TSTP Solution File: SCT076-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT076-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 22:03:45 EDT 2022
% Result : Unsatisfiable 1.56s 1.88s
% Output : Refutation 1.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.06 % Problem : SCT076-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.07 % Command : tptp2X_and_run_prover9 %d %s
% 0.06/0.25 % Computer : n009.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Sat Jul 2 06:08:07 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.66/1.03 ============================== Prover9 ===============================
% 0.66/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.66/1.03 Process 6468 was started by sandbox on n009.cluster.edu,
% 0.66/1.03 Sat Jul 2 06:08:07 2022
% 0.66/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6315_n009.cluster.edu".
% 0.66/1.03 ============================== end of head ===========================
% 0.66/1.03
% 0.66/1.03 ============================== INPUT =================================
% 0.66/1.03
% 0.66/1.03 % Reading from file /tmp/Prover9_6315_n009.cluster.edu
% 0.66/1.03
% 0.66/1.03 set(prolog_style_variables).
% 0.66/1.03 set(auto2).
% 0.66/1.03 % set(auto2) -> set(auto).
% 0.66/1.03 % set(auto) -> set(auto_inference).
% 0.66/1.03 % set(auto) -> set(auto_setup).
% 0.66/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.66/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.66/1.03 % set(auto) -> set(auto_limits).
% 0.66/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.66/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.66/1.03 % set(auto) -> set(auto_denials).
% 0.66/1.03 % set(auto) -> set(auto_process).
% 0.66/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.66/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.66/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.66/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.66/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.66/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.66/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.66/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.66/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.66/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.66/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.66/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.66/1.03 % set(auto2) -> assign(stats, some).
% 0.66/1.03 % set(auto2) -> clear(echo_input).
% 0.66/1.03 % set(auto2) -> set(quiet).
% 0.66/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.66/1.03 % set(auto2) -> clear(print_given).
% 0.66/1.03 assign(lrs_ticks,-1).
% 0.66/1.03 assign(sos_limit,10000).
% 0.66/1.03 assign(order,kbo).
% 0.66/1.03 set(lex_order_vars).
% 0.66/1.03 clear(print_given).
% 0.66/1.03
% 0.66/1.03 % formulas(sos). % not echoed (709 formulas)
% 0.66/1.03
% 0.66/1.03 ============================== end of input ==========================
% 0.66/1.03
% 0.66/1.03 % From the command line: assign(max_seconds, 300).
% 0.66/1.03
% 0.66/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.66/1.03
% 0.66/1.03 % Formulas that are not ordinary clauses:
% 0.66/1.03
% 0.66/1.03 ============================== end of process non-clausal formulas ===
% 0.66/1.03
% 0.66/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.66/1.03
% 0.66/1.03 ============================== PREDICATE ELIMINATION =================
% 0.66/1.03 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.66/1.03 2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.66/1.03 3 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.66/1.03 4 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.66/1.03 5 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.66/1.03 6 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.66/1.03 7 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.66/1.03 8 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.66/1.03 9 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.66/1.03 10 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.66/1.03 11 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.66/1.03 12 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.66/1.03 13 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.66/1.03 14 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.66/1.03 15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.66/1.03 16 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.66/1.03 17 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.66/1.03 18 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.66/1.03 19 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.66/1.03 20 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,2,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,3,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(1,a,4,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(1,a,5,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,6,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,7,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)). [resolve(1,a,10,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,11,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,12,a)].
% 0.66/1.03 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(1,a,13,a)].
% 0.66/1.05 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(1,a,14,a)].
% 0.66/1.05 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(1,a,15,a)].
% 0.66/1.05 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(1,a,16,a)].
% 0.66/1.05 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)). [resolve(1,a,17,a)].
% 0.66/1.05 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(1,a,18,a)].
% 0.66/1.05 21 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.66/1.05 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(21,a,2,a)].
% 0.66/1.05 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(21,a,3,a)].
% 0.66/1.05 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(21,a,4,a)].
% 0.66/1.05 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,5,a)].
% 0.66/1.05 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(21,a,6,a)].
% 0.66/1.05 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(21,a,7,a)].
% 0.66/1.05 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(21,a,10,a)].
% 0.66/1.05 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(21,a,11,a)].
% 0.66/1.05 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(21,a,12,a)].
% 0.66/1.05 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(21,a,13,a)].
% 0.66/1.05 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(21,a,14,a)].
% 0.66/1.05 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(21,a,15,a)].
% 0.66/1.05 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(21,a,16,a)].
% 0.66/1.05 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(21,a,17,a)].
% 0.66/1.05 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(21,a,18,a)].
% 0.66/1.05 22 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].
