TSTP Solution File: SCT024-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT024-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 22:03:29 EDT 2022
% Result : Unsatisfiable 285.34s 285.62s
% Output : Refutation 285.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT024-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 2 08:35:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.97/1.30 ============================== Prover9 ===============================
% 0.97/1.30 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.30 Process 25045 was started by sandbox2 on n029.cluster.edu,
% 0.97/1.30 Sat Jul 2 08:35:25 2022
% 0.97/1.30 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24892_n029.cluster.edu".
% 0.97/1.30 ============================== end of head ===========================
% 0.97/1.30
% 0.97/1.30 ============================== INPUT =================================
% 0.97/1.30
% 0.97/1.30 % Reading from file /tmp/Prover9_24892_n029.cluster.edu
% 0.97/1.30
% 0.97/1.30 set(prolog_style_variables).
% 0.97/1.30 set(auto2).
% 0.97/1.30 % set(auto2) -> set(auto).
% 0.97/1.30 % set(auto) -> set(auto_inference).
% 0.97/1.30 % set(auto) -> set(auto_setup).
% 0.97/1.30 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.30 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.30 % set(auto) -> set(auto_limits).
% 0.97/1.30 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.30 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.30 % set(auto) -> set(auto_denials).
% 0.97/1.30 % set(auto) -> set(auto_process).
% 0.97/1.30 % set(auto2) -> assign(new_constants, 1).
% 0.97/1.30 % set(auto2) -> assign(fold_denial_max, 3).
% 0.97/1.30 % set(auto2) -> assign(max_weight, "200.000").
% 0.97/1.30 % set(auto2) -> assign(max_hours, 1).
% 0.97/1.30 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.97/1.30 % set(auto2) -> assign(max_seconds, 0).
% 0.97/1.30 % set(auto2) -> assign(max_minutes, 5).
% 0.97/1.30 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.97/1.30 % set(auto2) -> set(sort_initial_sos).
% 0.97/1.30 % set(auto2) -> assign(sos_limit, -1).
% 0.97/1.30 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.97/1.30 % set(auto2) -> assign(max_megs, 400).
% 0.97/1.30 % set(auto2) -> assign(stats, some).
% 0.97/1.30 % set(auto2) -> clear(echo_input).
% 0.97/1.30 % set(auto2) -> set(quiet).
% 0.97/1.30 % set(auto2) -> clear(print_initial_clauses).
% 0.97/1.30 % set(auto2) -> clear(print_given).
% 0.97/1.30 assign(lrs_ticks,-1).
% 0.97/1.30 assign(sos_limit,10000).
% 0.97/1.30 assign(order,kbo).
% 0.97/1.30 set(lex_order_vars).
% 0.97/1.30 clear(print_given).
% 0.97/1.30
% 0.97/1.30 % formulas(sos). % not echoed (713 formulas)
% 0.97/1.30
% 0.97/1.30 ============================== end of input ==========================
% 0.97/1.30
% 0.97/1.30 % From the command line: assign(max_seconds, 300).
% 0.97/1.30
% 0.97/1.30 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.97/1.30
% 0.97/1.30 % Formulas that are not ordinary clauses:
% 0.97/1.30
% 0.97/1.30 ============================== end of process non-clausal formulas ===
% 0.97/1.30
% 0.97/1.30 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.30
% 0.97/1.30 ============================== PREDICATE ELIMINATION =================
% 0.97/1.30 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.97/1.30 2 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.97/1.30 3 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),A),D) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.97/1.30 4 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.97/1.30 5 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.97/1.30 6 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.97/1.30 7 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),B),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.97/1.30 8 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.97/1.30 9 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.97/1.30 10 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.97/1.30 11 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.97/1.30 12 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.97/1.30 13 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,A),B),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.97/1.30 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.97/1.30 15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.97/1.30 16 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.97/1.30 17 -class_Lattices_Oupper__semilattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.97/1.30 18 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,A),D),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.97/1.30 19 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,A),B),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.97/1.30 20 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.97/1.30 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),B) = B. [resolve(1,a,2,a)].
