TSTP Solution File: SEU368+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU368+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 : Tue Jul 19 13:31:19 EDT 2022
% Result : Theorem 0.75s 1.06s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU368+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 19:51:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.75/1.00 ============================== Prover9 ===============================
% 0.75/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.00 Process 18427 was started by sandbox on n018.cluster.edu,
% 0.75/1.00 Sun Jun 19 19:51:20 2022
% 0.75/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18274_n018.cluster.edu".
% 0.75/1.00 ============================== end of head ===========================
% 0.75/1.00
% 0.75/1.00 ============================== INPUT =================================
% 0.75/1.00
% 0.75/1.00 % Reading from file /tmp/Prover9_18274_n018.cluster.edu
% 0.75/1.00
% 0.75/1.00 set(prolog_style_variables).
% 0.75/1.00 set(auto2).
% 0.75/1.00 % set(auto2) -> set(auto).
% 0.75/1.00 % set(auto) -> set(auto_inference).
% 0.75/1.00 % set(auto) -> set(auto_setup).
% 0.75/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.00 % set(auto) -> set(auto_limits).
% 0.75/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.00 % set(auto) -> set(auto_denials).
% 0.75/1.00 % set(auto) -> set(auto_process).
% 0.75/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.00 % set(auto2) -> assign(stats, some).
% 0.75/1.00 % set(auto2) -> clear(echo_input).
% 0.75/1.00 % set(auto2) -> set(quiet).
% 0.75/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.00 % set(auto2) -> clear(print_given).
% 0.75/1.00 assign(lrs_ticks,-1).
% 0.75/1.00 assign(sos_limit,10000).
% 0.75/1.00 assign(order,kbo).
% 0.75/1.00 set(lex_order_vars).
% 0.75/1.00 clear(print_given).
% 0.75/1.00
% 0.75/1.00 % formulas(sos). % not echoed (53 formulas)
% 0.75/1.00
% 0.75/1.00 ============================== end of input ==========================
% 0.75/1.00
% 0.75/1.00 % From the command line: assign(max_seconds, 300).
% 0.75/1.00
% 0.75/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.00
% 0.75/1.00 % Formulas that are not ordinary clauses:
% 0.75/1.00 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 2 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 3 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 4 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 5 (all A (-empty_carrier(A) & one_sorted_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & -empty(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 6 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A))) # label(rc2_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 7 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 8 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 9 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 10 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 11 (all A (-empty(A) -> -empty_carrier(incl_POSet(A)) & strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))) # label(fc6_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 12 (all A all B (-empty(A) & relation_of2(B,A,A) -> -empty_carrier(rel_str_of(A,B)) & strict_rel_str(rel_str_of(A,B)))) # label(fc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.00 13 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 14 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 15 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 16 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 17 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 18 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 19 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 20 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 21 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 22 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 23 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 24 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 25 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 26 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 27 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 28 (all A all B (reflexive(B) & antisymmetric(B) & transitive(B) & v1_partfun1(B,A,A) & relation_of2(B,A,A) -> strict_rel_str(rel_str_of(A,B)) & reflexive_relstr(rel_str_of(A,B)) & transitive_relstr(rel_str_of(A,B)) & antisymmetric_relstr(rel_str_of(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 29 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 30 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 31 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 32 (all A all B (relation_of2(B,A,A) -> (all C all D (rel_str_of(A,B) = rel_str_of(C,D) -> A = C & B = D)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 33 (all A (rel_str(A) -> (strict_rel_str(A) -> A = rel_str_of(the_carrier(A),the_InternalRel(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 34 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 35 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 36 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 37 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 38 (all A all B (relation_of2(B,A,A) -> strict_rel_str(rel_str_of(A,B)) & rel_str(rel_str_of(A,B)))) # label(dt_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 39 (all A relation(inclusion_relation(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 40 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 41 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 42 (all A all B all C (relation_of2_as_subset(C,A,B) -> element(C,powerset(cartesian_product2(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 43 (exists A (rel_str(A) & strict_rel_str(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 44 (all A (reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & rel_str(A) -> relation(the_InternalRel(A)) & reflexive(the_InternalRel(A)) & antisymmetric(the_InternalRel(A)) & transitive(the_InternalRel(A)) & v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 45 (all A inclusion_order(A) = inclusion_relation(A)) # label(redefinition_k1_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 46 (all A (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A),A,A) & relation_of2_as_subset(inclusion_order(A),A,A))) # label(dt_k1_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 47 (all A (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))) # label(dt_k2_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 48 (all A (rel_str(A) -> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 49 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 50 (all A (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))) # label(fc5_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 51 (all A incl_POSet(A) = rel_str_of(A,inclusion_order(A))) # label(d1_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 52 -(all A (the_carrier(incl_POSet(A)) = A & the_InternalRel(incl_POSet(A)) = inclusion_order(A))) # label(t1_yellow_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.01
% 0.75/1.01 ============================== end of process non-clausal formulas ===
% 0.75/1.01
% 0.75/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.01
% 0.75/1.01 ============================== PREDICATE ELIMINATION =================
% 0.75/1.01 53 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(4)].
