%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU244+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : 300s
% DateTime : Sat Jun 21 05:27:22 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU244+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:32:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(is_transitive_in_type, type, (
% 0.12/0.37 is_transitive_in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(set_union2_type, type, (
% 0.12/0.37 set_union2: ( $i * $i ) > $i)).
% 0.12/0.37 tff(relation_rng_type, type, (
% 0.12/0.37 relation_rng: $i > $i)).
% 0.12/0.37 tff(tptp_fun_A_0_type, type, (
% 0.12/0.37 tptp_fun_A_0: $i)).
% 0.12/0.37 tff(relation_dom_type, type, (
% 0.12/0.37 relation_dom: $i > $i)).
% 0.12/0.37 tff(relation_field_type, type, (
% 0.12/0.37 relation_field: $i > $i)).
% 0.12/0.37 tff(relation_type, type, (
% 0.12/0.37 relation: $i > $o)).
% 0.12/0.37 tff(well_ordering_type, type, (
% 0.12/0.37 well_ordering: $i > $o)).
% 0.12/0.37 tff(well_orders_type, type, (
% 0.12/0.37 well_orders: ( $i * $i ) > $o)).
% 0.12/0.37 tff(transitive_type, type, (
% 0.12/0.37 transitive: $i > $o)).
% 0.12/0.37 tff(connected_type, type, (
% 0.12/0.37 connected: $i > $o)).
% 0.12/0.37 tff(antisymmetric_type, type, (
% 0.12/0.37 antisymmetric: $i > $o)).
% 0.12/0.37 tff(reflexive_type, type, (
% 0.12/0.37 reflexive: $i > $o)).
% 0.12/0.37 tff(well_founded_relation_type, type, (
% 0.12/0.37 well_founded_relation: $i > $o)).
% 0.12/0.37 tff(is_connected_in_type, type, (
% 0.12/0.37 is_connected_in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(is_reflexive_in_type, type, (
% 0.12/0.37 is_reflexive_in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(is_well_founded_in_type, type, (
% 0.12/0.37 is_well_founded_in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(is_antisymmetric_in_type, type, (
% 0.12/0.37 is_antisymmetric_in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((~![A: $i] : ((~relation(A)) | (well_orders(A, relation_field(A)) <=> well_ordering(A)))) <=> (~![A: $i] : ((~relation(A)) | (well_orders(A, relation_field(A)) <=> well_ordering(A))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![A: $i] : (relation(A) => (well_orders(A, relation_field(A)) <=> well_ordering(A)))) <=> (~![A: $i] : ((~relation(A)) | (well_orders(A, relation_field(A)) <=> well_ordering(A))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,axiom,(~![A: $i] : (relation(A) => (well_orders(A, relation_field(A)) <=> well_ordering(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_wellord1')).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (~![A: $i] : ((~relation(A)) | (well_orders(A, relation_field(A)) <=> well_ordering(A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![A: $i] : ((~relation(A)) | (well_orders(A, relation_field(A)) <=> well_ordering(A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![A: $i] : ((~relation(A)) | (well_orders(A, relation_field(A)) <=> well_ordering(A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![A: $i] : ((~relation(A)) | (well_orders(A, relation_field(A)) <=> well_ordering(A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.37 tff(8,plain,(
% 0.12/0.37 ~((~relation(A!0)) | (well_orders(A!0, relation_field(A!0)) <=> well_ordering(A!0)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (relation(A!0)),
% 0.12/0.37 inference(or_elim,[status(thm)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_relat_1')).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.37 tff(18,plain,(
% 0.12/0.37 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!0)) | (relation_field(A!0) = set_union2(relation_dom(A!0), relation_rng(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!0)) | (relation_field(A!0) = set_union2(relation_dom(A!0), relation_rng(A!0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!0)) | (relation_field(A!0) = set_union2(relation_dom(A!0), relation_rng(A!0))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!0)) | (relation_field(A!0) = set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (relation_field(A!0) = set_union2(relation_dom(A!0), relation_rng(A!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (set_union2(relation_dom(A!0), relation_rng(A!0)) = relation_field(A!0)),
% 0.12/0.37 inference(symmetry,[status(thm)],[23])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))) <=> is_transitive_in(A!0, relation_field(A!0))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (is_transitive_in(A!0, relation_field(A!0)) <=> is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.37 inference(symmetry,[status(thm)],[25])).
