TSTP Solution File: SCT059-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT059-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 22:03:40 EDT 2022
% Result : Timeout 300.02s 300.25s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT059-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 22:53:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.97/1.23 ============================== Prover9 ===============================
% 0.97/1.23 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.23 Process 14020 was started by sandbox2 on n026.cluster.edu,
% 0.97/1.23 Fri Jul 1 22:53:05 2022
% 0.97/1.23 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13867_n026.cluster.edu".
% 0.97/1.23 ============================== end of head ===========================
% 0.97/1.23
% 0.97/1.23 ============================== INPUT =================================
% 0.97/1.23
% 0.97/1.23 % Reading from file /tmp/Prover9_13867_n026.cluster.edu
% 0.97/1.23
% 0.97/1.23 set(prolog_style_variables).
% 0.97/1.23 set(auto2).
% 0.97/1.23 % set(auto2) -> set(auto).
% 0.97/1.23 % set(auto) -> set(auto_inference).
% 0.97/1.23 % set(auto) -> set(auto_setup).
% 0.97/1.23 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.23 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.23 % set(auto) -> set(auto_limits).
% 0.97/1.23 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.23 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.23 % set(auto) -> set(auto_denials).
% 0.97/1.23 % set(auto) -> set(auto_process).
% 0.97/1.23 % set(auto2) -> assign(new_constants, 1).
% 0.97/1.23 % set(auto2) -> assign(fold_denial_max, 3).
% 0.97/1.23 % set(auto2) -> assign(max_weight, "200.000").
% 0.97/1.23 % set(auto2) -> assign(max_hours, 1).
% 0.97/1.23 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.97/1.23 % set(auto2) -> assign(max_seconds, 0).
% 0.97/1.23 % set(auto2) -> assign(max_minutes, 5).
% 0.97/1.23 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.97/1.23 % set(auto2) -> set(sort_initial_sos).
% 0.97/1.23 % set(auto2) -> assign(sos_limit, -1).
% 0.97/1.23 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.97/1.23 % set(auto2) -> assign(max_megs, 400).
% 0.97/1.23 % set(auto2) -> assign(stats, some).
% 0.97/1.23 % set(auto2) -> clear(echo_input).
% 0.97/1.23 % set(auto2) -> set(quiet).
% 0.97/1.23 % set(auto2) -> clear(print_initial_clauses).
% 0.97/1.23 % set(auto2) -> clear(print_given).
% 0.97/1.23 assign(lrs_ticks,-1).
% 0.97/1.23 assign(sos_limit,10000).
% 0.97/1.23 assign(order,kbo).
% 0.97/1.23 set(lex_order_vars).
% 0.97/1.23 clear(print_given).
% 0.97/1.23
% 0.97/1.23 % formulas(sos). % not echoed (543 formulas)
% 0.97/1.23
% 0.97/1.23 ============================== end of input ==========================
% 0.97/1.23
% 0.97/1.23 % From the command line: assign(max_seconds, 300).
% 0.97/1.23
% 0.97/1.23 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.97/1.23
% 0.97/1.23 % Formulas that are not ordinary clauses:
% 0.97/1.23
% 0.97/1.23 ============================== end of process non-clausal formulas ===
% 0.97/1.23
% 0.97/1.23 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.23
% 0.97/1.23 ============================== PREDICATE ELIMINATION =================
% 0.97/1.23 1 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.97/1.23 2 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.97/1.23 3 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.97/1.23 4 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.97/1.23 5 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.97/1.23 6 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.97/1.23 7 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(A),B,C,A,A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),B),A) | -hBOOL(c_in(D,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_fold__inf__le__inf_0) # label(axiom). [assumption].
% 0.97/1.23 8 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.97/1.23 9 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.97/1.23 10 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.97/1.23 11 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.97/1.23 12 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.97/1.23 13 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.97/1.23 14 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.97/1.23 15 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.97/1.23 16 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.97/1.23 17 -class_Lattices_Olower__semilattice(A) | c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(A),B,c_Set_Oinsert(C,D,A),A,A) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(A),B,D,A,A)) | -c_Finite__Set_Ofinite(D,A) # label(cls_fold__inf__insert_0) # label(axiom). [assumption].
% 0.97/1.23 18 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.97/1.23 19 -class_Lattices_Olower__semilattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(A),A,A) # label(cls_fun__left__comm__idem__inf_0) # label(axiom). [assumption].