% 0.97/1.30 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),tc_fun(C,A)),E) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),E)). [resolve(1,a,3,a)].
% 0.97/1.30 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),E)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),E)). [resolve(1,a,4,a)].
% 0.97/1.30 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(D,E,tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(1,a,5,a)].
% 0.97/1.30 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D),tc_fun(C,A)). [resolve(1,a,6,a)].
% 0.97/1.30 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),B),tc_fun(D,A)). [resolve(1,a,7,a)].
% 0.97/1.30 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = B | -c_lessequals(D,B,tc_fun(C,A)). [resolve(1,a,10,a)].
% 0.97/1.30 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) != D | c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,11,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = D | -c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,12,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(E,tc_fun(D,A)),B),C,tc_fun(D,A)). [resolve(1,a,13,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(D,A)),E),C,tc_fun(D,A)). [resolve(1,a,14,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(1,a,15,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(D,tc_fun(C,A)),B). [resolve(1,a,16,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_fun(C,A)),D). [resolve(1,a,17,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,18,a)].
% 0.97/1.35 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.97/1.35 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),A) = A. [resolve(21,a,2,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),tc_bool),C) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C)). [resolve(21,a,3,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),C)). [resolve(21,a,4,a)].
% 0.97/1.35 Derived: c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,5,a)].
% 0.97/1.35 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B),tc_bool). [resolve(21,a,6,a)].
% 0.97/1.35 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),A),tc_bool). [resolve(21,a,7,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = A | -c_lessequals(B,A,tc_bool). [resolve(21,a,10,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) != B | c_lessequals(A,B,tc_bool). [resolve(21,a,11,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = B | -c_lessequals(A,B,tc_bool). [resolve(21,a,12,a)].
% 0.97/1.35 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(C,tc_bool),A),B,tc_bool). [resolve(21,a,13,a)].
% 0.97/1.35 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),C),B,tc_bool). [resolve(21,a,14,a)].
% 0.97/1.35 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,15,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),A). [resolve(21,a,16,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),B). [resolve(21,a,17,a)].
% 0.97/1.35 Derived: c_lessequals(A,hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,tc_bool),C),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(21,a,18,a)].
% 0.97/1.35 22 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.97/1.35 23 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.97/1.35 24 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.97/1.35 25 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.97/1.35 26 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.97/1.35 27 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),A),D) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.97/1.35 28 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.97/1.35 29 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.97/1.35 30 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.97/1.35 31 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.97/1.35 32 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.97/1.35 33 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.97/1.35 34 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.97/1.35 35 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.97/1.35 36 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.97/1.35 37 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,A),C),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.97/1.35 38 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.97/1.35 39 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.97/1.35 40 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.97/1.35 41 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,A),C),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = B | -c_lessequals(B,D,tc_fun(C,A)). [resolve(22,a,23,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) != B | c_lessequals(B,D,tc_fun(C,A)). [resolve(22,a,24,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = D | -c_lessequals(D,B,tc_fun(C,A)). [resolve(22,a,25,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),E)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),E)). [resolve(22,a,26,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),tc_fun(C,A)),E) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),E)). [resolve(22,a,27,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)) | -c_lessequals(B,C,tc_fun(D,A)). [resolve(22,a,28,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),D,tc_fun(C,A)). [resolve(22,a,31,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),B,tc_fun(C,A)). [resolve(22,a,32,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D). [resolve(22,a,33,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),B) = B. [resolve(22,a,34,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),B). [resolve(22,a,35,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(D,A)),E),tc_fun(D,A)). [resolve(22,a,36,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(E,tc_fun(D,A)),C),tc_fun(D,A)). [resolve(22,a,37,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(22,a,38,a)].
% 0.97/1.35 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(D,E,tc_fun(C,A)). [resolve(22,a,39,a)].