% 0.12/0.37 tff(27,assumption,(~well_ordering(A!0)), introduced(assumption)).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (^[A: $i] : refl(((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))) <=> ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))) <=> ![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (^[A: $i] : rewrite(((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (^[A: $i] : trans(monotonicity(rewrite((well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A))) <=> (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))), ((relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> (relation(A) => (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))))), rewrite((relation(A) => (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))), ((relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![A: $i] : (relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.37 tff(35,axiom,(![A: $i] : (relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_wellord1')).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.12/0.37 tff(38,plain,(
% 0.12/0.37 ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[37])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!0)) | (~(((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!0)) | (~(((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (((~relation(A!0)) | (~(((~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0)) | (~well_founded_relation(A!0))) <=> well_ordering(A!0)))) <=> ((~relation(A!0)) | (~(((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!0)) | (~(((~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0)) | (~well_founded_relation(A!0))) <=> well_ordering(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!0)) | (~(((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0)))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[42])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!0)) | (~(((~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0)) | (~well_founded_relation(A!0))) <=> well_ordering(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!0)) | (~(((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[43, 41])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!0)) | (~(((~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0)) | (~well_founded_relation(A!0))) <=> well_ordering(A!0))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!0)) | (~(((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (~(((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[46, 40, 9])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 ((((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0)) | ((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) | well_ordering(A!0)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) | well_ordering(A!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 ((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[49, 27])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))) <=> is_connected_in(A!0, relation_field(A!0))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))) <=> well_orders(A!0, relation_field(A!0))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (well_orders(A!0, relation_field(A!0)) <=> well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.37 inference(symmetry,[status(thm)],[52])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (~(well_orders(A!0, relation_field(A!0)) <=> well_ordering(A!0))),
% 0.12/0.38 inference(or_elim,[status(thm)],[8])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 ((well_orders(A!0, relation_field(A!0)) <=> well_ordering(A!0)) | well_orders(A!0, relation_field(A!0)) | well_ordering(A!0)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (well_orders(A!0, relation_field(A!0)) | well_ordering(A!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (well_orders(A!0, relation_field(A!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[56, 27])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B)))) <=> ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B)))) <=> ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[61])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[62, 60])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B)))) <=> ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[64])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((well_orders(A, B) <=> ((((is_reflexive_in(A, B) & is_transitive_in(A, B)) & is_antisymmetric_in(A, B)) & is_connected_in(A, B)) & is_well_founded_in(A, B))) <=> (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))), (![B: $i] : (well_orders(A, B) <=> ((((is_reflexive_in(A, B) & is_transitive_in(A, B)) & is_antisymmetric_in(A, B)) & is_connected_in(A, B)) & is_well_founded_in(A, B))) <=> ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))), ((relation(A) => ![B: $i] : (well_orders(A, B) <=> ((((is_reflexive_in(A, B) & is_transitive_in(A, B)) & is_antisymmetric_in(A, B)) & is_connected_in(A, B)) & is_well_founded_in(A, B)))) <=> (relation(A) => ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B)))))), rewrite((relation(A) => ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B)))) <=> ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))), ((relation(A) => ![B: $i] : (well_orders(A, B) <=> ((((is_reflexive_in(A, B) & is_transitive_in(A, B)) & is_antisymmetric_in(A, B)) & is_connected_in(A, B)) & is_well_founded_in(A, B)))) <=> ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (![A: $i] : (relation(A) => ![B: $i] : (well_orders(A, B) <=> ((((is_reflexive_in(A, B) & is_transitive_in(A, B)) & is_antisymmetric_in(A, B)) & is_connected_in(A, B)) & is_well_founded_in(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[67])).