% 0.97/1.23 20 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.97/1.23 21 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.97/1.23 22 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.97/1.23 23 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,2,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),D,tc_fun(B,A)). [resolve(1,a,5,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),C,tc_fun(B,A)). [resolve(1,a,6,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,D,tc_fun(B,A),tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),E),C),tc_fun(B,A)) | -hBOOL(c_in(E,D,tc_fun(B,A))) | -c_Finite__Set_Ofinite(D,tc_fun(B,A)). [resolve(1,a,7,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = C | -c_lessequals(C,D,tc_fun(B,A)). [resolve(1,a,8,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) != C | c_lessequals(C,D,tc_fun(B,A)). [resolve(1,a,9,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = D | -c_lessequals(D,C,tc_fun(B,A)). [resolve(1,a,10,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),C),E),tc_fun(D,A)). [resolve(1,a,11,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),E),C),tc_fun(D,A)). [resolve(1,a,12,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)). [resolve(1,a,13,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)). [resolve(1,a,14,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,c_Set_Oinsert(D,E,tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,E,tc_fun(B,A),tc_fun(B,A))) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(1,a,17,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),C). [resolve(1,a,18,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(1,a,19,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),E)). [resolve(1,a,20,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)). [resolve(1,a,21,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D). [resolve(1,a,22,a)].
% 0.97/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(1,a,23,a)].
% 0.97/1.23 24 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.97/1.23 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(24,a,2,a)].
% 0.97/1.23 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),B,tc_bool). [resolve(24,a,5,a)].
% 0.97/1.23 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),A,tc_bool). [resolve(24,a,6,a)].
% 0.97/1.23 Derived: c_lessequals(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,B,tc_bool,tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C),A),tc_bool) | -hBOOL(c_in(C,B,tc_bool)) | -c_Finite__Set_Ofinite(B,tc_bool). [resolve(24,a,7,a)].
% 1.01/1.26 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -c_lessequals(A,B,tc_bool). [resolve(24,a,8,a)].
% 1.01/1.26 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) != A | c_lessequals(A,B,tc_bool). [resolve(24,a,9,a)].
% 1.01/1.26 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = B | -c_lessequals(B,A,tc_bool). [resolve(24,a,10,a)].
% 1.01/1.26 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C),tc_bool). [resolve(24,a,11,a)].
% 1.01/1.26 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C),B),tc_bool). [resolve(24,a,12,a)].
% 1.01/1.26 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(24,a,13,a)].
% 1.01/1.26 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(24,a,14,a)].
% 1.01/1.26 Derived: c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,c_Set_Oinsert(B,C,tc_bool),tc_bool,tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,C,tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(24,a,17,a)].
% 1.01/1.26 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),A). [resolve(24,a,18,a)].
% 1.01/1.26 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),tc_bool,tc_bool). [resolve(24,a,19,a)].
% 1.01/1.26 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),C)). [resolve(24,a,20,a)].
% 1.01/1.26 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)). [resolve(24,a,21,a)].
% 1.01/1.26 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B). [resolve(24,a,22,a)].
% 1.01/1.26 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(24,a,23,a)].
% 1.01/1.26 25 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.01/1.26 26 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 1.01/1.26 27 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 1.01/1.26 28 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 1.01/1.26 29 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 1.01/1.26 30 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 1.01/1.26 31 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 1.01/1.26 32 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),C,D,A,A),A) | -hBOOL(c_in(B,D,A)) | -c_Finite__Set_Ofinite(D,A) # label(cls_sup__le__fold__sup_0) # label(axiom). [assumption].
% 1.01/1.26 33 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 1.01/1.26 34 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 1.01/1.26 35 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 1.01/1.26 36 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 1.01/1.26 37 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 1.01/1.26 38 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 1.01/1.26 39 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 1.01/1.26 40 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 1.01/1.26 41 -class_Lattices_Oupper__semilattice(A) | c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),B,c_Set_Oinsert(C,D,A),A,A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),B,D,A,A)) | -c_Finite__Set_Ofinite(D,A) # label(cls_fold__sup__insert_0) # label(axiom). [assumption].
