TSTP Solution File: SCT002-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT002-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 22:03:22 EDT 2022
% Result : Unsatisfiable 76.36s 76.68s
% Output : Refutation 76.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SCT002-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 06:52:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.96/1.29 ============================== Prover9 ===============================
% 0.96/1.29 Prover9 (32) version 2009-11A, November 2009.
% 0.96/1.29 Process 12128 was started by sandbox2 on n007.cluster.edu,
% 0.96/1.29 Sat Jul 2 06:52:41 2022
% 0.96/1.29 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_11975_n007.cluster.edu".
% 0.96/1.29 ============================== end of head ===========================
% 0.96/1.29
% 0.96/1.29 ============================== INPUT =================================
% 0.96/1.29
% 0.96/1.29 % Reading from file /tmp/Prover9_11975_n007.cluster.edu
% 0.96/1.29
% 0.96/1.29 set(prolog_style_variables).
% 0.96/1.29 set(auto2).
% 0.96/1.29 % set(auto2) -> set(auto).
% 0.96/1.29 % set(auto) -> set(auto_inference).
% 0.96/1.29 % set(auto) -> set(auto_setup).
% 0.96/1.29 % set(auto_setup) -> set(predicate_elim).
% 0.96/1.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.96/1.29 % set(auto) -> set(auto_limits).
% 0.96/1.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.96/1.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.96/1.29 % set(auto) -> set(auto_denials).
% 0.96/1.29 % set(auto) -> set(auto_process).
% 0.96/1.29 % set(auto2) -> assign(new_constants, 1).
% 0.96/1.29 % set(auto2) -> assign(fold_denial_max, 3).
% 0.96/1.29 % set(auto2) -> assign(max_weight, "200.000").
% 0.96/1.29 % set(auto2) -> assign(max_hours, 1).
% 0.96/1.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.96/1.29 % set(auto2) -> assign(max_seconds, 0).
% 0.96/1.29 % set(auto2) -> assign(max_minutes, 5).
% 0.96/1.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.96/1.29 % set(auto2) -> set(sort_initial_sos).
% 0.96/1.29 % set(auto2) -> assign(sos_limit, -1).
% 0.96/1.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.96/1.29 % set(auto2) -> assign(max_megs, 400).
% 0.96/1.29 % set(auto2) -> assign(stats, some).
% 0.96/1.29 % set(auto2) -> clear(echo_input).
% 0.96/1.29 % set(auto2) -> set(quiet).
% 0.96/1.29 % set(auto2) -> clear(print_initial_clauses).
% 0.96/1.29 % set(auto2) -> clear(print_given).
% 0.96/1.29 assign(lrs_ticks,-1).
% 0.96/1.29 assign(sos_limit,10000).
% 0.96/1.29 assign(order,kbo).
% 0.96/1.29 set(lex_order_vars).
% 0.96/1.29 clear(print_given).
% 0.96/1.29
% 0.96/1.29 % formulas(sos). % not echoed (677 formulas)
% 0.96/1.29
% 0.96/1.29 ============================== end of input ==========================
% 0.96/1.29
% 0.96/1.29 % From the command line: assign(max_seconds, 300).
% 0.96/1.29
% 0.96/1.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.96/1.29
% 0.96/1.29 % Formulas that are not ordinary clauses:
% 0.96/1.29
% 0.96/1.29 ============================== end of process non-clausal formulas ===
% 0.96/1.29
% 0.96/1.29 ============================== PROCESS INITIAL CLAUSES ===============
% 0.96/1.29
% 0.96/1.29 ============================== PREDICATE ELIMINATION =================
% 0.96/1.29 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.96/1.29 2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.96/1.29 3 -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].
% 0.96/1.29 4 -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].
% 0.96/1.29 5 -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].
% 0.96/1.29 6 -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].
% 0.96/1.29 7 -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].
% 0.96/1.29 8 -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].
% 0.96/1.29 9 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.96/1.29 10 -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].
% 0.96/1.29 11 -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].
% 0.96/1.29 12 -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].
% 0.96/1.29 13 -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].
% 0.96/1.29 14 -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].
% 0.96/1.29 15 -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].
% 0.96/1.29 16 -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].
% 0.96/1.29 17 -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].
% 0.96/1.29 18 -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].
% 0.96/1.29 19 -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].
% 0.96/1.29 20 -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].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,2,a)].
% 0.96/1.29 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,3,a)].
% 0.96/1.29 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,4,a)].
% 0.96/1.29 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,5,a)].
% 0.96/1.29 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,6,a)].
% 0.96/1.29 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,7,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)). [resolve(1,a,9,a)].
% 0.96/1.29 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,10,a)].
% 0.96/1.29 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,11,a)].