% 0.75/1.01 54 one_sorted_str(c1) # label(rc3_struct_0) # label(axiom). [clausify(3)].
% 0.75/1.01 55 one_sorted_str(c6) # label(existence_l1_struct_0) # label(axiom). [clausify(35)].
% 0.75/1.01 56 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(40)].
% 0.75/1.01 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(53,b,54,a)].
% 0.75/1.01 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(53,b,55,a)].
% 0.75/1.01 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -rel_str(A). [resolve(53,b,56,b)].
% 0.75/1.01 57 empty_carrier(A) | -one_sorted_str(A) | -empty(f1(A)) # label(rc5_struct_0) # label(axiom). [clausify(5)].
% 0.75/1.01 Derived: empty_carrier(c1) | -empty(f1(c1)). [resolve(57,b,54,a)].
% 0.75/1.01 Derived: empty_carrier(c6) | -empty(f1(c6)). [resolve(57,b,55,a)].
% 0.75/1.01 Derived: empty_carrier(A) | -empty(f1(A)) | -rel_str(A). [resolve(57,b,56,b)].
% 0.75/1.01 58 empty_carrier(A) | -one_sorted_str(A) | element(f1(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(5)].
% 0.75/1.01 Derived: empty_carrier(c1) | element(f1(c1),powerset(the_carrier(c1))). [resolve(58,b,54,a)].
% 0.75/1.01 Derived: empty_carrier(c6) | element(f1(c6),powerset(the_carrier(c6))). [resolve(58,b,55,a)].
% 0.75/1.01 Derived: empty_carrier(A) | element(f1(A),powerset(the_carrier(A))) | -rel_str(A). [resolve(58,b,56,b)].
% 0.75/1.01 59 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(48)].
% 0.75/1.01 60 rel_str(c2) # label(rc2_orders_2) # label(axiom). [clausify(6)].
% 0.75/1.01 61 rel_str(c5) # label(existence_l1_orders_2) # label(axiom). [clausify(34)].
% 0.75/1.01 62 rel_str(c7) # label(rc1_orders_2) # label(axiom). [clausify(43)].
% 0.75/1.01 63 rel_str(incl_POSet(A)) # label(dt_k2_yellow_1) # label(axiom). [clausify(47)].
% 0.75/1.01 64 -relation_of2(A,B,B) | rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(38)].
% 0.75/1.01 Derived: relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(59,a,60,a)].
% 0.75/1.01 Derived: relation_of2_as_subset(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)). [resolve(59,a,61,a)].
% 0.75/1.01 Derived: relation_of2_as_subset(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)). [resolve(59,a,62,a)].
% 0.75/1.01 Derived: relation_of2_as_subset(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))). [resolve(59,a,63,a)].
% 0.75/1.01 Derived: relation_of2_as_subset(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(59,a,64,b)].
