TSTP Solution File: SCT080-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT080-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 22:03:47 EDT 2022
% Result : Unsatisfiable 37.16s 37.47s
% Output : Refutation 37.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT080-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n015.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 : Sat Jul 2 06:04:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.06/1.42 ============================== Prover9 ===============================
% 1.06/1.42 Prover9 (32) version 2009-11A, November 2009.
% 1.06/1.42 Process 32212 was started by sandbox on n015.cluster.edu,
% 1.06/1.42 Sat Jul 2 06:04:44 2022
% 1.06/1.42 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32058_n015.cluster.edu".
% 1.06/1.42 ============================== end of head ===========================
% 1.06/1.42
% 1.06/1.42 ============================== INPUT =================================
% 1.06/1.42
% 1.06/1.42 % Reading from file /tmp/Prover9_32058_n015.cluster.edu
% 1.06/1.42
% 1.06/1.42 set(prolog_style_variables).
% 1.06/1.42 set(auto2).
% 1.06/1.42 % set(auto2) -> set(auto).
% 1.06/1.42 % set(auto) -> set(auto_inference).
% 1.06/1.42 % set(auto) -> set(auto_setup).
% 1.06/1.42 % set(auto_setup) -> set(predicate_elim).
% 1.06/1.42 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.06/1.42 % set(auto) -> set(auto_limits).
% 1.06/1.42 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.06/1.42 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.06/1.42 % set(auto) -> set(auto_denials).
% 1.06/1.42 % set(auto) -> set(auto_process).
% 1.06/1.42 % set(auto2) -> assign(new_constants, 1).
% 1.06/1.42 % set(auto2) -> assign(fold_denial_max, 3).
% 1.06/1.42 % set(auto2) -> assign(max_weight, "200.000").
% 1.06/1.42 % set(auto2) -> assign(max_hours, 1).
% 1.06/1.42 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.06/1.42 % set(auto2) -> assign(max_seconds, 0).
% 1.06/1.42 % set(auto2) -> assign(max_minutes, 5).
% 1.06/1.42 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.06/1.42 % set(auto2) -> set(sort_initial_sos).
% 1.06/1.42 % set(auto2) -> assign(sos_limit, -1).
% 1.06/1.42 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.06/1.42 % set(auto2) -> assign(max_megs, 400).
% 1.06/1.42 % set(auto2) -> assign(stats, some).
% 1.06/1.42 % set(auto2) -> clear(echo_input).
% 1.06/1.42 % set(auto2) -> set(quiet).
% 1.06/1.42 % set(auto2) -> clear(print_initial_clauses).
% 1.06/1.42 % set(auto2) -> clear(print_given).
% 1.06/1.42 assign(lrs_ticks,-1).
% 1.06/1.42 assign(sos_limit,10000).
% 1.06/1.42 assign(order,kbo).
% 1.06/1.42 set(lex_order_vars).
% 1.06/1.42 clear(print_given).
% 1.06/1.42
% 1.06/1.42 % formulas(sos). % not echoed (688 formulas)
% 1.06/1.42
% 1.06/1.42 ============================== end of input ==========================
% 1.06/1.42
% 1.06/1.42 % From the command line: assign(max_seconds, 300).
% 1.06/1.42
% 1.06/1.42 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.06/1.42
% 1.06/1.42 % Formulas that are not ordinary clauses:
% 1.06/1.42
% 1.06/1.42 ============================== end of process non-clausal formulas ===
% 1.06/1.42
% 1.06/1.42 ============================== PROCESS INITIAL CLAUSES ===============
% 1.06/1.42
% 1.06/1.42 ============================== PREDICATE ELIMINATION =================
% 1.06/1.42 1 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.06/1.42 2 -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].
% 1.06/1.42 3 -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].
% 1.06/1.42 4 -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].
% 1.06/1.42 5 -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].
% 1.06/1.42 6 -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].
% 1.06/1.42 7 -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].
% 1.06/1.42 8 -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].
% 1.06/1.42 9 -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].
% 1.06/1.42 10 -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].
% 1.06/1.42 11 -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].
% 1.06/1.42 12 -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].
% 1.06/1.42 13 -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].
% 1.06/1.42 14 -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].
% 1.06/1.42 15 -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].
% 1.06/1.42 16 -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].
% 1.06/1.42 17 -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].
% 1.06/1.42 18 -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].