% 0.96/1.29 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,13,a)].
% 0.96/1.34 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,14,a)].
% 0.96/1.34 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,15,a)].
% 0.96/1.34 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,16,a)].
% 0.96/1.34 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,17,a)].
% 0.96/1.34 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,18,a)].
% 0.96/1.34 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(21,a,2,a)].
% 0.96/1.34 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(21,a,3,a)].
% 0.96/1.34 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(21,a,4,a)].
% 0.96/1.34 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(21,a,5,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(21,a,6,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(21,a,7,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(21,a,9,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(21,a,10,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(21,a,11,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(21,a,13,a)].
% 0.96/1.34 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(21,a,14,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(21,a,15,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(21,a,16,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,17,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(21,a,18,a)].
% 0.96/1.34 22 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.96/1.34 23 -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].
% 0.96/1.34 24 -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].
% 0.96/1.34 25 -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].
% 0.96/1.34 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].
% 0.96/1.34 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].
% 0.96/1.34 28 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.96/1.34 29 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.96/1.34 30 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.96/1.34 31 -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].
% 0.96/1.34 32 -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].
% 0.96/1.34 33 -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].
% 0.96/1.34 34 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.96/1.34 35 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.96/1.34 36 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.96/1.34 37 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.96/1.34 38 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.96/1.34 39 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.96/1.34 40 -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].
% 0.96/1.34 41 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.96/1.34 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(22,a,23,a)].
% 0.96/1.34 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(22,a,24,a)].
% 0.96/1.34 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(22,a,25,a)].
% 0.96/1.34 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(22,a,26,a)].
% 0.96/1.34 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(22,a,27,a)].
% 0.96/1.34 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(22,a,28,a)].
% 0.96/1.34 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(22,a,31,a)].
% 0.96/1.34 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(22,a,32,a)].
% 0.96/1.34 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(22,a,33,a)].
% 0.96/1.34 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(22,a,34,a)].
% 0.96/1.34 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(22,a,35,a)].
% 0.96/1.34 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(22,a,36,a)].
% 0.96/1.34 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(22,a,37,a)].
% 0.96/1.34 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(22,a,40,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(22,a,41,a)].
% 0.96/1.34 42 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(42,a,23,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(42,a,24,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(42,a,25,a)].
% 0.96/1.34 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(42,a,26,a)].
% 0.96/1.34 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(42,a,27,a)].
% 0.96/1.34 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(42,a,28,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(42,a,31,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(42,a,32,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(42,a,33,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(42,a,34,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(42,a,35,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(42,a,36,a)].
% 0.96/1.38 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(42,a,37,a)].
% 0.96/1.38 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(42,a,40,a)].
% 0.96/1.38 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(42,a,41,a)].
% 0.96/1.38 43 c_Order__Relation_Ostrict__linear__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C) | -c_Relation_Oirrefl(B,C) | -c_Relation_Otrans(B,C) # label(cls_strict__linear__order__on__def_3) # label(axiom). [assumption].
% 0.96/1.38 44 c_Relation_Ototal__on(A,B,C) | -c_Order__Relation_Ostrict__linear__order__on(A,B,C) # label(cls_strict__linear__order__on__def_2) # label(axiom). [assumption].
% 0.96/1.38 45 c_Relation_Otrans(A,B) | -c_Order__Relation_Ostrict__linear__order__on(C,A,B) # label(cls_strict__linear__order__on__def_0) # label(axiom). [assumption].
% 0.96/1.38 46 c_Relation_Oirrefl(A,B) | -c_Order__Relation_Ostrict__linear__order__on(C,A,B) # label(cls_strict__linear__order__on__def_1) # label(axiom). [assumption].
% 0.96/1.38 47 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oequiv(c_Relation_ODomain(A,B,B),A,B) # label(cls_comp__equivI_0) # label(axiom). [assumption].
% 0.96/1.38 48 c_lessequals(A,c_Product__Type_OSigma(B,c_COMBK(B,tc_fun(C,tc_bool),C),C,C),tc_fun(tc_prod(C,C),tc_bool)) | -c_Equiv__Relations_Oequiv(B,A,C) # label(cls_equiv__type_0) # label(axiom). [assumption].
% 0.96/1.38 49 c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__subset_0) # label(axiom). [assumption].
% 0.96/1.38 50 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(B,E,C)) | -c_lessequals(c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,D,C) # label(cls_subset__equiv__class_0) # label(axiom). [assumption].