% 1.01/1.26 42 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.01/1.26 43 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 1.01/1.26 44 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 1.01/1.26 45 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 1.01/1.26 46 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 1.01/1.26 47 -class_Lattices_Oupper__semilattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(A),A,A) # label(cls_fun__left__comm__idem__sup_0) # label(axiom). [assumption].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),E),B),C,tc_fun(D,A)). [resolve(25,a,26,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),B),E),C,tc_fun(D,A)). [resolve(25,a,27,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(25,a,28,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)). [resolve(25,a,29,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D,E,tc_fun(B,A),tc_fun(B,A)),tc_fun(B,A)) | -hBOOL(c_in(C,E,tc_fun(B,A))) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(25,a,32,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = D | -c_lessequals(C,D,tc_fun(B,A)). [resolve(25,a,33,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) != D | c_lessequals(C,D,tc_fun(B,A)). [resolve(25,a,34,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = C | -c_lessequals(D,C,tc_fun(B,A)). [resolve(25,a,35,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)). [resolve(25,a,36,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),B),D),tc_fun(C,A)). [resolve(25,a,37,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),B),tc_fun(C,A)). [resolve(25,a,38,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C,c_Set_Oinsert(D,E,tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C,E,tc_fun(B,A),tc_fun(B,A))) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(25,a,41,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(25,a,42,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)). [resolve(25,a,43,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)). [resolve(25,a,44,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C). [resolve(25,a,45,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D). [resolve(25,a,46,a)].
% 1.01/1.26 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(25,a,47,a)].
% 1.01/1.26 48 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.01/1.29 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),C),A),B,tc_bool). [resolve(48,a,26,a)].
% 1.01/1.29 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C),B,tc_bool). [resolve(48,a,27,a)].
% 1.01/1.29 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(48,a,28,a)].
% 1.01/1.29 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(48,a,29,a)].
% 1.01/1.29 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B,C,tc_bool,tc_bool),tc_bool) | -hBOOL(c_in(A,C,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(48,a,32,a)].
% 1.01/1.29 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -c_lessequals(A,B,tc_bool). [resolve(48,a,33,a)].
% 1.01/1.29 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | c_lessequals(A,B,tc_bool). [resolve(48,a,34,a)].
% 1.01/1.29 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -c_lessequals(B,A,tc_bool). [resolve(48,a,35,a)].
% 1.01/1.29 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(48,a,36,a)].
% 1.01/1.29 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),tc_bool). [resolve(48,a,37,a)].
% 1.01/1.29 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),tc_bool). [resolve(48,a,38,a)].
% 1.01/1.29 Derived: c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A,c_Set_Oinsert(B,C,tc_bool),tc_bool,tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A,C,tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(48,a,41,a)].
% 1.01/1.29 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(48,a,42,a)].
% 1.01/1.29 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)). [resolve(48,a,43,a)].
% 1.01/1.29 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)). [resolve(48,a,44,a)].
% 1.01/1.29 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A). [resolve(48,a,45,a)].
% 1.01/1.29 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B). [resolve(48,a,46,a)].
% 1.01/1.29 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool). [resolve(48,a,47,a)].
% 1.01/1.29 49 -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(1,a,19,a)].
% 1.01/1.29 50 c_Finite__Set_Ofold(A,B,c_Set_Oinsert(C,D,E),E,F) = hAPP(hAPP(A,C),c_Finite__Set_Ofold(A,B,D,E,F)) | -c_Finite__Set_Ofinite(D,E) | -c_Finite__Set_Ofun__left__comm__idem(A,E,F) # label(cls_fun__left__comm__idem_Ofold__insert__idem_0) # label(axiom). [assumption].
% 1.01/1.29 51 c_Finite__Set_Ofold(A,B,c_Set_Oinsert(C,D,E),E,F) = c_Finite__Set_Ofold(A,hAPP(hAPP(A,C),B),D,E,F) | -c_Finite__Set_Ofinite(D,E) | -c_Finite__Set_Ofun__left__comm__idem(A,E,F) # label(cls_fun__left__comm__idem_Ofold__insert__idem2_0) # label(axiom). [assumption].
% 1.01/1.29 52 hAPP(hAPP(A,B),hAPP(hAPP(A,B),C)) = hAPP(hAPP(A,B),C) | -c_Finite__Set_Ofun__left__comm__idem(A,D,E) # label(cls_fun__left__comm__idem_Ofun__left__idem_0) # label(axiom). [assumption].
% 1.01/1.29 53 c_Fun_Ocomp(hAPP(A,B),hAPP(A,B),C,C,C) = hAPP(A,B) | -c_Finite__Set_Ofun__left__comm__idem(A,D,C) # label(cls_fun__left__comm__idem_Ofun__comp__idem_0) # label(axiom). [assumption].