% 0.75/1.01 65 -rel_str(A) | -strict_rel_str(A) | rel_str_of(the_carrier(A),the_InternalRel(A)) = A # label(abstractness_v1_orders_2) # label(axiom). [clausify(33)].
% 0.75/1.01 Derived: -strict_rel_str(c2) | rel_str_of(the_carrier(c2),the_InternalRel(c2)) = c2. [resolve(65,a,60,a)].
% 0.75/1.01 Derived: -strict_rel_str(c5) | rel_str_of(the_carrier(c5),the_InternalRel(c5)) = c5. [resolve(65,a,61,a)].
% 0.75/1.01 Derived: -strict_rel_str(c7) | rel_str_of(the_carrier(c7),the_InternalRel(c7)) = c7. [resolve(65,a,62,a)].
% 0.75/1.01 Derived: -strict_rel_str(incl_POSet(A)) | rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A). [resolve(65,a,63,a)].
% 0.75/1.01 Derived: -strict_rel_str(rel_str_of(A,B)) | rel_str_of(the_carrier(rel_str_of(A,B)),the_InternalRel(rel_str_of(A,B))) = rel_str_of(A,B) | -relation_of2(B,A,A). [resolve(65,a,64,b)].
% 0.75/1.01 66 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | relation(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(44)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | relation(the_InternalRel(c2)). [resolve(66,d,60,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | relation(the_InternalRel(c5)). [resolve(66,d,61,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | relation(the_InternalRel(c7)). [resolve(66,d,62,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | relation(the_InternalRel(incl_POSet(A))). [resolve(66,d,63,a)].
% 0.75/1.01 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | relation(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(66,d,64,b)].
% 0.75/1.01 67 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | reflexive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(44)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(67,d,60,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | reflexive(the_InternalRel(c5)). [resolve(67,d,61,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | reflexive(the_InternalRel(c7)). [resolve(67,d,62,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | reflexive(the_InternalRel(incl_POSet(A))). [resolve(67,d,63,a)].
% 0.75/1.01 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | reflexive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(67,d,64,b)].
% 0.75/1.01 68 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | antisymmetric(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(44)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | antisymmetric(the_InternalRel(c2)). [resolve(68,d,60,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | antisymmetric(the_InternalRel(c5)). [resolve(68,d,61,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | antisymmetric(the_InternalRel(c7)). [resolve(68,d,62,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | antisymmetric(the_InternalRel(incl_POSet(A))). [resolve(68,d,63,a)].
% 0.75/1.01 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | antisymmetric(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(68,d,64,b)].
% 0.75/1.01 69 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | transitive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(44)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | transitive(the_InternalRel(c2)). [resolve(69,d,60,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | transitive(the_InternalRel(c5)). [resolve(69,d,61,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | transitive(the_InternalRel(c7)). [resolve(69,d,62,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | transitive(the_InternalRel(incl_POSet(A))). [resolve(69,d,63,a)].
% 0.75/1.01 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | transitive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(69,d,64,b)].
% 0.75/1.01 70 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(fc2_orders_2) # label(axiom). [clausify(44)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | v1_partfun1(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(70,d,60,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | v1_partfun1(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)). [resolve(70,d,61,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | v1_partfun1(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)). [resolve(70,d,62,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | v1_partfun1(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))). [resolve(70,d,63,a)].
% 0.75/1.01 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | v1_partfun1(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(70,d,64,b)].
% 0.75/1.01 71 empty_carrier(A) | -empty(the_carrier(A)) | -rel_str(A). [resolve(53,b,56,b)].
% 0.75/1.01 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(71,c,60,a)].
% 0.75/1.01 Derived: empty_carrier(c5) | -empty(the_carrier(c5)). [resolve(71,c,61,a)].
% 0.75/1.01 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(71,c,62,a)].
% 0.75/1.01 Derived: empty_carrier(incl_POSet(A)) | -empty(the_carrier(incl_POSet(A))). [resolve(71,c,63,a)].
% 0.75/1.01 Derived: empty_carrier(rel_str_of(A,B)) | -empty(the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(71,c,64,b)].