% 0.96/1.38 51 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)),C)) | -c_Equiv__Relations_Oequiv(F,D,C) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 0.96/1.38 52 hBOOL(c_in(A,c_Relation_OImage(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),C)) | -hBOOL(c_in(A,D,C)) | -c_Equiv__Relations_Oequiv(D,B,C) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 0.96/1.38 53 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 0.96/1.38 54 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 0.96/1.38 55 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 0.96/1.38 56 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 0.96/1.38 57 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 0.96/1.38 58 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 0.96/1.38 59 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 0.96/1.38 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(A,c_Product__Type_OSigma(c_Relation_ODomain(A,B,B),c_COMBK(c_Relation_ODomain(A,B,B),tc_fun(B,tc_bool),B),B,B),tc_fun(tc_prod(B,B),tc_bool)). [resolve(47,b,48,b)].
% 0.96/1.38 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(47,b,49,c)].
% 0.96/1.38 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)). [resolve(47,b,50,d)].
% 0.96/1.38 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)),B)). [resolve(47,b,51,c)].
% 0.96/1.38 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(C,c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(47,b,52,c)].
% 0.96/1.38 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(47,b,53,c)].
% 0.96/1.38 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)). [resolve(47,b,55,d)].
% 0.96/1.38 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_Otrans(A,B). [resolve(47,b,59,b)].
% 0.96/1.38 60 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) = A | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv__comp__eq_0) # label(axiom). [assumption].
% 0.96/1.38 61 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 0.96/1.38 Derived: c_Relation_Orefl__on(c_Relation_ODomain(A,B,B),A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(61,b,47,b)].
% 0.96/1.55 62 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 0.96/1.55 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(62,b,47,b)].
% 0.96/1.55 63 c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -hBOOL(c_in(C,F,V6)) | -c_Equiv__Relations_Ocongruent2(V7,A,B,V6,D,E) | -c_Equiv__Relations_Oequiv(F,V7,V6) # label(cls_congruent2__implies__congruent_0) # label(axiom). [assumption].
% 0.96/1.55 Derived: c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -hBOOL(c_in(C,c_Relation_ODomain(F,V6,V6),V6)) | -c_Equiv__Relations_Ocongruent2(F,A,B,V6,D,E) | c_Relation_Orel__comp(c_Relation_Oconverse(F,V6,V6),F,V6,V6,V6) != F. [resolve(63,d,47,b)].
% 0.96/1.55 64 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(D,A,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_2) # label(axiom). [assumption].
% 0.96/1.55 Derived: hBOOL(c_in(A,c_Relation_ODomain(B,C,C),C)) | -hBOOL(c_in(c_Pair(D,A,C,C),B,tc_prod(C,C))) | c_Relation_Orel__comp(c_Relation_Oconverse(B,C,C),B,C,C,C) != B. [resolve(64,c,47,b)].
% 0.96/1.55 65 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(A,D,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_1) # label(axiom). [assumption].
% 0.96/1.55 66 -hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -c_Relation_Oirrefl(C,B) # label(cls_irrefl__def_0) # label(axiom). [assumption].
% 0.96/1.55 67 c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(A,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),B) # label(cls_irrefl__diff__Id_0) # label(axiom). [assumption].
% 0.96/1.55 68 c_Relation_Oirrefl(A,B) | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),B,B),A,tc_prod(B,B))) # label(cls_irrefl__def_1) # label(axiom). [assumption].
% 0.96/1.55 Derived: -hBOOL(c_in(c_Pair(A,A,B,B),c_HOL_Ominus__class_Ominus(C,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),tc_prod(B,B))). [resolve(66,b,67,a)].
% 0.96/1.55 Derived: -hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),B,B),C,tc_prod(B,B))). [resolve(66,b,68,a)].
% 0.96/1.55 69 hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -c_Nitpick_Orefl_H(C,B) # label(cls_Nitpick_Orefl_H__def_0) # label(axiom). [assumption].
% 0.96/1.55 70 c_Nitpick_Orefl_H(A,B) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),B,B),A,tc_prod(B,B))) # label(cls_Nitpick_Orefl_H__def_1) # label(axiom). [assumption].
% 0.96/1.55 Derived: hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),B,B),C,tc_prod(B,B))). [resolve(69,b,70,a)].
% 0.96/1.55 71 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 0.96/1.55 72 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 0.96/1.55 Derived: A = A. [resolve(71,b,72,a)].
% 0.96/1.55
% 0.96/1.55 ============================== end predicate elimination =============
% 0.96/1.55
% 0.96/1.55 Auto_denials: (non-Horn, no changes).
