061 hBOOL(hAPP(hAPP(v_Q,A),v_s1)) | -hBOOL(hAPP(hAPP(v_P,A),v_s)). [resolve(635,b,631,a)].
% 3.24/3.56 3062 hBOOL(hAPP(hAPP(v_R,A),v_s_H)) | -hBOOL(hAPP(hAPP(v_Q,A),v_s1)). [resolve(636,b,632,a)].
% 3.24/3.56 12965 hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)). [resolve(3061,b,630,a)].
% 3.24/3.56 13114 $F. [resolve(3062,b,12965,a),unit_del(a,633)].
% 3.24/3.56
% 3.24/3.56 % SZS output end Refutation
% 3.24/3.56 ============================== end of proof ==========================
% 3.24/3.56
% 3.24/3.56 ============================== STATISTICS ============================
% 3.24/3.56
% 3.24/3.56 Given=2494. Generated=80964. Kept=12893. proofs=1.
% 3.24/3.56 Usable=2446. Sos=9384. Demods=1082. Limbo=0, Disabled=1778. Hints=0.
% 3.24/3.56 Megabytes=22.25.
% 3.24/3.56 User_CPU=2.48, System_CPU=0.07, Wall_clock=3.
% 3.24/3.56
% 3.24/3.56 ============================== end of statistics =====================
% 3.24/3.56
% 3.24/3.56 ============================== end of search =========================
% 3.24/3.56
% 3.24/3.56 THEOREM PROVED
% 3.24/3.56 % SZS status Unsatisfiable
% 3.24/3.56
% 3.24/3.56 Exiting with 1 proof.
% 3.24/3.56
% 3.24/3.56 Process 3367 exit (max_proofs) Tue Jun 14 18:25:16 2022
% 3.24/3.56 Prover9 interrupted
%------------------------------------------------------------------------------