% 1.06/1.42 19 -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].
% 1.06/1.42 20 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(1,a,2,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(1,a,3,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(1,a,4,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,7,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,8,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(1,a,9,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,10,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,11,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(1,a,12,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(1,a,13,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(1,a,16,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(1,a,17,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,18,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(1,a,19,a)].
% 1.06/1.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(1,a,20,a)].
% 1.06/1.42 21 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.06/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(21,a,2,a)].
% 1.06/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(21,a,3,a)].
% 1.06/1.42 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(21,a,4,a)].
% 1.06/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(21,a,7,a)].
% 1.06/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(21,a,8,a)].
% 1.06/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(21,a,9,a)].
% 1.06/1.42 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(21,a,10,a)].
% 1.06/1.42 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(21,a,11,a)].
% 1.06/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(21,a,12,a)].
% 1.06/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(21,a,13,a)].
% 1.06/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(21,a,16,a)].
% 1.06/1.42 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(21,a,17,a)].
% 1.06/1.42 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(21,a,18,a)].
% 1.06/1.42 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(21,a,19,a)].
% 1.06/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(21,a,20,a)].
% 1.06/1.42 22 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.06/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(22,a,2,a)].
% 1.06/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(22,a,3,a)].
% 1.06/1.42 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(22,a,4,a)].
% 1.06/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(22,a,7,a)].
% 1.06/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(22,a,8,a)].
% 1.06/1.44 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(22,a,9,a)].
% 1.06/1.44 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(22,a,10,a)].
% 1.06/1.44 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(22,a,11,a)].
% 1.06/1.44 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(22,a,12,a)].
% 1.06/1.44 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(22,a,13,a)].
% 1.06/1.44 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(22,a,16,a)].
% 1.06/1.44 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(22,a,17,a)].
% 1.06/1.44 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(22,a,18,a)].
% 1.06/1.44 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(22,a,19,a)].
% 1.06/1.44 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(22,a,20,a)].
% 1.06/1.44 23 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.06/1.44 24 -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].
% 1.06/1.44 25 -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].
% 1.06/1.44 26 -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].
% 1.06/1.44 27 -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].
% 1.06/1.44 28 -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].
% 1.06/1.44 29 -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].
% 1.06/1.44 30 -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].
% 1.06/1.44 31 -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].
% 1.06/1.44 32 -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].
% 1.06/1.44 33 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.06/1.44 34 -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].
% 1.06/1.44 35 -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].
% 1.06/1.44 36 -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].
% 1.06/1.44 37 -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].
% 1.06/1.44 38 -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].
% 1.06/1.44 39 -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].
% 1.06/1.44 40 -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].
% 1.06/1.44 41 -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].
% 1.06/1.44 42 -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].
% 1.06/1.44 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(23,a,24,a)].
% 1.06/1.44 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(23,a,25,a)].
% 1.06/1.44 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(23,a,26,a)].
% 1.06/1.44 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(23,a,27,a)].
% 1.06/1.44 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(23,a,28,a)].
% 1.06/1.44 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(23,a,29,a)].
% 1.06/1.44 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(23,a,30,a)].
% 1.06/1.44 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(23,a,33,a)].
% 1.06/1.44 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(23,a,34,a)].
% 1.06/1.44 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(23,a,35,a)].
% 1.06/1.44 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(23,a,36,a)].
% 1.06/1.44 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(23,a,37,a)].
% 1.06/1.44 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(23,a,38,a)].
% 1.06/1.45 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(23,a,41,a)].
% 1.06/1.45 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(23,a,42,a)].
% 1.06/1.45 43 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(43,a,24,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(43,a,25,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(43,a,26,a)].
% 1.06/1.45 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(43,a,27,a)].
% 1.06/1.45 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(43,a,28,a)].
% 1.06/1.45 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(43,a,29,a)].
% 1.06/1.45 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(43,a,30,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(43,a,33,a)].
% 1.06/1.45 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(43,a,34,a)].
% 1.06/1.45 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(43,a,35,a)].
% 1.06/1.45 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(43,a,36,a)].
% 1.06/1.45 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(43,a,37,a)].
% 1.06/1.45 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(43,a,38,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(43,a,41,a)].
% 1.06/1.45 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(43,a,42,a)].
% 1.06/1.45 44 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(44,a,24,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(44,a,25,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(44,a,26,a)].