% 1.01/1.29 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,c_Set_Oinsert(D,E,tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,E,tc_fun(B,A),tc_fun(B,A))) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(49,b,50,c)].
% 1.01/1.29 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,c_Set_Oinsert(D,E,tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),C),E,tc_fun(B,A),tc_fun(B,A)) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(49,b,51,c)].
% 1.01/1.29 Derived: -class_Lattices_Olattice(A) | c_Fun_Ocomp(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),tc_fun(B,A),tc_fun(B,A),tc_fun(B,A)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C). [resolve(49,b,53,b)].
% 1.01/1.29 54 c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),tc_bool,tc_bool). [resolve(24,a,19,a)].
% 1.01/1.29 Derived: c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,c_Set_Oinsert(B,C,tc_bool),tc_bool,tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,C,tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(54,a,50,c)].
% 1.01/1.29 Derived: c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,c_Set_Oinsert(B,C,tc_bool),tc_bool,tc_bool) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),A),C,tc_bool,tc_bool) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(54,a,51,c)].
% 1.01/1.29 Derived: c_Fun_Ocomp(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),tc_bool,tc_bool,tc_bool) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A). [resolve(54,a,53,b)].
% 1.01/1.29 55 -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(25,a,47,a)].
% 1.01/1.29 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C,c_Set_Oinsert(D,E,tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C,E,tc_fun(B,A),tc_fun(B,A))) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(55,b,50,c)].
% 1.01/1.29 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C,c_Set_Oinsert(D,E,tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C),E,tc_fun(B,A),tc_fun(B,A)) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(55,b,51,c)].
% 1.01/1.29 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D). [resolve(55,b,52,b)].
% 1.01/1.29 Derived: -class_Lattices_Olattice(A) | c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),tc_fun(B,A),tc_fun(B,A),tc_fun(B,A)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C). [resolve(55,b,53,b)].
% 1.09/1.38 56 c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool). [resolve(48,a,47,a)].
% 1.09/1.38 Derived: c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A,c_Set_Oinsert(B,C,tc_bool),tc_bool,tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A,C,tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(56,a,50,c)].
% 1.09/1.38 Derived: c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A,c_Set_Oinsert(B,C,tc_bool),tc_bool,tc_bool) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),C,tc_bool,tc_bool) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(56,a,51,c)].
% 1.09/1.38 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B). [resolve(56,a,52,b)].
% 1.09/1.38 Derived: c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),tc_bool,tc_bool,tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A). [resolve(56,a,53,b)].
% 1.09/1.38 57 hAPP(A,B) = hAPP(B,C) | -hBOOL(c_in(B,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) | -c_Arrow__Order__Mirabelle_Odictator(A,C) # label(cls_dictator__def_0) # label(axiom). [assumption].
% 1.09/1.38 58 hAPP(A,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B),B) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(cls_dictator__def_2) # label(axiom). [assumption].
% 1.09/1.38 59 c_Arrow__Order__Mirabelle_Odictator(A,B) | hBOOL(c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) # label(cls_dictator__def_1) # label(axiom). [assumption].
% 1.09/1.38 Derived: hAPP(A,B) = hAPP(B,C) | -hBOOL(c_in(B,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) | hAPP(A,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C),C). [resolve(57,c,58,b)].
% 1.09/1.38 Derived: hAPP(A,B) = hAPP(B,C) | -hBOOL(c_in(B,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) | hBOOL(c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))). [resolve(57,c,59,a)].
% 1.09/1.38 60 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.09/1.38 61 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.09/1.38 Derived: A = A. [resolve(60,b,61,a)].
% 1.09/1.38
% 1.09/1.38 ============================== end predicate elimination =============
% 1.09/1.38
% 1.09/1.38 Auto_denials: (non-Horn, no changes).
% 1.09/1.38
% 1.09/1.38 Term ordering decisions:
% 1.09/1.38 Function symbol KB weights: tc_bool=1. v_x=1. tc_Arrow__Order__Mirabelle_Oalt=1. t_a=1. c_Arrow__Order__Mirabelle_OProf=1. tc_Arrow__Order__Mirabelle_Oindi=1. v_P____=1. v_P_H____=1. hAPP=1. tc_fun=1. tc_prod=1. c_Relation_Oconverse=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Relation_OField=1. c_Relation_OId__on=1. v_sko__Arrow__Order__Mirabelle__Xdictator__def__1=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Orderings_Obot__class_Obot=1. c_RelatCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------