% 0.75/1.01 72 empty_carrier(A) | -empty(f1(A)) | -rel_str(A). [resolve(57,b,56,b)].
% 0.75/1.01 Derived: empty_carrier(c2) | -empty(f1(c2)). [resolve(72,c,60,a)].
% 0.75/1.01 Derived: empty_carrier(c5) | -empty(f1(c5)). [resolve(72,c,61,a)].
% 0.75/1.01 Derived: empty_carrier(c7) | -empty(f1(c7)). [resolve(72,c,62,a)].
% 0.75/1.01 Derived: empty_carrier(incl_POSet(A)) | -empty(f1(incl_POSet(A))). [resolve(72,c,63,a)].
% 0.75/1.01 Derived: empty_carrier(rel_str_of(A,B)) | -empty(f1(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(72,c,64,b)].
% 0.75/1.01 73 empty_carrier(A) | element(f1(A),powerset(the_carrier(A))) | -rel_str(A). [resolve(58,b,56,b)].
% 0.75/1.01 Derived: empty_carrier(c2) | element(f1(c2),powerset(the_carrier(c2))). [resolve(73,c,60,a)].
% 0.75/1.01 Derived: empty_carrier(c5) | element(f1(c5),powerset(the_carrier(c5))). [resolve(73,c,61,a)].
% 0.75/1.01 Derived: empty_carrier(c7) | element(f1(c7),powerset(the_carrier(c7))). [resolve(73,c,62,a)].
% 0.75/1.01 Derived: empty_carrier(incl_POSet(A)) | element(f1(incl_POSet(A)),powerset(the_carrier(incl_POSet(A)))). [resolve(73,c,63,a)].
% 0.75/1.01 Derived: empty_carrier(rel_str_of(A,B)) | element(f1(rel_str_of(A,B)),powerset(the_carrier(rel_str_of(A,B)))) | -relation_of2(B,A,A). [resolve(73,c,64,b)].
% 0.75/1.01 74 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(31)].
% 0.75/1.01 75 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(10)].
% 0.75/1.01 76 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(31)].
% 0.75/1.01 Derived: element(A,powerset(A)). [resolve(74,b,75,a)].
% 0.75/1.01 77 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | strict_rel_str(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(28)].
% 0.75/1.01 78 reflexive(inclusion_order(A)) # label(dt_k1_yellow_1) # label(axiom). [clausify(46)].
% 0.75/1.01 Derived: -antisymmetric(inclusion_order(A)) | -transitive(inclusion_order(A)) | -v1_partfun1(inclusion_order(A),B,B) | -relation_of2(inclusion_order(A),B,B) | strict_rel_str(rel_str_of(B,inclusion_order(A))). [resolve(77,a,78,a)].
% 0.75/1.01 79 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | reflexive_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(28)].
% 0.75/1.01 Derived: -antisymmetric(inclusion_order(A)) | -transitive(inclusion_order(A)) | -v1_partfun1(inclusion_order(A),B,B) | -relation_of2(inclusion_order(A),B,B) | reflexive_relstr(rel_str_of(B,inclusion_order(A))). [resolve(79,a,78,a)].
% 0.75/1.01 80 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | transitive_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(28)].
% 0.75/1.01 Derived: -antisymmetric(inclusion_order(A)) | -transitive(inclusion_order(A)) | -v1_partfun1(inclusion_order(A),B,B) | -relation_of2(inclusion_order(A),B,B) | transitive_relstr(rel_str_of(B,inclusion_order(A))). [resolve(80,a,78,a)].
% 0.75/1.01 81 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | antisymmetric_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(28)].
% 0.75/1.01 Derived: -antisymmetric(inclusion_order(A)) | -transitive(inclusion_order(A)) | -v1_partfun1(inclusion_order(A),B,B) | -relation_of2(inclusion_order(A),B,B) | antisymmetric_relstr(rel_str_of(B,inclusion_order(A))). [resolve(81,a,78,a)].
% 0.75/1.01 82 -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(67,d,60,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c2))). [resolve(82,d,77,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(82,d,79,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(82,d,80,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(82,d,81,a)].