% 0.97/1.35 42 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.97/1.35 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = A | -c_lessequals(A,B,tc_bool). [resolve(42,a,23,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) != A | c_lessequals(A,B,tc_bool). [resolve(42,a,24,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = B | -c_lessequals(B,A,tc_bool). [resolve(42,a,25,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),C)). [resolve(42,a,26,a)].
% 0.97/1.35 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),tc_bool),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C)). [resolve(42,a,27,a)].
% 0.97/1.35 Derived: c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(42,a,28,a)].
% 0.97/1.36 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),B,tc_bool). [resolve(42,a,31,a)].
% 0.97/1.36 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),A,tc_bool). [resolve(42,a,32,a)].
% 0.97/1.36 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B). [resolve(42,a,33,a)].
% 0.97/1.36 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),A) = A. [resolve(42,a,34,a)].
% 0.97/1.36 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),A). [resolve(42,a,35,a)].
% 0.97/1.36 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C),tc_bool). [resolve(42,a,36,a)].
% 0.97/1.36 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_bool),B),tc_bool). [resolve(42,a,37,a)].
% 0.97/1.36 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(42,a,38,a)].
% 0.97/1.36 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(42,a,39,a)].
% 0.97/1.36 43 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].
% 0.97/1.36 44 c_lessequals(hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),tc_fun(B,tc_bool)) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_equiv__class__subset_0) # label(axiom). [assumption].
% 0.97/1.36 45 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].
% 0.97/1.36 46 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(B,E,C)) | -c_lessequals(hAPP(c_Relation_OImage(D,C,C),hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))),hAPP(c_Relation_OImage(D,C,C),hAPP(c_Set_Oinsert(A,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,D,C) # label(cls_subset__equiv__class_0) # label(axiom). [assumption].
% 0.97/1.36 47 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(E,hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(D,C,C),hAPP(c_Set_Oinsert(A,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))),tc_fun(C,tc_bool)),hAPP(c_Relation_OImage(D,C,C),hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))))),C)) | -c_Equiv__Relations_Oequiv(F,D,C) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 0.97/1.36 48 hBOOL(c_in(A,hAPP(c_Relation_OImage(B,C,C),hAPP(c_Set_Oinsert(A,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))),C)) | -hBOOL(c_in(A,D,C)) | -c_Equiv__Relations_Oequiv(D,B,C) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 0.97/1.36 49 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) = hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 0.97/1.36 50 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) = hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 0.97/1.36 51 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) != hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 0.97/1.36 52 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) != hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -c_Equiv__Relations_Oequiv(E,A,B) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(C,E,B)) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 0.97/1.36 53 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) = hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(C,E,B)) | -c_Equiv__Relations_Oequiv(E,A,B) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 0.97/1.36 54 hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) != hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(C,E,B)) | -c_Equiv__Relations_Oequiv(E,A,B) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 0.97/1.36 55 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 0.97/1.36 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),tc_fun(B,tc_bool)) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(43,b,44,c)].
% 0.97/1.36 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(43,b,45,b)].
% 0.97/1.36 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(hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),tc_fun(B,tc_bool)). [resolve(43,b,46,d)].
% 0.97/1.36 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,hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),tc_fun(B,tc_bool)),hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))),B)). [resolve(43,b,47,c)].
% 0.97/1.36 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(C,hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(43,b,48,c)].
% 0.97/1.36 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) = hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(43,b,49,c)].
% 0.97/1.36 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) != hAPP(c_Relation_OImage(A,B,B),hAPP(c_Set_Oinsert(D,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))) | 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(43,b,51,d)].
% 0.97/1.57 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_Otrans(A,B). [resolve(43,b,55,b)].
% 0.97/1.57 56 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].
% 0.97/1.57 57 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 0.97/1.57 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(57,b,43,b)].
% 0.97/1.57 58 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 0.97/1.57 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(58,b,43,b)].
% 0.97/1.57 59 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].
% 0.97/1.57 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(59,d,43,b)].
% 0.97/1.57 60 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].
% 0.97/1.57 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(60,c,43,b)].
% 0.97/1.57 61 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].