% 0.66/1.05 23 c_Equiv__Relations_Oquotient(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) | -c_in(c_Pair(A,D,B,B),C,tc_prod(B,B)) | -c_in(D,E,B) | -c_in(A,E,B) | -c_Equiv__Relations_Oequiv(E,C,B) # label(cls_eq__equiv__class__iff2_1) # label(axiom). [assumption].
% 0.66/1.05 24 c_Equiv__Relations_Oquotient(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) | -c_in(D,E,B) | -c_in(A,E,B) | -c_Equiv__Relations_Oequiv(E,C,B) | c_in(c_Pair(A,D,B,B),C,tc_prod(B,B)) # label(cls_eq__equiv__class__iff2_0) # label(axiom). [assumption].
% 0.66/1.05 25 c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__subset_0) # label(axiom). [assumption].
% 0.66/1.05 26 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)) | A = B | -c_in(B,c_Equiv__Relations_Oquotient(D,E,C),tc_fun(C,tc_bool)) | -c_in(A,c_Equiv__Relations_Oquotient(D,E,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(D,E,C) # label(cls_quotient__disj_0) # label(axiom). [assumption].
% 0.66/1.05 27 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].
% 0.66/1.05 28 c_in(A,c_Relation_OImage(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),C) | -c_in(A,D,C) | -c_Equiv__Relations_Oequiv(D,B,C) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 0.66/1.05 29 c_in(c_Pair(A,B,C,C),D,tc_prod(C,C)) | -c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)),C) | -c_Equiv__Relations_Oequiv(F,D,C) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 0.66/1.05 30 c_in(c_Pair(A,B,C,C),D,tc_prod(C,C)) | -c_in(B,E,C) | -c_lessequals(c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,D,C) # label(cls_subset__equiv__class_0) # label(axiom). [assumption].
% 0.66/1.05 31 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 0.66/1.05 32 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 0.66/1.05 33 A = B | -c_in(c_Pair(C,D,E,E),F,tc_prod(E,E)) | -c_in(D,B,E) | -c_in(C,A,E) | -c_in(B,c_Equiv__Relations_Oquotient(V6,F,E),tc_fun(E,tc_bool)) | -c_in(A,c_Equiv__Relations_Oquotient(V6,F,E),tc_fun(E,tc_bool)) | -c_Equiv__Relations_Oequiv(V6,F,E) # label(cls_quotient__eqI_0) # label(axiom). [assumption].
% 0.66/1.05 34 -c_in(A,B,C) | -c_in(D,B,C) | -c_in(B,c_Equiv__Relations_Oquotient(E,F,C),tc_fun(C,tc_bool)) | -c_in(B,c_Equiv__Relations_Oquotient(E,F,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,F,C) | c_in(c_Pair(D,A,C,C),F,tc_prod(C,C)) # label(cls_quotient__eq__iff_0) # label(axiom). [assumption].
% 0.66/1.05 35 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_in(D,E,C) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 0.66/1.05 36 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_Equiv__Relations_Oequiv(E,A,C) | c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_in(D,E,C) | -c_in(B,E,C) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 0.66/1.05 37 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) | -c_in(D,E,C) | -c_in(B,E,C) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 0.66/1.05 38 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_in(D,E,C) | -c_in(B,E,C) | -c_Equiv__Relations_Oequiv(E,A,C) | c_in(c_Pair(B,D,C,C),A,tc_prod(C,C)) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oquotient(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) | -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(D,c_Relation_ODomain(A,B,B),B) | -c_in(C,c_Relation_ODomain(A,B,B),B). [resolve(22,b,23,e)].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oquotient(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) | -c_in(D,c_Relation_ODomain(A,B,B),B) | -c_in(C,c_Relation_ODomain(A,B,B),B) | c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)). [resolve(22,b,24,d)].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)) | -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)). [resolve(22,b,25,c)].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)) | C = D | -c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) | -c_in(C,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)). [resolve(22,b,26,e)].
% 0.66/1.05 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(22,b,27,b)].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_in(C,c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),B) | -c_in(C,c_Relation_ODomain(A,B,B),B). [resolve(22,b,28,c)].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)),B). [resolve(22,b,29,c)].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(D,c_Relation_ODomain(A,B,B),B) | -c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)). [resolve(22,b,30,d)].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)). [resolve(22,b,31,c)].
% 0.66/1.05 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | C = D | -c_in(c_Pair(E,F,B,B),A,tc_prod(B,B)) | -c_in(F,D,B) | -c_in(E,C,B) | -c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) | -c_in(C,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)). [resolve(22,b,33,g)].
% 0.82/1.10 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | -c_in(C,D,B) | -c_in(E,D,B) | -c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) | -c_in(D,c_Equiv__Relations_Oquotient(c_Relation_ODomain(A,B,B),A,B),tc_fun(B,tc_bool)) | c_in(c_Pair(E,C,B,B),A,tc_prod(B,B)). [resolve(22,b,34,e)].