% 0.75/1.01 83 -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | reflexive(the_InternalRel(c5)). [resolve(67,d,61,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -antisymmetric(the_InternalRel(c5)) | -transitive(the_InternalRel(c5)) | -v1_partfun1(the_InternalRel(c5),A,A) | -relation_of2(the_InternalRel(c5),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c5))). [resolve(83,d,77,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -antisymmetric(the_InternalRel(c5)) | -transitive(the_InternalRel(c5)) | -v1_partfun1(the_InternalRel(c5),A,A) | -relation_of2(the_InternalRel(c5),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c5))). [resolve(83,d,79,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -antisymmetric(the_InternalRel(c5)) | -transitive(the_InternalRel(c5)) | -v1_partfun1(the_InternalRel(c5),A,A) | -relation_of2(the_InternalRel(c5),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c5))). [resolve(83,d,80,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -antisymmetric(the_InternalRel(c5)) | -transitive(the_InternalRel(c5)) | -v1_partfun1(the_InternalRel(c5),A,A) | -relation_of2(the_InternalRel(c5),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c5))). [resolve(83,d,81,a)].
% 0.75/1.01 84 -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | reflexive(the_InternalRel(c7)). [resolve(67,d,62,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -antisymmetric(the_InternalRel(c7)) | -transitive(the_InternalRel(c7)) | -v1_partfun1(the_InternalRel(c7),A,A) | -relation_of2(the_InternalRel(c7),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c7))). [resolve(84,d,77,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -antisymmetric(the_InternalRel(c7)) | -transitive(the_InternalRel(c7)) | -v1_partfun1(the_InternalRel(c7),A,A) | -relation_of2(the_InternalRel(c7),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c7))). [resolve(84,d,79,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -antisymmetric(the_InternalRel(c7)) | -transitive(the_InternalRel(c7)) | -v1_partfun1(the_InternalRel(c7),A,A) | -relation_of2(the_InternalRel(c7),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c7))). [resolve(84,d,80,a)].
% 0.75/1.01 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -antisymmetric(the_InternalRel(c7)) | -transitive(the_InternalRel(c7)) | -v1_partfun1(the_InternalRel(c7),A,A) | -relation_of2(the_InternalRel(c7),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c7))). [resolve(84,d,81,a)].
% 0.75/1.01 85 -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | reflexive(the_InternalRel(incl_POSet(A))). [resolve(67,d,63,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -antisymmetric(the_InternalRel(incl_POSet(A))) | -transitive(the_InternalRel(incl_POSet(A))) | -v1_partfun1(the_InternalRel(incl_POSet(A)),B,B) | -relation_of2(the_InternalRel(incl_POSet(A)),B,B) | strict_rel_str(rel_str_of(B,the_InternalRel(incl_POSet(A)))). [resolve(85,d,77,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -antisymmetric(the_InternalRel(incl_POSet(A))) | -transitive(the_InternalRel(incl_POSet(A))) | -v1_partfun1(the_InternalRel(incl_POSet(A)),B,B) | -relation_of2(the_InternalRel(incl_POSet(A)),B,B) | reflexive_relstr(rel_str_of(B,the_InternalRel(incl_POSet(A)))). [resolve(85,d,79,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -antisymmetric(the_InternalRel(incl_POSet(A))) | -transitive(the_InternalRel(incl_POSet(A))) | -v1_partfun1(the_InternalRel(incl_POSet(A)),B,B) | -relation_of2(the_InternalRel(incl_POSet(A)),B,B) | transitive_relstr(rel_str_of(B,the_InternalRel(incl_POSet(A)))). [resolve(85,d,80,a)].
% 0.75/1.01 Derived: -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -antisymmetric(the_InternalRel(incl_POSet(A))) | -transitive(the_InternalRel(incl_POSet(A))) | -v1_partfun1(the_InternalRel(incl_POSet(A)),B,B) | -relation_of2(the_InternalRel(incl_POSet(A)),B,B) | antisymmetric_relstr(rel_str_of(B,the_InternalRel(incl_POSet(A)))). [resolve(85,d,81,a)].