% 1.06/1.45 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(44,a,27,a)].
% 1.06/1.45 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(44,a,28,a)].
% 1.06/1.45 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(44,a,29,a)].
% 1.06/1.45 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(44,a,30,a)].
% 1.06/1.45 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(44,a,33,a)].
% 1.06/1.45 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(44,a,34,a)].
% 1.06/1.53 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(44,a,35,a)].
% 1.06/1.53 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(44,a,36,a)].
% 1.06/1.53 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(44,a,37,a)].
% 1.06/1.53 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(44,a,38,a)].
% 1.06/1.53 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(44,a,41,a)].
% 1.06/1.53 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(44,a,42,a)].
% 1.06/1.53 45 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.06/1.53 46 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.06/1.53 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(45,a,46,a)].
% 1.06/1.53 47 c_Arrow__Order__Mirabelle_OIIA(v_F) # label(cls_assms_I3_J_0) # label(axiom). [assumption].
% 1.06/1.53 48 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,E))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,E,D)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,E,D)))) | -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))),D),c_Arrow__Order__Mirabelle_OProf)) | -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))),E),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_OIIA(C) # label(cls_IIA__def_0) # label(axiom). [assumption].
% 1.06/1.53 49 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,E))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,E)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,E)))) | -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))),E),c_Arrow__Order__Mirabelle_OProf)) | -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))),D),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_OIIA(C) # label(cls_IIA__def_1) # label(axiom). [assumption].
% 1.06/1.53 50 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,E))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,E,D)))) | -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))),D),c_Arrow__Order__Mirabelle_OProf)) | -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))),E),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_OIIA(C) # label(cls_IIA__def_2) # label(axiom). [assumption].
% 1.06/1.53 51 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,E))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,E)))) | -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))),E),c_Arrow__Order__Mirabelle_OProf)) | -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))),D),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_OIIA(C) # label(cls_IIA__def_3) # label(axiom). [assumption].
% 1.06/1.53 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,C))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,D))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,C)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,C)))) | -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))),C),c_Arrow__Order__Mirabelle_OProf)) | -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))),D),c_Arrow__Order__Mirabelle_OProf)). [resolve(47,a,48,g)].
% 1.06/1.55 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,C))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,D))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,C,D)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,C,D)))) | -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))),D),c_Arrow__Order__Mirabelle_OProf)) | -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))),C),c_Arrow__Order__Mirabelle_OProf)). [resolve(47,a,49,g)].
% 1.06/1.55 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,C))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,C)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,C)))) | -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))),C),c_Arrow__Order__Mirabelle_OProf)) | -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))),D),c_Arrow__Order__Mirabelle_OProf)). [resolve(47,a,50,g)].
% 1.06/1.55 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,C))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,C,D)))) | -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))),D),c_Arrow__Order__Mirabelle_OProf)) | -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))),C),c_Arrow__Order__Mirabelle_OProf)). [resolve(47,a,51,g)].
% 1.06/1.55 52 c_Arrow__Order__Mirabelle_Ounanimity(v_F) # label(cls_u_0) # label(axiom). [assumption].
% 1.06/1.55 53 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(A,B,D)))) | -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))),D),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_Ounanimity(C) # label(cls_unanimity__def_0) # label(axiom). [assumption].
% 1.06/1.72 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,C))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(A,B,C)))) | -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))),C),c_Arrow__Order__Mirabelle_OProf)). [resolve(52,a,53,d)].
% 1.06/1.72
% 1.06/1.72 ============================== end predicate elimination =============
% 1.06/1.72
% 1.06/1.72 Auto_denials: (non-Horn, no changes).