% 0.82/1.10 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | c_in(c_Pair(C,D,B,B),A,tc_prod(B,B)) | -c_in(D,c_Relation_ODomain(A,B,B),B). [resolve(22,b,35,d)].
% 0.82/1.10 39 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].
% 0.82/1.10 40 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 0.82/1.10 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(40,b,22,b)].
% 0.82/1.10 41 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 0.82/1.10 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(41,b,22,b)].
% 0.82/1.10 42 c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -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].
% 0.82/1.10 Derived: c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -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(42,d,22,b)].
% 0.82/1.10 43 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 0.82/1.10 Derived: c_Relation_Otrans(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(43,b,22,b)].
% 0.82/1.10 44 c_in(A,B,C) | -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].
% 0.82/1.10 Derived: c_in(A,c_Relation_ODomain(B,C,C),C) | -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(44,c,22,b)].
% 0.82/1.10 45 c_in(A,B,C) | -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].
% 0.82/1.10 46 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.82/1.10 47 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.82/1.10 48 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.82/1.10 49 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.82/1.10 50 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.82/1.10 51 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.82/1.10 52 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.82/1.10 53 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.82/1.10 54 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.82/1.10 55 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.82/1.10 56 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.82/1.10 57 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.82/1.10 58 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.82/1.10 59 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.82/1.10 60 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.82/1.10 61 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.82/1.10 62 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.82/1.10 63 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.82/1.10 64 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.82/1.10 65 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.82/1.10 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(46,a,47,a)].
% 0.82/1.10 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(46,a,48,a)].
% 0.82/1.10 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(46,a,49,a)].
% 0.82/1.10 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(46,a,50,a)].
% 0.82/1.10 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(46,a,51,a)].
% 0.82/1.10 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(46,a,52,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(46,a,53,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(46,a,56,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(46,a,57,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(46,a,58,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(46,a,59,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(46,a,60,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(46,a,61,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(46,a,64,a)].
% 0.82/1.11 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(46,a,65,a)].
% 0.82/1.11 66 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.82/1.11 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(66,a,47,a)].
% 0.82/1.11 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(66,a,48,a)].
% 0.82/1.11 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(66,a,49,a)].
% 0.82/1.11 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(66,a,50,a)].
% 0.82/1.11 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(66,a,51,a)].
% 0.82/1.11 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(66,a,52,a)].
% 0.82/1.11 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(66,a,53,a)].
% 0.82/1.11 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(66,a,56,a)].
% 0.82/1.11 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(66,a,57,a)].
% 0.82/1.11 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(66,a,58,a)].
% 0.82/1.11 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(66,a,59,a)].
% 0.82/1.11 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(66,a,60,a)].
% 0.82/1.11 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(66,a,61,a)].
% 0.82/1.11 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(66,a,64,a)].
% 0.82/1.11 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(66,a,65,a)].
% 0.82/1.11 67 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].
% 1.05/1.33 68 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].
% 1.05/1.33 69 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].
% 1.05/1.33 70 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].
% 1.05/1.33 71 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].
% 1.05/1.33 72 c_Nitpick_Orefl_H(A,B) | -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].
% 1.05/1.33 Derived: c_in(c_Pair(A,A,B,B),C,tc_prod(B,B)) | -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(71,b,72,a)].
% 1.05/1.33 73 -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].
% 1.05/1.33 74 c_Relation_Oirrefl(A,B) | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),B,B),A,tc_prod(B,B)) # label(cls_irrefl__def_1) # label(axiom). [assumption].
% 1.05/1.33 75 c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(A,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),B) # label(cls_irrefl__diff__Id_0) # label(axiom). [assumption].
% 1.05/1.33 Derived: -c_in(c_Pair(A,A,B,B),C,tc_prod(B,B)) | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),B,B),C,tc_prod(B,B)). [resolve(73,b,74,a)].
% 1.05/1.33 Derived: -c_in(c_Pair(A,A,B,B),c_HOL_Ominus__class_Ominus(C,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),tc_prod(B,B)). [resolve(73,b,75,a)].
% 1.05/1.33 76 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.05/1.33 77 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.05/1.33 Derived: A = A. [resolve(76,b,77,a)].
% 1.05/1.33
% 1.05/1.33 ============================== end predicate elimination =============
% 1.05/1.33
% 1.05/1.33 Auto_denials: (non-Horn, no changes).