% 0.12/0.38 tff(69,axiom,(![A: $i] : (relation(A) => ![B: $i] : (well_orders(A, B) <=> ((((is_reflexive_in(A, B) & is_transitive_in(A, B)) & is_antisymmetric_in(A, B)) & is_connected_in(A, B)) & is_well_founded_in(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_wellord1')).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.12/0.38 tff(72,plain,(
% 0.12/0.38 ![A: $i] : ((~relation(A)) | ![B: $i] : (well_orders(A, B) <=> (is_reflexive_in(A, B) & is_transitive_in(A, B) & is_antisymmetric_in(A, B) & is_connected_in(A, B) & is_well_founded_in(A, B))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[71])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.12/0.38 tff(74,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))) | ((~relation(A!0)) | ![B: $i] : (~(((~is_transitive_in(A!0, B)) | (~is_antisymmetric_in(A!0, B)) | (~is_connected_in(A!0, B)) | (~is_well_founded_in(A!0, B)) | (~is_reflexive_in(A!0, B))) <=> well_orders(A!0, B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))) | (~relation(A!0)) | ![B: $i] : (~(((~is_transitive_in(A!0, B)) | (~is_antisymmetric_in(A!0, B)) | (~is_connected_in(A!0, B)) | (~is_well_founded_in(A!0, B)) | (~is_reflexive_in(A!0, B))) <=> well_orders(A!0, B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))) | ((~relation(A!0)) | ![B: $i] : (~(((~is_transitive_in(A!0, B)) | (~is_antisymmetric_in(A!0, B)) | (~is_connected_in(A!0, B)) | (~is_well_founded_in(A!0, B)) | (~is_reflexive_in(A!0, B))) <=> well_orders(A!0, B))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(77,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~(((~is_transitive_in(A, B)) | (~is_antisymmetric_in(A, B)) | (~is_connected_in(A, B)) | (~is_well_founded_in(A, B)) | (~is_reflexive_in(A, B))) <=> well_orders(A, B))))) | (~relation(A!0)) | ![B: $i] : (~(((~is_transitive_in(A!0, B)) | (~is_antisymmetric_in(A!0, B)) | (~is_connected_in(A!0, B)) | (~is_well_founded_in(A!0, B)) | (~is_reflexive_in(A!0, B))) <=> well_orders(A!0, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.38 tff(78,plain,
% 0.12/0.38 (![B: $i] : (~(((~is_transitive_in(A!0, B)) | (~is_antisymmetric_in(A!0, B)) | (~is_connected_in(A!0, B)) | (~is_well_founded_in(A!0, B)) | (~is_reflexive_in(A!0, B))) <=> well_orders(A!0, B)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[77, 74, 9])).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 ((~![B: $i] : (~(((~is_transitive_in(A!0, B)) | (~is_antisymmetric_in(A!0, B)) | (~is_connected_in(A!0, B)) | (~is_well_founded_in(A!0, B)) | (~is_reflexive_in(A!0, B))) <=> well_orders(A!0, B)))) | (~(((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) <=> well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(80,plain,
% 0.12/0.38 (~(((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) <=> well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.12/0.38 tff(81,plain,
% 0.12/0.38 ((((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) <=> well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))))) | (~well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(82,plain,
% 0.12/0.38 ((~((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))))) | (~well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.12/0.38 tff(83,plain,
% 0.12/0.38 (~((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[82, 58])).
% 0.12/0.38 tff(84,plain,
% 0.12/0.38 (((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) | is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(85,plain,
% 0.12/0.38 (is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.12/0.38 tff(86,plain,
% 0.12/0.38 (is_connected_in(A!0, relation_field(A!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[85, 51])).
% 0.12/0.38 tff(87,plain,
% 0.12/0.38 (^[A: $i] : refl(((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(88,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[87])).
% 0.12/0.38 tff(89,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(90,plain,
% 0.12/0.38 (^[A: $i] : rewrite((relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(91,plain,
% 0.12/0.38 (![A: $i] : (relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[90])).
% 0.12/0.38 tff(92,axiom,(![A: $i] : (relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d14_relat_2')).
% 0.12/0.38 tff(93,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.12/0.38 tff(94,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.12/0.38 tff(95,plain,(
% 0.12/0.38 ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[94])).