% 1.06/1.72
% 1.06/1.72 Term ordering decisions:
% 1.06/1.72 Function symbol KB weights: tc_Arrow__Order__Mirabelle_Oalt=1. tc_bool=1. tc_nat=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OLin=1. c_Arrow__Order__Mirabelle_OProf=1. v_F=1. v_Lba____=1. v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1=1. hAPP=1. tc_fun=1. tc_prod=1. c_Complete__Lattice_OSup__class_OSup=1. c_Collect=1. c_Complete__Lattice_OInf__class_OInf=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Set_OPow=1. c_Inductive_Ocomplete__lattice__class_Olfp=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1=1. c_in=1. c_Orderings_Obot__class_Obot=1. c_Orderings_Otop__class_Otop=1. c_COMBI=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_COMBK=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Arrow__Order__Mirabelle_Obelow=1. c_FuncSet_Oextensional=1. c_Relation_Oconverse=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. v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1=1. c_Pair=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_FuncSet_OPi=1. c_FuncSet_Orestrict=1. c_Hilbert__Choice_Oinv__into=1. c_COMBC=1. c_Relation_OImage=1. v_sko__Arrow__Order__Mirabelle__XIIA__def__1=1. v_sko__local__X3__1=1. c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1=1. c_Product__Type_OSigma=1. c_ATP__Linkup_Osko__Set__Xbex__Un__1__3=1. c_SetInterval_Oord_OatLeastAtMost=1. c_SetInterval_Oord_OgreaterThanLessThan=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1=1. c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1=1. c_Finite__Set_Osetsum=1. c_List_Osko__Equiv__Relations__XquotientE__1__1=1. c_Fun_Ofun__upd=1. v_sko__local__X4__1=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_FuncSet_Osko__FuncSet__XrestrictI__1__1=1. c_SetInterval_Oord_OatLeastLessThan=1. c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2=1. c_FuncSet_Osko__FuncSet__XfuncsetI__1__1=1. c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1=1. c_FuncSet_Ocompose=1. v_sko__local__X2__1=1. v_sko__local__Xpairwise__neutrality__1=1. v_sko__local__X1__1=1.
% 37.16/37.47
% 37.16/37.47 ============================== end of process initial clauses ========
% 37.16/37.47
% 37.16/37.47 ============================== CLAUSES FOR SEARCH ====================
% 37.16/37.47
% 37.16/37.47 ============================== end of clauses for search =============
% 37.16/37.47
% 37.16/37.47 ============================== SEARCH ================================
% 37.16/37.47
% 37.16/37.47 % Starting search at 0.41 seconds.
% 37.16/37.47
% 37.16/37.47 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 80 (0.00 of 1.48 sec).
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=64.000, iters=3494
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=59.000, iters=3359
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=58.000, iters=3494
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=53.000, iters=3343
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=52.000, iters=3361
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=47.000, iters=3340
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=44.000, iters=3449
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=42.000, iters=3386
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=41.000, iters=3354
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=39.000, iters=3382
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=38.000, iters=3369
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=36.000, iters=3471
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=35.000, iters=3384
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=34.000, iters=3342
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=33.000, iters=3368
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=32.000, iters=3378
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=31.000, iters=3348
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=29.000, iters=3352
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=27.000, iters=3685
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=26.000, iters=3438
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=24.000, iters=3431
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=23.000, iters=3474
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=22.000, iters=3456
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=4128, wt=191.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=4127, wt=187.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=6309, wt=39.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=13024, wt=38.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=7411, wt=37.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=12242, wt=35.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=7652, wt=34.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=13031, wt=33.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=9429, wt=32.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=13022, wt=31.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=6639, wt=30.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=5760, wt=28.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=6301, wt=27.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=13021, wt=26.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=13019, wt=25.000
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=21.000, iters=3448
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=13226, wt=20.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=13269, wt=19.000
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=13771, wt=18.000
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=20.000, iters=3381
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=19.000, iters=3340
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=14641, wt=17.000
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=18.000, iters=3340
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=15502, wt=16.000
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=17.000, iters=3335
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=16252, wt=15.000
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=16.000, iters=3334
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=18360, wt=14.000
% 37.16/37.47
% 37.16/37.47 Low Water (keep): wt=15.000, iters=3354
% 37.16/37.47
% 37.16/37.47 Low Water (displace): id=31933, wt=13.000
% 37.16/37.47
% 37.16/37.47 ============================== PROOF =================================
% 37.16/37.47 % SZS status Unsatisfiable
% 37.16/37.47 % SZS output start Refutation
% 37.16/37.47
% 37.16/37.47 % Proof 1 at 35.51 (+ 0.65) seconds.
% 37.16/37.47 % Length of proof is 21.
% 37.16/37.47 % Level of proof is 5.
% 37.16/37.47 % Maximum clause weight is 48.000.
% 37.16/37.47 % Given clauses 11878.
% 37.16/37.47
% 37.16/37.47 197 hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)) # label(cls_COMBB__def_0) # label(axiom). [assumption].