% 0.96/1.55
% 0.96/1.55 Term ordering decisions:
% 0.96/1.55 Function symbol KB weights: tc_bool=1. t_a=1. v_x=1. tc_Arrow__Order__Mirabelle_Oalt=1. t_b=1. v_y=1. v_L=1. v_r=1. v_R=1. v_c=1. t_c=1. tc_fun=1. tc_prod=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Relation_OField=1. c_Relation_OId__on=1. c_snd=1. v_sko__Wellfounded__Xacc__Xinduct__1=1. v_sko__Wellfounded__Xacc__Xinducts__1=1. c_ATP__Linkup_Osko__Relation__XIdE__1__1=1. c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1=1. c_ATP__Linkup_Osko__Relation__XtransI__1__1=1. c_ATP__Linkup_Osko__Relation__XtransI__1__2=1. c_ATP__Linkup_Osko__Relation__XtransI__1__3=1. c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1=1. c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2=1. c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3=1. c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1=1. c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1=1. c_Orderings_Obot__class_Obot=1. c_Relation_OId=1. c_in=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_Relation_Oconverse=1. c_Relation_ODomain=1. c_COMBK=1. c_Relation_ORange=1. c_ATP__Linkup_Osko__Relation__XId__onE__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1=1. c_FunDef_Oin__rel=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1=1. c_List_Osko__Recdef__Xtfl__wf__induct__1__1=1. v_sko__Transitive__Closure__Xrtrancl__Xcases__1=1. v_sko__Transitive__Closure__Xtrancl__Xcases__1=1. c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1=1. c_Pair=1. c_Product__Type_OSigma=1. c_Relation_OImage=1. c_Set_Oimage=1. c_Relation_Oinv__image=1. c_split=1. c_curry=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2=1. c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomainE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1=1. c_ATP__Linkup_Osko__Relation__XRangeE__1__1=1. c_ATP__Linkup_Osko__Relation__XRange__iff__1__1=1. c_Relation_Orel__comp=1. c_Recdef_Ocut=1. c_ATP__Linkup_Osko__Relation__XImageE__1__1=1. c_ATP__Linkup_Osko__Relation__XImage__iff__1__1=1. c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1=1. c_List_Osko__Recdef__Xcuts__eq__1__1=1. c_Predicate_Oinv__imagep=1. c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1=1.
% 2.33/2.65
% 2.33/2.65 ============================== end of process initial clauses ========
% 2.33/2.65
% 2.33/2.65 ============================== CLAUSES FOR SEARCH ====================
% 2.33/2.65
% 2.33/2.65 ============================== end of clauses for search =============
% 2.33/2.65
% 2.33/2.65 ============================== SEARCH ================================
% 2.33/2.65
% 2.33/2.65 % Starting search at 0.35 seconds.
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=56.000, iters=3472
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=50.000, iters=3341
% 2.33/2.65
% 2.33/2.65 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 67 (0.00 of 0.78 sec).
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=49.000, iters=3385
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=48.000, iters=3356
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=46.000, iters=3355
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=45.000, iters=3441
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=44.000, iters=3387
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% 2.33/2.65 Low Water (keep): wt=43.000, iters=3486
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% 2.33/2.65 Low Water (keep): wt=42.000, iters=3378
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=41.000, iters=3425
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=40.000, iters=3343
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=39.000, iters=3398
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=38.000, iters=3363
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% 2.33/2.65 Low Water (keep): wt=37.000, iters=3349
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=36.000, iters=3399
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% 2.33/2.65 Low Water (keep): wt=34.000, iters=3345
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=33.000, iters=3384
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=32.000, iters=3440
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=31.000, iters=3380
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=30.000, iters=3340
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=29.000, iters=3453
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=28.000, iters=3369
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=27.000, iters=3346
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=26.000, iters=3353
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=25.000, iters=3369
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=24.000, iters=3353
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=23.000, iters=3341
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=22.000, iters=3348
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=21.000, iters=3480
% 2.33/2.65
% 2.33/2.65 Low Water (keep): wt=20.000, iters=3337
% 76.36/76.68
% 76.36/76.68 Low Water (keep): wt=19.000, iters=3339
% 76.36/76.68
% 76.36/76.68 Low Water (keep): wt=18.000, iters=3336
% 76.36/76.68
% 76.36/76.68 Low Water (displace): id=2629, wt=103.000
% 76.36/76.68
% 76.36/76.68 Low Water (displace): id=5277, wt=45.000
% 76.36/76.68
% 76.36/76.68 Low Water (displace): id=12679, wt=16.000
% 76.36/76.68
% 76.36/76.68 Low Water (displace): id=13096, wt=15.000
% 76.36/76.68
% 76.36/76.68 Low Water (keep): wt=17.000, iters=3334
% 76.36/76.68
% 76.36/76.68 Low Water (displace): id=17803, wt=14.000
% 76.36/76.68
% 76.36/76.68 Low Water (keep): wt=16.000, iters=3333
% 76.36/76.68
% 76.36/76.68 Low Water (keep): wt=15.000, iters=3335
% 76.36/76.68
% 76.36/76.68 ============================== PROOF =================================
% 76.36/76.68 % SZS status Unsatisfiable
% 76.36/76.68 % SZS output start Refutation
% 76.36/76.68
% 76.36/76.68 % Proof 1 at 73.85 (+ 1.62) seconds.