% 0.12/0.38 tff(96,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.12/0.38 tff(97,plain,
% 0.12/0.38 (((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | ((~relation(A!0)) | (connected(A!0) <=> is_connected_in(A!0, relation_field(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | (~relation(A!0)) | (connected(A!0) <=> is_connected_in(A!0, relation_field(A!0))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(98,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | ((~relation(A!0)) | (connected(A!0) <=> is_connected_in(A!0, relation_field(A!0))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(99,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | (~relation(A!0)) | (connected(A!0) <=> is_connected_in(A!0, relation_field(A!0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.12/0.38 tff(100,plain,
% 0.12/0.38 (connected(A!0) <=> is_connected_in(A!0, relation_field(A!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[99, 96, 9])).
% 0.12/0.38 tff(101,plain,
% 0.12/0.38 ((~(connected(A!0) <=> is_connected_in(A!0, relation_field(A!0)))) | connected(A!0) | (~is_connected_in(A!0, relation_field(A!0)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(102,plain,
% 0.12/0.38 (connected(A!0) | (~is_connected_in(A!0, relation_field(A!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.12/0.38 tff(103,plain,
% 0.12/0.38 (connected(A!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[102, 86])).
% 0.12/0.38 tff(104,plain,
% 0.12/0.38 (is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))) <=> is_antisymmetric_in(A!0, relation_field(A!0))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.38 tff(105,plain,
% 0.12/0.38 (((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) | is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(106,plain,
% 0.12/0.38 (is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[105, 83])).
% 0.12/0.38 tff(107,plain,
% 0.12/0.38 (is_antisymmetric_in(A!0, relation_field(A!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[106, 104])).
% 0.12/0.38 tff(108,plain,
% 0.12/0.38 (^[A: $i] : refl(((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(109,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[108])).
% 0.12/0.38 tff(110,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(111,plain,
% 0.12/0.38 (^[A: $i] : rewrite((relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(112,plain,
% 0.12/0.38 (![A: $i] : (relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[111])).
% 0.12/0.39 tff(113,axiom,(![A: $i] : (relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_relat_2')).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.12/0.39 tff(115,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.12/0.39 tff(116,plain,(
% 0.12/0.39 ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[115])).
% 0.12/0.39 tff(117,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.12/0.39 tff(118,plain,
% 0.12/0.39 (((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | ((~relation(A!0)) | (antisymmetric(A!0) <=> is_antisymmetric_in(A!0, relation_field(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | (~relation(A!0)) | (antisymmetric(A!0) <=> is_antisymmetric_in(A!0, relation_field(A!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(119,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | ((~relation(A!0)) | (antisymmetric(A!0) <=> is_antisymmetric_in(A!0, relation_field(A!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(120,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | (~relation(A!0)) | (antisymmetric(A!0) <=> is_antisymmetric_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.12/0.39 tff(121,plain,
% 0.12/0.39 (antisymmetric(A!0) <=> is_antisymmetric_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[120, 117, 9])).
% 0.12/0.39 tff(122,plain,
% 0.12/0.39 ((~(antisymmetric(A!0) <=> is_antisymmetric_in(A!0, relation_field(A!0)))) | antisymmetric(A!0) | (~is_antisymmetric_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(123,plain,
% 0.12/0.39 (antisymmetric(A!0) | (~is_antisymmetric_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.12/0.39 tff(124,plain,
% 0.12/0.39 (antisymmetric(A!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[123, 107])).
% 0.12/0.39 tff(125,plain,
% 0.12/0.39 (((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) | is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(126,plain,
% 0.12/0.39 (is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[125, 83])).
% 0.12/0.39 tff(127,plain,
% 0.12/0.39 (is_transitive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[126, 25])).
% 0.12/0.39 tff(128,plain,
% 0.12/0.39 (^[A: $i] : refl(((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(129,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[128])).
% 0.12/0.39 tff(130,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(131,plain,
% 0.12/0.39 (^[A: $i] : rewrite((relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(132,plain,
% 0.12/0.39 (![A: $i] : (relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[131])).
% 0.12/0.39 tff(133,axiom,(![A: $i] : (relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d16_relat_2')).
% 0.12/0.39 tff(134,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.12/0.39 tff(135,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.12/0.39 tff(136,plain,(
% 0.12/0.39 ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[135])).