% 0.75/1.01 86 -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | reflexive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(67,d,64,b)].
% 0.75/1.01 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | strict_rel_str(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(86,d,77,a)].
% 0.75/1.02 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | reflexive_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(86,d,79,a)].
% 0.75/1.02 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | transitive_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(86,d,80,a)].
% 0.75/1.02 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | antisymmetric_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(86,d,81,a)].
% 0.75/1.02 87 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(37)].
% 0.75/1.02 88 relation_of2_as_subset(inclusion_order(A),A,A) # label(dt_k1_yellow_1) # label(axiom). [clausify(46)].
% 0.75/1.02 89 relation_of2_as_subset(f6(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(36)].
% 0.75/1.02 Derived: relation_of2(inclusion_order(A),A,A). [resolve(87,a,88,a)].
% 0.75/1.02 Derived: relation_of2(f6(A,B),A,B). [resolve(87,a,89,a)].
% 0.75/1.02 90 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(37)].
% 0.75/1.02 91 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(42)].
% 0.75/1.02 Derived: element(inclusion_order(A),powerset(cartesian_product2(A,A))). [resolve(91,a,88,a)].
% 0.75/1.02 Derived: element(f6(A,B),powerset(cartesian_product2(A,B))). [resolve(91,a,89,a)].
% 0.75/1.02 Derived: element(A,powerset(cartesian_product2(B,C))) | -relation_of2(A,B,C). [resolve(91,a,90,a)].
% 0.75/1.02 92 relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(59,a,60,a)].
% 0.75/1.02 Derived: relation_of2(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(92,a,87,a)].
% 0.75/1.02 Derived: element(the_InternalRel(c2),powerset(cartesian_product2(the_carrier(c2),the_carrier(c2)))). [resolve(92,a,91,a)].
% 0.75/1.02 93 relation_of2_as_subset(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)). [resolve(59,a,61,a)].
% 0.75/1.02 Derived: relation_of2(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)). [resolve(93,a,87,a)].
% 0.75/1.02 Derived: element(the_InternalRel(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))). [resolve(93,a,91,a)].
% 0.75/1.02 94 relation_of2_as_subset(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)). [resolve(59,a,62,a)].
% 0.75/1.02 Derived: relation_of2(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)). [resolve(94,a,87,a)].
% 0.75/1.02 Derived: element(the_InternalRel(c7),powerset(cartesian_product2(the_carrier(c7),the_carrier(c7)))). [resolve(94,a,91,a)].
% 0.75/1.02 95 relation_of2_as_subset(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))). [resolve(59,a,63,a)].
% 0.75/1.02 Derived: relation_of2(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))). [resolve(95,a,87,a)].
% 0.75/1.02 Derived: element(the_InternalRel(incl_POSet(A)),powerset(cartesian_product2(the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))))). [resolve(95,a,91,a)].
% 0.75/1.06 96 relation_of2_as_subset(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(59,a,64,b)].
% 0.75/1.06 Derived: -relation_of2(A,B,B) | relation_of2(the_InternalRel(rel_str_of(B,A)),the_carrier(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))). [resolve(96,a,87,a)].
% 0.75/1.06 Derived: -relation_of2(A,B,B) | element(the_InternalRel(rel_str_of(B,A)),powerset(cartesian_product2(the_carrier(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))))). [resolve(96,a,91,a)].
% 0.75/1.06
% 0.75/1.06 ============================== end predicate elimination =============
% 0.75/1.06
% 0.75/1.06 Auto_denials: (non-Horn, no changes).
% 0.75/1.06
% 0.75/1.06 Term ordering decisions:
% 0.75/1.06 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. rel_str_of=1. cartesian_product2=1. f4=1. f6=1. the_InternalRel=1. incl_POSet=1. the_carrier=1. inclusion_order=1. powerset=1. inclusion_relation=1. f1=1. f2=1. f3=1. f5=1.