% 76.36/76.68 % Length of proof is 97.
% 76.36/76.68 % Level of proof is 22.
% 76.36/76.68 % Maximum clause weight is 35.000.
% 76.36/76.68 % Given clauses 25004.
% 76.36/76.68
% 76.36/76.68 94 c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_fun(B,tc_bool)) = A # label(cls_Un__absorb_0) # label(axiom). [assumption].
% 76.36/76.68 102 hAPP(c_COMBK(A,B,C),D) = A # label(cls_COMBK__def_0) # label(axiom). [assumption].
% 76.36/76.68 113 c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # label(cls_Un__upper2_0) # label(axiom). [assumption].
% 76.36/76.68 114 c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # label(cls_Un__upper1_0) # label(axiom). [assumption].
% 76.36/76.68 125 c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)) # label(cls_empty__subsetI_0) # label(axiom). [assumption].
% 76.36/76.68 126 -class_Orderings_Obot(A) | c_lessequals(c_Orderings_Obot__class_Obot(A),B,A) # label(cls_bot__least_0) # label(axiom). [assumption].
% 76.36/76.68 188 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__eq__iff_2) # label(axiom). [assumption].
% 76.36/76.68 288 -class_HOL_Oord(A) | c_lessequals(hAPP(B,C),hAPP(D,C),A) | -c_lessequals(B,D,tc_fun(E,A)) # label(cls_le__funD_0) # label(axiom). [assumption].
% 76.36/76.68 291 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(A,D,C)) | -c_lessequals(D,B,tc_fun(C,tc_bool)) # label(cls_subset__iff_0) # label(axiom). [assumption].
% 76.36/76.68 328 c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_fun(B,tc_bool)) = A # label(cls_Int__absorb_0) # label(axiom). [assumption].
% 76.36/76.68 329 c_Relation_OField(A,B) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(A,B,B),c_Relation_ORange(A,B,B),tc_fun(B,tc_bool)) # label(cls_Field__def_0) # label(axiom). [assumption].
% 76.36/76.68 330 c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(A,B,B),c_Relation_ORange(A,B,B),tc_fun(B,tc_bool)) = c_Relation_OField(A,B). [copy(329),flip(a)].
% 76.36/76.68 336 c_lessequals(A,A,tc_fun(B,tc_bool)) # label(cls_equalityE_0) # label(axiom). [assumption].
% 76.36/76.68 338 hBOOL(hAPP(A,B)) | -hBOOL(hAPP(C,B)) | -c_lessequals(C,A,tc_fun(D,tc_bool)) # label(cls_predicate1D_0) # label(axiom). [assumption].
% 76.36/76.68 339 c_Wellfounded_Owf(A,B) | -c_lessequals(A,C,tc_fun(tc_prod(B,B),tc_bool)) | -c_Wellfounded_Owf(C,B) # label(cls_wf__subset_0) # label(axiom). [assumption].
% 76.36/76.68 388 c_Transitive__Closure_Otrancl(A,B) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(A,B),A,B,B,B),tc_fun(tc_prod(B,B),tc_bool)) # label(cls_trancl__unfold_0) # label(axiom). [assumption].
% 76.36/76.68 389 c_Lattices_Oupper__semilattice__class_Osup(A,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(A,B),A,B,B,B),tc_fun(tc_prod(B,B),tc_bool)) = c_Transitive__Closure_Otrancl(A,B). [copy(388),flip(a)].
% 76.36/76.68 400 c_Relation_OImage(c_Relation_OId__on(A,B),C,B,B) = c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_fun(B,tc_bool)) # label(cls_Image__Id__on_0) # label(axiom). [assumption].
% 76.36/76.68 439 A = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | -c_lessequals(A,c_Relation_OImage(C,A,B,B),tc_fun(B,tc_bool)) | -c_Wellfounded_Owf(C,B) # label(cls_wfE__pf_0) # label(axiom). [assumption].
% 76.36/76.68 440 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = B | -c_lessequals(B,c_Relation_OImage(C,B,A,A),tc_fun(A,tc_bool)) | -c_Wellfounded_Owf(C,A). [copy(439),flip(a)].
% 76.36/76.68 443 c_Wellfounded_Owf(A,B) | -hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(A,B),c_Wellfounded_Oacc(A,B),B)) # label(cls_acc__wfI_0) # label(axiom). [assumption].
% 76.36/76.68 490 -hBOOL(c_in(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B)) # label(cls_emptyE_0) # label(axiom). [assumption].