% 0.12/0.39 tff(137,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.12/0.39 tff(138,plain,
% 0.12/0.39 (((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | ((~relation(A!0)) | (transitive(A!0) <=> is_transitive_in(A!0, relation_field(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | (~relation(A!0)) | (transitive(A!0) <=> is_transitive_in(A!0, relation_field(A!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(139,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | ((~relation(A!0)) | (transitive(A!0) <=> is_transitive_in(A!0, relation_field(A!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(140,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | (~relation(A!0)) | (transitive(A!0) <=> is_transitive_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.12/0.39 tff(141,plain,
% 0.12/0.39 (transitive(A!0) <=> is_transitive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[140, 137, 9])).
% 0.12/0.39 tff(142,plain,
% 0.12/0.39 ((~(transitive(A!0) <=> is_transitive_in(A!0, relation_field(A!0)))) | transitive(A!0) | (~is_transitive_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(143,plain,
% 0.12/0.39 (transitive(A!0) | (~is_transitive_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.12/0.39 tff(144,plain,
% 0.12/0.39 (transitive(A!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[143, 127])).
% 0.12/0.39 tff(145,plain,
% 0.12/0.39 (is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))) <=> is_well_founded_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.39 tff(146,plain,
% 0.12/0.39 (((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) | is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(147,plain,
% 0.12/0.39 (is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[146, 83])).
% 0.12/0.39 tff(148,plain,
% 0.12/0.39 (is_well_founded_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[147, 145])).
% 0.12/0.39 tff(149,plain,
% 0.12/0.39 (^[A: $i] : refl(((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))) <=> ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(150,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[149])).
% 0.12/0.39 tff(151,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(152,plain,
% 0.12/0.39 (^[A: $i] : rewrite((relation(A) => (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))) <=> ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(153,plain,
% 0.12/0.39 (![A: $i] : (relation(A) => (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[152])).
% 0.12/0.39 tff(154,axiom,(![A: $i] : (relation(A) => (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_wellord1')).
% 0.12/0.39 tff(155,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.12/0.39 tff(156,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.12/0.39 tff(157,plain,(
% 0.12/0.39 ![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[156])).
% 0.12/0.39 tff(158,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.12/0.39 tff(159,plain,
% 0.12/0.39 (((~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))) | ((~relation(A!0)) | (well_founded_relation(A!0) <=> is_well_founded_in(A!0, relation_field(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))) | (~relation(A!0)) | (well_founded_relation(A!0) <=> is_well_founded_in(A!0, relation_field(A!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(160,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))) | ((~relation(A!0)) | (well_founded_relation(A!0) <=> is_well_founded_in(A!0, relation_field(A!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(161,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (well_founded_relation(A) <=> is_well_founded_in(A, relation_field(A))))) | (~relation(A!0)) | (well_founded_relation(A!0) <=> is_well_founded_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.12/0.39 tff(162,plain,
% 0.12/0.39 (well_founded_relation(A!0) <=> is_well_founded_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[161, 158, 9])).
% 0.12/0.39 tff(163,plain,
% 0.12/0.39 ((~(well_founded_relation(A!0) <=> is_well_founded_in(A!0, relation_field(A!0)))) | well_founded_relation(A!0) | (~is_well_founded_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(164,plain,
% 0.12/0.39 (well_founded_relation(A!0) | (~is_well_founded_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.12/0.39 tff(165,plain,
% 0.12/0.39 (well_founded_relation(A!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[164, 148])).
% 0.12/0.39 tff(166,plain,
% 0.12/0.39 (is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))) <=> is_reflexive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.39 tff(167,plain,
% 0.12/0.39 (((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) | is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(168,plain,
% 0.12/0.39 (is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[167, 83])).
% 0.12/0.39 tff(169,plain,
% 0.12/0.39 (is_reflexive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[168, 166])).
% 0.12/0.39 tff(170,plain,
% 0.12/0.39 (^[A: $i] : refl(((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(171,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[170])).
% 0.12/0.39 tff(172,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(173,plain,
% 0.12/0.39 (^[A: $i] : rewrite((relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(174,plain,
% 0.12/0.39 (![A: $i] : (relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[173])).
% 0.12/0.39 tff(175,axiom,(![A: $i] : (relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_relat_2')).
% 0.12/0.39 tff(176,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.12/0.39 tff(177,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.12/0.39 tff(178,plain,(
% 0.12/0.39 ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[177])).