% 0.75/1.06
% 0.75/1.06 ============================== end of process initial clauses ========
% 0.75/1.06
% 0.75/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.06
% 0.75/1.06 ============================== end of clauses for search =============
% 0.75/1.06
% 0.75/1.06 ============================== SEARCH ================================
% 0.75/1.06
% 0.75/1.06 % Starting search at 0.04 seconds.
% 0.75/1.06
% 0.75/1.06 ============================== PROOF =================================
% 0.75/1.06 % SZS status Theorem
% 0.75/1.06 % SZS output start Refutation
% 0.75/1.06
% 0.75/1.06 % Proof 1 at 0.07 (+ 0.00) seconds.
% 0.75/1.06 % Length of proof is 37.
% 0.75/1.06 % Level of proof is 7.
% 0.75/1.06 % Maximum clause weight is 21.000.
% 0.75/1.06 % Given clauses 265.
% 0.75/1.06
% 0.75/1.06 32 (all A all B (relation_of2(B,A,A) -> (all C all D (rel_str_of(A,B) = rel_str_of(C,D) -> A = C & B = D)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.06 33 (all A (rel_str(A) -> (strict_rel_str(A) -> A = rel_str_of(the_carrier(A),the_InternalRel(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.06 37 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.06 45 (all A inclusion_order(A) = inclusion_relation(A)) # label(redefinition_k1_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.06 46 (all A (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A),A,A) & relation_of2_as_subset(inclusion_order(A),A,A))) # label(dt_k1_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.06 47 (all A (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))) # label(dt_k2_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.06 48 (all A (rel_str(A) -> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.06 51 (all A incl_POSet(A) = rel_str_of(A,inclusion_order(A))) # label(d1_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.06 52 -(all A (the_carrier(incl_POSet(A)) = A & the_InternalRel(incl_POSet(A)) = inclusion_order(A))) # label(t1_yellow_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.06 59 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(48)].
% 0.75/1.06 63 rel_str(incl_POSet(A)) # label(dt_k2_yellow_1) # label(axiom). [clausify(47)].
% 0.75/1.06 65 -rel_str(A) | -strict_rel_str(A) | rel_str_of(the_carrier(A),the_InternalRel(A)) = A # label(abstractness_v1_orders_2) # label(axiom). [clausify(33)].
% 0.75/1.06 87 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(37)].
% 0.75/1.06 88 relation_of2_as_subset(inclusion_order(A),A,A) # label(dt_k1_yellow_1) # label(axiom). [clausify(46)].
% 0.75/1.06 95 relation_of2_as_subset(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))). [resolve(59,a,63,a)].
% 0.75/1.06 107 strict_rel_str(incl_POSet(A)) # label(dt_k2_yellow_1) # label(axiom). [clausify(47)].
% 0.75/1.06 113 inclusion_order(A) = inclusion_relation(A) # label(redefinition_k1_yellow_1) # label(axiom). [clausify(45)].
% 0.75/1.06 118 rel_str_of(A,inclusion_order(A)) = incl_POSet(A) # label(d1_yellow_1) # label(axiom). [clausify(51)].
% 0.75/1.06 119 incl_POSet(A) = rel_str_of(A,inclusion_relation(A)). [copy(118),rewrite([113(1)]),flip(a)].
% 0.75/1.06 127 the_carrier(incl_POSet(c8)) != c8 | inclusion_order(c8) != the_InternalRel(incl_POSet(c8)) # label(t1_yellow_1) # label(negated_conjecture). [clausify(52)].
% 0.75/1.06 128 the_carrier(rel_str_of(c8,inclusion_relation(c8))) != c8 | the_InternalRel(rel_str_of(c8,inclusion_relation(c8))) != inclusion_relation(c8). [copy(127),rewrite([119(2),113(9),119(11)]),flip(b)].
% 0.75/1.06 140 -relation_of2(A,B,B) | rel_str_of(C,D) != rel_str_of(B,A) | C = B # label(free_g1_orders_2) # label(axiom). [clausify(32)].