% 76.36/76.68 501 c_Relation_ODomain(c_Transitive__Closure_Otrancl(A,B),B,B) = c_Relation_ODomain(A,B,B) # label(cls_trancl__domain_0) # label(axiom). [assumption].
% 76.36/76.68 520 c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_bool)) # label(cls_Id__on__empty_0) # label(axiom). [assumption].
% 76.36/76.68 521 c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A). [copy(520),flip(a)].
% 76.36/76.68 528 c_Relation_ODomain(c_Relation_OId__on(A,B),B,B) = A # label(cls_Domain__Id__on_0) # label(axiom). [assumption].
% 76.36/76.68 532 c_Relation_ORange(c_Transitive__Closure_Otrancl(A,B),B,B) = c_Relation_ORange(A,B,B) # label(cls_trancl__range_0) # label(axiom). [assumption].
% 76.36/76.68 540 -class_Orderings_Obot(A) | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,A)),v_x) = c_Orderings_Obot__class_Obot(A) # label(cls_bot__fun__eq_0) # label(axiom). [assumption].
% 76.36/76.68 561 c_Relation_ORange(c_Relation_OId__on(A,B),B,B) = A # label(cls_Range__Id__on_0) # label(axiom). [assumption].
% 76.36/76.68 567 -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)) # label(cls_bot1E_0) # label(axiom). [assumption].
% 76.36/76.68 597 c_Relation_Otrans(c_Relation_OId__on(A,B),B) # label(cls_trans__Id__on_0) # label(axiom). [assumption].
% 76.36/76.68 598 c_Transitive__Closure_Otrancl(A,B) = A | -c_Relation_Otrans(A,B) # label(cls_trancl__id_0) # label(axiom). [assumption].
% 76.36/76.68 605 hBOOL(c_in(A,c_Wellfounded_Oacc(B,C),C)) | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(B,A,C),A,C,C),B,tc_prod(C,C))) # label(cls_acc_OaccI_0) # label(axiom). [assumption].
% 76.36/76.68 649 hBOOL(c_in(c_Pair(A,B,C,C),c_Transitive__Closure_Otrancl(D,C),tc_prod(C,C))) | -hBOOL(c_in(c_Pair(E,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(c_Pair(A,E,C,C),D,tc_prod(C,C))) # label(cls_r__r__into__trancl_0) # label(axiom). [assumption].
% 76.36/76.68 664 hBOOL(c_in(A,c_Relation_ORange(B,C,D),D)) | -hBOOL(c_in(c_Pair(E,A,C,D),B,tc_prod(C,D))) # label(cls_Range__iff_1) # label(axiom). [assumption].
% 76.36/76.68 675 hBOOL(c_in(A,B,C)) | -hBOOL(hAPP(B,A)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 76.36/76.68 676 hBOOL(hAPP(A,B)) | -hBOOL(c_in(B,A,C)) # label(cls_mem__def_0) # label(axiom). [assumption].
% 76.36/76.68 679 c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 76.36/76.68 680 -hBOOL(c_in(c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 76.36/76.68 681 hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 76.36/76.68 682 hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 76.36/76.68 696 class_Orderings_Oorder(tc_bool) # label(clsarity_bool__Orderings_Oorder) # label(axiom). [assumption].
% 76.36/76.68 697 class_Orderings_Obot(tc_bool) # label(clsarity_bool__Orderings_Obot) # label(axiom). [assumption].
% 76.36/76.68 699 class_HOL_Oord(tc_bool) # label(clsarity_bool__HOL_Oord) # label(axiom). [assumption].
% 76.36/76.68 1675 c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B),hAPP(C,B),tc_bool). [resolve(288,c,125,a),unit_del(a,699)].
% 76.36/76.68 1991 c_lessequals(c_Relation_ORange(A,B,B),c_Relation_OField(A,B),tc_fun(B,tc_bool)). [para(330(a,1),113(a,2))].
% 76.36/76.68 2545 c_lessequals(A,c_Transitive__Closure_Otrancl(A,B),tc_fun(tc_prod(B,B),tc_bool)). [para(389(a,1),114(a,2))].
% 76.36/76.68 2767 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = B | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(A,tc_bool)),tc_fun(A,tc_bool)) | -c_Wellfounded_Owf(c_Relation_OId__on(C,A),A). [para(400(a,1),440(b,2))].
% 76.36/76.68 3042 c_Relation_OField(c_Transitive__Closure_Otrancl(A,B),B) = c_Relation_OField(A,B). [para(501(a,1),330(a,1,1)),rewrite([532(3),330(5)]),flip(a)].