% 0.12/0.39 tff(179,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.12/0.39 tff(180,plain,
% 0.12/0.39 (((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | ((~relation(A!0)) | (reflexive(A!0) <=> is_reflexive_in(A!0, relation_field(A!0))))) <=> ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | (~relation(A!0)) | (reflexive(A!0) <=> is_reflexive_in(A!0, relation_field(A!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(181,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | ((~relation(A!0)) | (reflexive(A!0) <=> is_reflexive_in(A!0, relation_field(A!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(182,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | (~relation(A!0)) | (reflexive(A!0) <=> is_reflexive_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.12/0.39 tff(183,plain,
% 0.12/0.39 (reflexive(A!0) <=> is_reflexive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[182, 179, 9])).
% 0.12/0.39 tff(184,plain,
% 0.12/0.39 ((~(reflexive(A!0) <=> is_reflexive_in(A!0, relation_field(A!0)))) | reflexive(A!0) | (~is_reflexive_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(185,plain,
% 0.12/0.39 (reflexive(A!0) | (~is_reflexive_in(A!0, relation_field(A!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.12/0.39 tff(186,plain,
% 0.12/0.39 (reflexive(A!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[185, 169])).
% 0.12/0.39 tff(187,plain,
% 0.12/0.39 ((~((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0)))) | (~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(188,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[187, 186, 165, 144, 124, 103, 50])).
% 0.12/0.39 tff(189,plain,(well_ordering(A!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(190,plain,
% 0.12/0.39 ((((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) <=> well_ordering(A!0)) | (~((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0)))) | (~well_ordering(A!0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(191,plain,
% 0.12/0.39 ((~((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0)))) | (~well_ordering(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[190, 47])).
% 0.12/0.39 tff(192,plain,
% 0.12/0.39 (~((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[191, 189])).
% 0.12/0.39 tff(193,plain,
% 0.12/0.39 (((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) | transitive(A!0)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(194,plain,
% 0.12/0.39 (transitive(A!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.12/0.39 tff(195,plain,
% 0.12/0.39 ((~(transitive(A!0) <=> is_transitive_in(A!0, relation_field(A!0)))) | (~transitive(A!0)) | is_transitive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(196,plain,
% 0.12/0.39 ((~transitive(A!0)) | is_transitive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[195, 141])).
% 0.12/0.39 tff(197,plain,
% 0.12/0.39 (is_transitive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[196, 194])).
% 0.12/0.39 tff(198,plain,
% 0.12/0.39 (is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[197, 26])).
% 0.12/0.39 tff(199,plain,
% 0.12/0.39 (is_reflexive_in(A!0, relation_field(A!0)) <=> is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(symmetry,[status(thm)],[166])).
% 0.12/0.39 tff(200,plain,
% 0.12/0.39 (((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) | reflexive(A!0)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(201,plain,
% 0.12/0.39 (reflexive(A!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[200, 192])).
% 0.12/0.39 tff(202,plain,
% 0.12/0.39 ((~(reflexive(A!0) <=> is_reflexive_in(A!0, relation_field(A!0)))) | (~reflexive(A!0)) | is_reflexive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(203,plain,
% 0.12/0.39 ((~reflexive(A!0)) | is_reflexive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[202, 183])).
% 0.12/0.39 tff(204,plain,
% 0.12/0.39 (is_reflexive_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[203, 201])).
% 0.12/0.39 tff(205,plain,
% 0.12/0.39 (is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[204, 199])).
% 0.12/0.39 tff(206,plain,
% 0.12/0.39 (is_well_founded_in(A!0, relation_field(A!0)) <=> is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.39 inference(symmetry,[status(thm)],[145])).
% 0.12/0.39 tff(207,plain,
% 0.12/0.39 (((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) | well_founded_relation(A!0)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(208,plain,
% 0.12/0.39 (well_founded_relation(A!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[207, 192])).
% 0.12/0.39 tff(209,plain,
% 0.12/0.39 ((~(well_founded_relation(A!0) <=> is_well_founded_in(A!0, relation_field(A!0)))) | (~well_founded_relation(A!0)) | is_well_founded_in(A!0, relation_field(A!0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(210,plain,
% 0.12/0.39 ((~well_founded_relation(A!0)) | is_well_founded_in(A!0, relation_field(A!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[209, 162])).