% 0.97/1.57 62 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].
% 0.97/1.57 63 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].
% 0.97/1.57 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(62,b,63,a)].
% 0.97/1.57 64 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].
% 0.97/1.57 65 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].
% 0.97/1.57 66 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].
% 0.97/1.57 67 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].
% 0.97/1.57 68 hBOOL(c_in(c_Pair(A,B,C,D),E,tc_prod(C,D))) | -c_FunDef_Oin__rel(E,A,B,C,D) # label(cls_in__rel__def_0) # label(axiom). [assumption].
% 0.97/1.57 69 c_FunDef_Oin__rel(A,B,C,D,E) | -hBOOL(c_in(c_Pair(B,C,D,E),A,tc_prod(D,E))) # label(cls_in__rel__def_1) # label(axiom). [assumption].
% 0.97/1.57 70 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 0.97/1.57 71 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 0.97/1.57 Derived: A = A. [resolve(70,b,71,a)].
% 0.97/1.57
% 0.97/1.57 ============================== end predicate elimination =============
% 0.97/1.57
% 0.97/1.57 Auto_denials: (non-Horn, no changes).
% 0.97/1.57
% 0.97/1.57 Term ordering decisions:
% 0.97/1.57 Function symbol KB weights: tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. t_a=1. v_x=1. v_P=1. t_b=1. v_i=1. v_r=1. v_a=1. v_b=1. hAPP=1. tc_fun=1. tc_prod=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_Transitive__Closure_Ortrancl=1. c_HOL_Ominus__class_Ominus=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=1. c_Complete__Lattice_OSup__class_OSup=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=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__Set__Xball__UNIV__1__1=1. c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2=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__Set__XUNIV__eq__I__1__1=1. c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2=1. c_ATP__Linkup_Osko__Set__Xbex__UNIV__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_Orderings_Otop__class_Otop=1. c_Relation_OId=1. v_F=1. v_Pa=1. c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1=1. c_in=1. c_Relation_Oconverse=1. c_Relation_OImage=1. c_Relation_ODomain=1. c_COMBK=1. c_Relation_ORange=1. c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1=1. c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2=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_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__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_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_Set_Oimage=1. c_Product__Type_OSigma=1. c_Relation_Oinv__image=1. c_split=1. c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1=1. c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__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__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_COMBB=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_List_Osko__Recdef__Xcuts__eq__1__1=1. c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1=1.
% 1.89/2.19
% 1.89/2.19 ============================== end of process initial clauses ========
% 1.89/2.19
% 1.89/2.19 ============================== CLAUSES FOR SEARCH ====================
% 1.89/2.19
% 1.89/2.19 ============================== end of clauses for search =============
% 1.89/2.19
% 1.89/2.19 ============================== SEARCH ================================
% 1.89/2.19
% 1.89/2.19 % Starting search at 0.37 seconds.
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=60.000, iters=3531
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=53.000, iters=3398
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=51.000, iters=3333
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=50.000, iters=3367
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=49.000, iters=3356
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=48.000, iters=3380
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=47.000, iters=3536
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=46.000, iters=3502
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=44.000, iters=3337
% 1.89/2.19
% 1.89/2.19 Low Water (keep): wt=43.000, iters=3396
% 1.89/2.19
% 1.89/2.19 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 47 (0.00 of 0.98 sec).