% 76.36/76.68 3129 c_Relation_OField(c_Relation_OId__on(A,B),B) = A. [para(528(a,1),330(a,1,1)),rewrite([561(2),94(3)]),flip(a)].
% 76.36/76.68 3431 c_Transitive__Closure_Otrancl(c_Relation_OId__on(A,B),B) = c_Relation_OId__on(A,B). [resolve(598,b,597,a)].
% 76.36/76.68 4158 hBOOL(c_in(A,c_Relation_ORange(B,C,C),C)) | hBOOL(c_in(A,c_Wellfounded_Oacc(B,C),C)). [resolve(664,b,605,b)].
% 76.36/76.68 4210 c_Transitive__Closure_Otrancl(v_L,tc_Arrow__Order__Mirabelle_Oalt) = v_L. [resolve(679,a,598,b)].
% 76.36/76.68 4228 hBOOL(c_in(c_Pair(v_y,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) | -hBOOL(c_in(c_Pair(v_x,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))). [resolve(681,a,649,c),rewrite([4210(7)])].
% 76.36/76.68 4258 hBOOL(hAPP(v_L,c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))). [resolve(682,a,676,b)].
% 76.36/76.68 4389 hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(697,a,540,a)].
% 76.36/76.68 4390 c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),A,tc_bool). [resolve(697,a,126,a)].
% 76.36/76.68 4803 c_Orderings_Obot__class_Obot(tc_bool) = A | -c_lessequals(A,c_Orderings_Obot__class_Obot(tc_bool),tc_bool). [resolve(4390,a,188,d),unit_del(a,696)].
% 76.36/76.68 5084 hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,A)). [resolve(4258,a,675,b)].
% 76.36/76.68 5622 -hBOOL(c_Orderings_Obot__class_Obot(tc_bool)). [para(4389(a,1),567(a,1))].
% 76.36/76.68 5816 c_Wellfounded_Owf(A,B) | -c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(A,B),B). [resolve(2545,a,339,b)].
% 76.36/76.68 6961 c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B),C,tc_bool). [para(102(a,1),1675(a,2))].
% 76.36/76.68 6963 hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B) = c_Orderings_Obot__class_Obot(tc_bool). [resolve(6961,a,4803,b),flip(a)].
% 76.36/76.68 6977 hAPP(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),B) = c_Orderings_Obot__class_Obot(tc_bool). [para(521(a,1),6963(a,1,1))].
% 76.36/76.68 7020 hBOOL(hAPP(c_Relation_OField(A,B),C)) | -hBOOL(hAPP(c_Relation_ORange(A,B,B),C)). [resolve(1991,a,338,c)].
% 76.36/76.68 7023 hBOOL(c_in(A,c_Relation_OField(B,C),C)) | -hBOOL(c_in(A,c_Relation_ORange(B,C,C),C)). [resolve(1991,a,291,c)].
% 76.36/76.68 47204 hBOOL(c_in(A,c_Wellfounded_Oacc(B,C),C)) | hBOOL(hAPP(c_Relation_ORange(B,C,C),A)). [resolve(4158,a,676,b)].
% 76.36/76.68 47207 hBOOL(hAPP(c_Relation_ORange(A,B,B),C)) | hBOOL(hAPP(c_Wellfounded_Oacc(A,B),C)). [resolve(47204,a,676,b)].
% 76.36/76.68 47945 hBOOL(hAPP(c_Wellfounded_Oacc(A,B),C)) | hBOOL(hAPP(c_Relation_OField(A,B),C)). [resolve(47207,a,7020,b)].
% 76.36/76.68 47952 hBOOL(hAPP(c_Wellfounded_Oacc(A,B),C)) | hBOOL(c_in(C,c_Relation_OField(A,B),D)). [resolve(47945,b,675,b)].
% 76.36/76.68 48253 hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(A,B),B),C)) | hBOOL(c_in(C,A,D)). [para(3129(a,1),47952(b,1,2))].
% 76.36/76.68 48281 hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B),B),C)). [resolve(48253,b,490,a)].
% 76.36/76.68 48287 hBOOL(c_in(A,c_Wellfounded_Oacc(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),C),C),D)). [resolve(48281,a,675,b)].
% 76.36/76.68 48332 c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B),B). [resolve(48287,a,443,b)].
% 76.36/76.68 48346 c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),B),B). [para(521(a,1),48332(a,1,1))].
% 76.36/76.68 48387 c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_prod(A,A)),B),B). [para(521(a,1),48346(a,1,1,1))].
% 76.36/76.68 52516 hBOOL(c_in(A,c_Relation_OField(B,C),C)) | hBOOL(c_in(A,c_Wellfounded_Oacc(B,C),C)). [resolve(7023,b,4158,a)].