% 37.16/37.47 277 c_Set_Ovimage(A,B,C,D) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(D),A,D,tc_fun(tc_fun(D,tc_bool),tc_bool),C),C,tc_fun(D,tc_bool),tc_bool),B),C) # label(cls_vimage__def_0) # label(axiom). [assumption].
% 37.16/37.47 355 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 37.16/37.47 386 hAPP(hAPP(c_COMBC(A,B,C,D),E),F) = hAPP(hAPP(A,F),E) # label(cls_COMBC__def_0) # label(axiom). [assumption].
% 37.16/37.47 387 hAPP(c_COMBI(A),B) = B # label(cls_COMBI__def_0) # label(axiom). [assumption].
% 37.16/37.47 504 c_Set_Ovimage(c_COMBI(A),B,A,A) = B # label(cls_vimage__ident_0) # label(axiom). [assumption].
% 37.16/37.47 505 hAPP(c_COMBC(c_COMBB(c_in(A),c_COMBI(A),A,tc_fun(tc_fun(A,tc_bool),tc_bool),A),A,tc_fun(A,tc_bool),tc_bool),B) = B. [copy(504),rewrite([277(2),355(13)])].
% 37.16/37.47 716 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))),c_COMBK(A,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),A),c_Arrow__Order__Mirabelle_OLin)) # label(cls_const__Lin__Prof_0) # label(axiom). [assumption].
% 37.16/37.47 717 hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),D)) | -hBOOL(hAPP(hAPP(c_in(E),C),F)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(E,A)),B),c_FuncSet_OPi(F,c_COMBK(D,tc_fun(A,tc_bool),E),E,A))) # label(cls_funcset__mem_0) # label(axiom). [assumption].
% 37.16/37.47 719 hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) # label(cls_CHAINED_0) # label(axiom). [assumption].
% 37.16/37.47 720 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_01) # label(axiom). [assumption].
% 37.16/37.47 721 -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 37.16/37.47 2803 hAPP(hAPP(c_in(A),B),C) = hAPP(C,B). [para(505(a,1),386(a,1,1)),rewrite([197(9),387(4)]),flip(a)].
% 37.16/37.47 3913 -hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))). [back_rewrite(721),rewrite([2803(19)])].
% 37.16/37.47 3914 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(720),rewrite([2803(47)])].
% 37.16/37.47 3915 hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)). [back_rewrite(719),rewrite([2803(10)])].
% 37.16/37.47 3916 hBOOL(hAPP(A,hAPP(B,C))) | -hBOOL(hAPP(D,C)) | -hBOOL(hAPP(c_FuncSet_OPi(D,c_COMBK(A,tc_fun(E,tc_bool),F),F,E),B)). [back_rewrite(717),rewrite([2803(4),2803(6),2803(13)])].
% 37.16/37.47 3917 hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(A,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) | -hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,A)). [back_rewrite(716),rewrite([2803(18),2803(19)])].
% 37.16/37.47 203470 hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,A))) | -hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,A)). [resolve(3916,c,3914,a)].
% 37.16/37.47 203493 hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))). [resolve(3917,b,3915,a)].
% 37.16/37.47 206951 $F. [resolve(203493,a,203470,b),unit_del(a,3913)].
% 37.16/37.47
% 37.16/37.47 % SZS output end Refutation
% 37.16/37.47 ============================== end of proof ==========================
% 37.16/37.47
% 37.16/37.47 ============================== STATISTICS ============================
% 37.16/37.47
% 37.16/37.47 Given=11878. Generated=1050579. Kept=206726. proofs=1.
% 37.16/37.47 Usable=11671. Sos=9998. Demods=1506. Limbo=1, Disabled=185840. Hints=0.
% 37.16/37.47 Megabytes=180.89.
% 37.16/37.47 User_CPU=35.51, System_CPU=0.65, Wall_clock=37.
% 37.16/37.47
% 37.16/37.47 ============================== end of statistics =====================
% 37.16/37.47
% 37.16/37.47 ============================== end of search =========================
% 37.16/37.47
% 37.16/37.47 THEOREM PROVED
% 37.16/37.47 % SZS status Unsatisfiable
% 37.16/37.47
% 37.16/37.47 Exiting with 1 proof.
% 37.16/37.47
% 37.16/37.47 Process 32212 exit (max_proofs) Sat Jul 2 06:05:21 2022
% 37.16/37.47 Prover9 interrupted
%------------------------------------------------------------------------------