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=41.000, iters=3343
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=40.000, iters=3351
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% 285.34/285.62 Low Water (keep): wt=39.000, iters=3348
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% 285.34/285.62 Low Water (keep): wt=38.000, iters=3489
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% 285.34/285.62 Low Water (keep): wt=37.000, iters=3391
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=36.000, iters=3339
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=35.000, iters=3415
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% 285.34/285.62 Low Water (keep): wt=34.000, iters=3348
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% 285.34/285.62 Low Water (keep): wt=33.000, iters=3431
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% 285.34/285.62 Low Water (keep): wt=32.000, iters=3359
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% 285.34/285.62 Low Water (keep): wt=31.000, iters=3334
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% 285.34/285.62 Low Water (keep): wt=30.000, iters=3456
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% 285.34/285.62 Low Water (keep): wt=29.000, iters=3343
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% 285.34/285.62 Low Water (keep): wt=28.000, iters=3363
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% 285.34/285.62 Low Water (keep): wt=27.000, iters=3372
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% 285.34/285.62 Low Water (keep): wt=26.000, iters=3370
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% 285.34/285.62 Low Water (keep): wt=25.000, iters=3360
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% 285.34/285.62 Low Water (keep): wt=24.000, iters=3335
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% 285.34/285.62 Low Water (keep): wt=23.000, iters=3333
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=22.000, iters=3417
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% 285.34/285.62 Low Water (keep): wt=21.000, iters=3459
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% 285.34/285.62 Low Water (keep): wt=20.000, iters=3359
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=19.000, iters=3349
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=8249, wt=76.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=3806, wt=67.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=12388, wt=61.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=13472, wt=60.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=11627, wt=58.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=9707, wt=57.000
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% 285.34/285.62 Low Water (displace): id=13457, wt=56.000
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% 285.34/285.62 Low Water (displace): id=12036, wt=55.000
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% 285.34/285.62 Low Water (displace): id=13468, wt=54.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=5836, wt=52.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=8262, wt=51.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=13556, wt=50.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=13591, wt=18.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=13767, wt=17.000
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=14417, wt=16.000
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=18.000, iters=3334
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=17.000, iters=3334
% 285.34/285.62
% 285.34/285.62 Low Water (displace): id=22416, wt=15.000
% 285.34/285.62
% 285.34/285.62 Low Water (keep): wt=16.000, iters=3337
% 285.34/285.62
% 285.34/285.62 ============================== PROOF =================================
% 285.34/285.62 % SZS status Unsatisfiable
% 285.34/285.62 % SZS output start Refutation
% 285.34/285.62
% 285.34/285.62 % Proof 1 at 275.26 (+ 9.15) seconds.
% 285.34/285.62 % Length of proof is 56.
% 285.34/285.62 % Level of proof is 11.
% 285.34/285.62 % Maximum clause weight is 50.000.
% 285.34/285.62 % Given clauses 30905.
% 285.34/285.62
% 285.34/285.62 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(B,A),D),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 285.34/285.62 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 285.34/285.62 127 hAPP(c_COMBK(A,B,C),D) = A # label(cls_COMBK__def_0) # label(axiom). [assumption].
% 285.34/285.62 188 -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].
% 285.34/285.62 230 hBOOL(hAPP(hAPP(c_Set_Oinsert(A,B),C),A)) # label(cls_insert__code_1) # label(axiom). [assumption].
% 285.34/285.62 299 -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].
% 285.34/285.62 314 hAPP(c_Set_Oinsert(A,B),C) = C | -hBOOL(c_in(A,C,B)) # label(cls_insert__absorb_0) # label(axiom). [assumption].
% 285.34/285.62 315 -class_Orderings_Otop(A) | c_lessequals(B,c_Orderings_Otop__class_Otop(A),A) # label(cls_top__greatest_0) # label(axiom). [assumption].
% 285.34/285.62 324 c_lessequals(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),tc_fun(B,tc_bool)) # label(cls_subset__UNIV_0) # label(axiom). [assumption].
% 285.34/285.62 435 -hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(C,B),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(C,B),B,B),c_Transitive__Closure_Otrancl(C,B),tc_prod(B,B))) # label(cls_irrefl__trancl__rD_0) # label(axiom). [assumption].
% 285.34/285.62 516 c_Transitive__Closure_Otrancl(A,B) = A | -c_Relation_Otrans(A,B) # label(cls_trancl__id_0) # label(axiom). [assumption].
% 285.34/285.62 651 c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)) = B | -hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(B,A),B,A)) # label(cls_UNIV__eq__I_0) # label(axiom). [assumption].
% 285.34/285.62 690 -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].