% 76.36/76.68 52518 hBOOL(c_in(A,c_Wellfounded_Oacc(B,C),C)) | hBOOL(hAPP(c_Relation_OField(B,C),A)). [resolve(52516,a,676,b)].
% 76.36/76.68 52520 hBOOL(hAPP(c_Relation_OField(A,B),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(A,B))) | c_Wellfounded_Owf(A,B). [resolve(52518,a,443,b)].
% 76.36/76.68 52522 hBOOL(hAPP(c_Relation_OField(A,B),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(c_Transitive__Closure_Otrancl(A,B),B))) | c_Wellfounded_Owf(A,B). [resolve(52520,b,5816,b),rewrite([3042(2)])].
% 76.36/76.68 71198 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = B | -c_Wellfounded_Owf(c_Relation_OId__on(B,A),A). [para(328(a,1),2767(b,2)),unit_del(b,336)].
% 76.36/76.68 71995 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = B | hBOOL(hAPP(B,c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(c_Relation_OId__on(B,A),A))). [resolve(71198,b,52522,b),rewrite([3129(6),3431(6)])].
% 76.36/76.68 71998 c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_prod(A,A)) = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)). [resolve(71198,b,48387,a),flip(a)].
% 76.36/76.68 71999 c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A) = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)). [resolve(71198,b,48346,a),flip(a)].
% 76.36/76.68 72001 c_Relation_OId__on(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_prod(A,A)) = c_0. [new_symbol(71998)].
% 76.36/76.68 72002 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_0. [back_rewrite(71998),rewrite([72001(6)]),flip(a)].
% 76.36/76.68 72233 c_Relation_OId__on(c_0,A) = c_0. [back_rewrite(71999),rewrite([72002(3),72002(5)])].
% 76.36/76.68 72236 c_0 = A | hBOOL(hAPP(A,c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(c_Relation_OId__on(A,B),B))). [back_rewrite(71995),rewrite([72002(3)])].
% 76.36/76.68 76090 hAPP(c_0,A) = c_Orderings_Obot__class_Obot(tc_bool). [back_rewrite(6977),rewrite([72002(3),72233(2)])].
% 76.36/76.68 76656 c_COMBK(A,B,C) = c_0 | hBOOL(A). [para(102(a,1),72236(b,1)),flip(a)].
% 76.36/76.68 76670 c_COMBK(c_in(A,B,C),D,E) = c_0 | hBOOL(hAPP(B,A)). [resolve(76656,b,676,b)].
% 76.36/76.68 76671 c_COMBK(hAPP(A,B),C,D) = c_0 | hBOOL(c_in(B,A,E)). [resolve(76656,b,675,b)].
% 76.36/76.68 78362 c_COMBK(hAPP(v_L,c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),B,C) = c_0. [resolve(76671,b,680,a)].
% 76.36/76.68 78364 hAPP(v_L,c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Orderings_Obot__class_Obot(tc_bool). [para(78362(a,1),102(a,1,1)),rewrite([76090(2)]),flip(a)].
% 76.36/76.68 78373 c_COMBK(c_in(c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,B),C,D) = c_0. [para(78364(a,1),76670(b,1)),unit_del(b,5622)].
% 76.36/76.68 79375 c_in(c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,B) = c_Orderings_Obot__class_Obot(tc_bool). [para(78373(a,1),102(a,1,1)),rewrite([76090(2)]),flip(a)].
% 76.36/76.68 99327 $F. [resolve(4228,b,5084,a),rewrite([79375(10)]),unit_del(a,5622)].
% 76.36/76.68
% 76.36/76.68 % SZS output end Refutation
% 76.36/76.68 ============================== end of proof ==========================
% 76.36/76.68
% 76.36/76.68 ============================== STATISTICS ============================
% 76.36/76.68
% 76.36/76.68 Given=25004. Generated=2720161. Kept=99154. proofs=1.
% 76.36/76.68 Usable=16396. Sos=9988. Demods=1398. Limbo=4, Disabled=73519. Hints=0.
% 76.36/76.68 Megabytes=91.55.
% 76.36/76.68 User_CPU=73.85, System_CPU=1.62, Wall_clock=75.
% 76.36/76.68
% 76.36/76.68 ============================== end of statistics =====================
% 76.36/76.68
% 76.36/76.68 ============================== end of search =========================
% 76.36/76.68
% 76.36/76.68 THEOREM PROVED
% 76.36/76.68 % SZS status Unsatisfiable
% 76.36/76.68
% 76.36/76.68 Exiting with 1 proof.
% 76.36/76.68
% 76.36/76.68 Process 12128 exit (max_proofs) Sat Jul 2 06:53:56 2022
% 76.36/76.68 Prover9 interrupted
%------------------------------------------------------------------------------