% 1.05/1.33
% 1.05/1.33 Term ordering decisions:
% 1.05/1.33 Function symbol KB weights: tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. t_a=1. c_Arrow__Order__Mirabelle_OLin=1. t_b=1. v_Lba____=1. v_a____=1. v_b____=1. v_r=1. tc_fun=1. tc_prod=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Relation_OId__on=1. c_fst=1. c_snd=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__Transitive__Closure__Xirrefl__trancl__rD__1__1=1. c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1=1. c_Orderings_Obot__class_Obot=1. c_Relation_OId=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_Relation_Oconverse=1. c_Relation_ODomain=1. c_COMBK=1. c_Relation_ORange=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Arrow__Order__Mirabelle_Obelow=1. c_Equiv__Relations_Oquotient=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_FunDef_Oin__rel=1. c_List_Osko__Recdef__Xtfl__wf__induct__1__1=1. v_sko__Transitive__Closure__Xrtrancl__Xcases__1=1. v_sko__Transitive__Closure__Xtrancl__Xcases__1=1. c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1=1. c_Pair=1. c_Product__Type_OSigma=1. c_Relation_OImage=1. c_Set_Oimage=1. c_Relation_Oinv__image=1. c_split=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2=1. c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomainE__1__1=1. c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1=1. c_ATP__Linkup_Osko__Relation__XRangeE__1__1=1. c_ATP__Linkup_Osko__Relation__XRange__iff__1__1=1. c_Relation_Orel__comp=1. c_Recdef_Ocut=1. c_ATP__Linkup_Osko__Relation__XImageE__1__1=1. c_ATP__Linkup_Osko__Relation__XImage__iff__1__1=1. c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1=1. c_List_Osko__Recdef__Xcuts__eq__1__1=1. c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1=1.
% 1.56/1.88
% 1.56/1.88 ============================== end of process initial clauses ========
% 1.56/1.88
% 1.56/1.88 ============================== CLAUSES FOR SEARCH ====================
% 1.56/1.88
% 1.56/1.88 ============================== end of clauses for search =============
% 1.56/1.88
% 1.56/1.88 ============================== SEARCH ================================
% 1.56/1.88
% 1.56/1.88 % Starting search at 0.40 seconds.
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=73.000, iters=3552
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=66.000, iters=3496
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=59.000, iters=3338
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=58.000, iters=3361
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=55.000, iters=3422
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=54.000, iters=3465
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=53.000, iters=3466
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=52.000, iters=3441
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=49.000, iters=3341
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=48.000, iters=3430
% 1.56/1.88
% 1.56/1.88 Low Water (keep): wt=47.000, iters=3351
% 1.56/1.88
% 1.56/1.88 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 42 (0.00 of 0.94 sec).
% 1.56/1.88
% 1.56/1.88 ============================== PROOF =================================
% 1.56/1.88 % SZS status Unsatisfiable
% 1.56/1.88 % SZS output start Refutation
% 1.56/1.88
% 1.56/1.88 % Proof 1 at 0.95 (+ 0.01) seconds.
% 1.56/1.88 % Length of proof is 5.
% 1.56/1.88 % Level of proof is 1.
% 1.56/1.88 % Maximum clause weight is 28.000.
% 1.56/1.88 % Given clauses 504.
% 1.56/1.88
% 1.56/1.88 635 -c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) | -c_in(c_Pair(B,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) | -c_in(C,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) # label(cls_Lin__irrefl_0) # label(axiom). [assumption].
% 1.56/1.88 714 c_in(v_Lba____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) # label(cls_CHAINED_0) # label(axiom). [assumption].
% 1.56/1.88 715 c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) # label(cls_CHAINED_0_01) # label(axiom). [assumption].
% 1.56/1.88 716 c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 1.56/1.88 4970 $F. [resolve(715,a,635,b),unit_del(a,716),unit_del(b,714)].
% 1.56/1.88
% 1.56/1.88 % SZS output end Refutation
% 1.56/1.88 ============================== end of proof ==========================
% 1.56/1.88
% 1.56/1.88 ============================== STATISTICS ============================
% 1.56/1.88
% 1.56/1.88 Given=504. Generated=8536. Kept=4786. proofs=1.
% 1.56/1.88 Usable=496. Sos=4043. Demods=601. Limbo=29, Disabled=1008. Hints=0.
% 1.56/1.88 Megabytes=17.02.
% 1.56/1.88 User_CPU=0.95, System_CPU=0.01, Wall_clock=1.
% 1.56/1.88
% 1.56/1.88 ============================== end of statistics =====================
% 1.56/1.88
% 1.56/1.88 ============================== end of search =========================
% 1.56/1.88
% 1.56/1.88 THEOREM PROVED
% 1.56/1.88 % SZS status Unsatisfiable
% 1.56/1.88
% 1.56/1.88 Exiting with 1 proof.
% 1.56/1.88
% 1.56/1.88 Process 6468 exit (max_proofs) Sat Jul 2 06:08:08 2022
% 1.56/1.88 Prover9 interrupted
%------------------------------------------------------------------------------