% 0.12/0.40 tff(211,plain,
% 0.12/0.40 (is_well_founded_in(A!0, relation_field(A!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[210, 208])).
% 0.12/0.40 tff(212,plain,
% 0.12/0.40 (is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[211, 206])).
% 0.12/0.40 tff(213,plain,
% 0.12/0.40 (is_connected_in(A!0, relation_field(A!0)) <=> is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.40 inference(symmetry,[status(thm)],[51])).
% 0.12/0.40 tff(214,plain,
% 0.12/0.40 (((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) | connected(A!0)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(215,plain,
% 0.12/0.40 (connected(A!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[214, 192])).
% 0.12/0.40 tff(216,plain,
% 0.12/0.40 ((~(connected(A!0) <=> is_connected_in(A!0, relation_field(A!0)))) | (~connected(A!0)) | is_connected_in(A!0, relation_field(A!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(217,plain,
% 0.12/0.40 ((~connected(A!0)) | is_connected_in(A!0, relation_field(A!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[216, 100])).
% 0.12/0.40 tff(218,plain,
% 0.12/0.40 (is_connected_in(A!0, relation_field(A!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[217, 215])).
% 0.12/0.40 tff(219,plain,
% 0.12/0.40 (is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[218, 213])).
% 0.12/0.40 tff(220,plain,
% 0.12/0.40 (is_antisymmetric_in(A!0, relation_field(A!0)) <=> is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.40 inference(symmetry,[status(thm)],[104])).
% 0.12/0.40 tff(221,plain,
% 0.12/0.40 (((~well_founded_relation(A!0)) | (~reflexive(A!0)) | (~transitive(A!0)) | (~antisymmetric(A!0)) | (~connected(A!0))) | antisymmetric(A!0)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(222,plain,
% 0.12/0.40 (antisymmetric(A!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[221, 192])).
% 0.12/0.40 tff(223,plain,
% 0.12/0.40 ((~(antisymmetric(A!0) <=> is_antisymmetric_in(A!0, relation_field(A!0)))) | (~antisymmetric(A!0)) | is_antisymmetric_in(A!0, relation_field(A!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(224,plain,
% 0.12/0.40 ((~antisymmetric(A!0)) | is_antisymmetric_in(A!0, relation_field(A!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[223, 121])).
% 0.12/0.40 tff(225,plain,
% 0.12/0.40 (is_antisymmetric_in(A!0, relation_field(A!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[224, 222])).
% 0.12/0.40 tff(226,plain,
% 0.12/0.40 (is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[225, 220])).
% 0.12/0.40 tff(227,plain,
% 0.12/0.40 ((~well_orders(A!0, relation_field(A!0))) <=> (~well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.12/0.40 tff(228,plain,
% 0.12/0.40 ((well_orders(A!0, relation_field(A!0)) <=> well_ordering(A!0)) | (~well_orders(A!0, relation_field(A!0))) | (~well_ordering(A!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(229,plain,
% 0.12/0.40 ((~well_orders(A!0, relation_field(A!0))) | (~well_ordering(A!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[228, 54])).
% 0.12/0.40 tff(230,plain,
% 0.12/0.40 (~well_orders(A!0, relation_field(A!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[229, 189])).
% 0.12/0.40 tff(231,plain,
% 0.12/0.40 (~well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[230, 227])).
% 0.12/0.40 tff(232,plain,
% 0.12/0.40 ((((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) <=> well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | ((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) | well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(233,plain,
% 0.12/0.40 (((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))) | well_orders(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[232, 80])).
% 0.12/0.40 tff(234,plain,
% 0.12/0.40 ((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[233, 231])).
% 0.12/0.40 tff(235,plain,
% 0.12/0.40 ((~((~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))))) | (~is_transitive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_antisymmetric_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_connected_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_well_founded_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0)))) | (~is_reflexive_in(A!0, set_union2(relation_dom(A!0), relation_rng(A!0))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(236,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[235, 234, 226, 219, 212, 205, 198])).
% 0.12/0.40 % SZS output end Proof
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------