% 285.34/285.62 691 -class_Orderings_Otop(A) | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,A)),v_x) = c_Orderings_Otop__class_Otop(A) # label(cls_top__fun__eq_0) # label(axiom). [assumption].
% 285.34/285.62 692 hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),B)) # label(cls_top1I_0) # label(axiom). [assumption].
% 285.34/285.62 695 hBOOL(c_in(A,B,C)) | -hBOOL(hAPP(B,A)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 285.34/285.62 696 hBOOL(hAPP(A,B)) | -hBOOL(c_in(B,A,C)) # label(cls_mem__def_0) # label(axiom). [assumption].
% 285.34/285.62 697 c_Relation_Otrans(hAPP(v_P,A),tc_Arrow__Order__Mirabelle_Oalt) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 285.34/285.62 698 c_Relation_Oirrefl(hAPP(v_P,A),tc_Arrow__Order__Mirabelle_Oalt) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 285.34/285.62 699 c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,A),tc_Arrow__Order__Mirabelle_Oalt) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 285.34/285.62 700 hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 285.34/285.62 701 -hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 285.34/285.62 705 hBOOL(c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(C),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) | -hBOOL(c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(C,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) | A = B | -c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(C,v_Pa(C)),tc_Arrow__Order__Mirabelle_Oalt) | -c_Relation_Oirrefl(hAPP(C,v_Pa(C)),tc_Arrow__Order__Mirabelle_Oalt) | -c_Relation_Otrans(hAPP(C,v_Pa(C)),tc_Arrow__Order__Mirabelle_Oalt) # label(cls_conjecture_8) # label(negated_conjecture). [assumption].
% 285.34/285.62 721 class_Orderings_Oorder(tc_bool) # label(clsarity_bool__Orderings_Oorder) # label(axiom). [assumption].
% 285.34/285.62 722 class_Orderings_Otop(tc_bool) # label(clsarity_bool__Orderings_Otop) # label(axiom). [assumption].
% 285.34/285.62 725 class_HOL_Oord(tc_bool) # label(clsarity_bool__HOL_Oord) # label(axiom). [assumption].
% 285.34/285.62 751 c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A,tc_bool),C),B,tc_bool). [resolve(21,a,14,a)].
% 285.34/285.62 2260 c_lessequals(hAPP(A,B),hAPP(c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),B),tc_bool). [resolve(324,a,299,c),unit_del(a,725)].
% 285.34/285.62 5037 hBOOL(c_in(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),C)). [resolve(695,b,692,a)].
% 285.34/285.62 5038 hBOOL(c_in(A,hAPP(c_Set_Oinsert(A,B),C),D)). [resolve(695,b,230,a)].
% 285.34/285.62 5052 hBOOL(c_in(A,c_COMBK(B,C,D),E)) | -hBOOL(B). [para(127(a,1),695(b,1))].
% 285.34/285.62 5121 c_Transitive__Closure_Otrancl(hAPP(v_P,A),tc_Arrow__Order__Mirabelle_Oalt) = hAPP(v_P,A). [resolve(697,a,516,b)].
% 285.34/285.62 5126 -hBOOL(c_in(c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,B),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))). [resolve(698,a,690,b)].
% 285.34/285.62 5130 hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))). [resolve(700,a,696,b)].
% 285.34/285.62 5195 hBOOL(c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) | -hBOOL(c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) | A = B. [resolve(705,d,699,a),unit_del(d,698),unit_del(e,697)].
% 285.34/285.62 5233 hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool). [resolve(722,a,691,a)].
% 285.34/285.62 5234 c_lessequals(A,c_Orderings_Otop__class_Otop(tc_bool),tc_bool). [resolve(722,a,315,a)].
% 285.34/285.62 5811 c_Orderings_Otop__class_Otop(tc_bool) = A | -c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),A,tc_bool). [resolve(5234,a,188,d),flip(b),unit_del(a,721)].
% 285.34/285.62 6339 c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)). [resolve(5037,a,651,b)].