% 0.75/1.06 141 -relation_of2(A,B,B) | rel_str_of(C,D) != rel_str_of(B,A) | D = A # label(free_g1_orders_2) # label(axiom). [clausify(32)].
% 0.75/1.06 156 -strict_rel_str(incl_POSet(A)) | rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A). [resolve(65,a,63,a)].
% 0.75/1.06 157 -strict_rel_str(rel_str_of(A,inclusion_relation(A))) | rel_str_of(the_carrier(rel_str_of(A,inclusion_relation(A))),the_InternalRel(rel_str_of(A,inclusion_relation(A)))) = rel_str_of(A,inclusion_relation(A)). [copy(156),rewrite([119(1),119(4),119(7),119(11)])].
% 0.75/1.06 232 relation_of2(inclusion_order(A),A,A). [resolve(87,a,88,a)].
% 0.75/1.06 233 relation_of2(inclusion_relation(A),A,A). [copy(232),rewrite([113(1)])].
% 0.75/1.06 245 relation_of2(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))). [resolve(95,a,87,a)].
% 0.75/1.06 246 relation_of2(the_InternalRel(rel_str_of(A,inclusion_relation(A))),the_carrier(rel_str_of(A,inclusion_relation(A))),the_carrier(rel_str_of(A,inclusion_relation(A)))). [copy(245),rewrite([119(1),119(4),119(7)])].
% 0.75/1.06 256 strict_rel_str(rel_str_of(A,inclusion_relation(A))). [back_rewrite(107),rewrite([119(1)])].
% 0.75/1.06 268 rel_str_of(the_carrier(rel_str_of(A,inclusion_relation(A))),the_InternalRel(rel_str_of(A,inclusion_relation(A)))) = rel_str_of(A,inclusion_relation(A)). [back_unit_del(157),unit_del(a,256)].
% 0.75/1.06 295 rel_str_of(A,inclusion_relation(A)) != rel_str_of(B,C) | inclusion_relation(A) = C. [resolve(233,a,141,a),flip(a),flip(b)].
% 0.75/1.06 333 rel_str_of(A,inclusion_relation(A)) != rel_str_of(B,C) | the_carrier(rel_str_of(A,inclusion_relation(A))) = B. [resolve(246,a,140,a),rewrite([268(8)]),flip(a),flip(b)].
% 0.75/1.06 398 the_InternalRel(rel_str_of(A,inclusion_relation(A))) = inclusion_relation(A). [resolve(295,a,268,a(flip)),flip(a)].
% 0.75/1.06 407 the_carrier(rel_str_of(c8,inclusion_relation(c8))) != c8. [back_rewrite(128),rewrite([398(12)]),xx(b)].
% 0.75/1.06 514 the_carrier(rel_str_of(A,inclusion_relation(A))) = A. [xx_res(333,a)].
% 0.75/1.06 515 $F. [resolve(514,a,407,a)].
% 0.75/1.06
% 0.75/1.06 % SZS output end Refutation
% 0.75/1.06 ============================== end of proof ==========================
% 0.75/1.06
% 0.75/1.06 ============================== STATISTICS ============================
% 0.75/1.06
% 0.75/1.06 Given=265. Generated=694. Kept=380. proofs=1.
% 0.75/1.06 Usable=236. Sos=61. Demods=16. Limbo=0, Disabled=261. Hints=0.
% 0.75/1.06 Megabytes=0.63.
% 0.75/1.06 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.75/1.06
% 0.75/1.06 ============================== end of statistics =====================
% 0.75/1.06
% 0.75/1.06 ============================== end of search =========================
% 0.75/1.06
% 0.75/1.06 THEOREM PROVED
% 0.75/1.06 % SZS status Theorem
% 0.75/1.06
% 0.75/1.06 Exiting with 1 proof.
% 0.75/1.06
% 0.75/1.06 Process 18427 exit (max_proofs) Sun Jun 19 19:51:20 2022
% 0.75/1.06 Prover9 interrupted
%------------------------------------------------------------------------------