% 285.34/285.62 6374 c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)) = c_0. [new_symbol(6339)].
% 285.34/285.62 6710 hAPP(c_0,v_x) = c_Orderings_Otop__class_Otop(tc_bool). [back_rewrite(5233),rewrite([6374(4)])].
% 285.34/285.62 7041 c_lessequals(hAPP(A,B),hAPP(c_0,B),tc_bool). [back_rewrite(2260),rewrite([6374(4)])].
% 285.34/285.62 7046 hBOOL(hAPP(c_0,A)). [back_rewrite(692),rewrite([6374(3)])].
% 285.34/285.62 7048 c_0 = A | -hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(A,B),A,B)). [back_rewrite(651),rewrite([6374(3)])].
% 285.34/285.62 7112 hBOOL(c_Orderings_Otop__class_Otop(tc_bool)). [para(6710(a,1),7046(a,1))].
% 285.34/285.62 7508 c_lessequals(A,hAPP(c_0,B),tc_bool). [resolve(7041,a,751,b)].
% 285.34/285.62 8141 hAPP(c_0,A) = c_Orderings_Otop__class_Otop(tc_bool). [resolve(5811,b,7508,a),flip(a)].
% 285.34/285.62 8545 hBOOL(c_in(A,c_COMBK(c_in(B,hAPP(c_Set_Oinsert(B,C),D),E),F,V6),V7)). [resolve(5052,b,5038,a)].
% 285.34/285.62 8650 hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),A)). [resolve(5130,a,695,b)].
% 285.34/285.62 10996 hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),A),hAPP(v_P,v_i)) = hAPP(v_P,v_i). [resolve(8650,a,314,b)].
% 285.34/285.62 59736 c_COMBK(c_in(A,hAPP(c_Set_Oinsert(A,B),C),D),E,F) = c_0. [resolve(8545,a,7048,b),flip(a)].
% 285.34/285.62 59737 c_in(A,hAPP(c_Set_Oinsert(A,B),C),D) = c_Orderings_Otop__class_Otop(tc_bool). [para(59736(a,1),127(a,1,1)),rewrite([8141(2)]),flip(a)].
% 285.34/285.62 62505 c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),A) = c_Orderings_Otop__class_Otop(tc_bool). [para(10996(a,1),59737(a,1,2))].
% 285.34/285.62 160585 v_b = v_a. [para(62505(a,1),5195(b,1)),flip(c),unit_del(a,701),unit_del(b,7112)].
% 285.34/285.62 160664 c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),A) = c_Orderings_Otop__class_Otop(tc_bool). [back_rewrite(62505),rewrite([160585(2)])].
% 285.34/285.62 161415 $F. [para(160664(a,1),435(a,1)),rewrite([5121(21)]),unit_del(a,7112),unit_del(b,5126)].
% 285.34/285.62
% 285.34/285.62 % SZS output end Refutation
% 285.34/285.62 ============================== end of proof ==========================
% 285.34/285.62
% 285.34/285.62 ============================== STATISTICS ============================
% 285.34/285.62
% 285.34/285.62 Given=30905. Generated=16435050. Kept=161254. proofs=1.
% 285.34/285.62 Usable=21431. Sos=9952. Demods=2769. Limbo=0, Disabled=130658. Hints=0.
% 285.34/285.62 Megabytes=165.19.
% 285.34/285.62 User_CPU=275.26, System_CPU=9.15, Wall_clock=285.
% 285.34/285.62
% 285.34/285.62 ============================== end of statistics =====================
% 285.34/285.62
% 285.34/285.62 ============================== end of search =========================
% 285.34/285.62
% 285.34/285.62 THEOREM PROVED
% 285.34/285.62 % SZS status Unsatisfiable
% 285.34/285.62
% 285.34/285.62 Exiting with 1 proof.
% 285.34/285.62
% 285.34/285.62 Process 25045 exit (max_proofs) Sat Jul 2 08:40:10 2022
% 285.34/285.62 Prover9 interrupted
%------------------------------------------------------------------------------