%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU257+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:27:24 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU257+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:31:50 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(well_founded_relation_type, type, (
% 0.20/0.38 well_founded_relation: $i > $o)).
% 0.20/0.38 tff(relation_restriction_type, type, (
% 0.20/0.38 relation_restriction: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_A_1_type, type, (
% 0.20/0.38 tptp_fun_A_1: $i)).
% 0.20/0.38 tff(tptp_fun_B_0_type, type, (
% 0.20/0.38 tptp_fun_B_0: $i)).
% 0.20/0.38 tff(antisymmetric_type, type, (
% 0.20/0.38 antisymmetric: $i > $o)).
% 0.20/0.38 tff(transitive_type, type, (
% 0.20/0.38 transitive: $i > $o)).
% 0.20/0.38 tff(connected_type, type, (
% 0.20/0.38 connected: $i > $o)).
% 0.20/0.38 tff(reflexive_type, type, (
% 0.20/0.38 reflexive: $i > $o)).
% 0.20/0.38 tff(well_ordering_type, type, (
% 0.20/0.38 well_ordering: $i > $o)).
% 0.20/0.38 tff(relation_type, type, (
% 0.20/0.38 relation: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 ((~(well_ordering(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~well_ordering(B!0)))) <=> (~(well_ordering(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~well_ordering(B!0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))) <=> (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : (relation(B) => (well_ordering(B) => well_ordering(relation_restriction(B, A))))) <=> (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,axiom,(~![A: $i, B: $i] : (relation(B) => (well_ordering(B) => well_ordering(relation_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t32_wellord1')).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.38 tff(9,plain,(
% 0.20/0.38 ~(well_ordering(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~well_ordering(B!0)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[8])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~(well_ordering(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~well_ordering(B!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (relation(B!0)),
% 0.20/0.38 inference(or_elim,[status(thm)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,(
% 0.20/0.38 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!0)) | relation(relation_restriction(B!0, A!1)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!0)) | relation(relation_restriction(B!0, A!1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!0)) | relation(relation_restriction(B!0, A!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!0)) | relation(relation_restriction(B!0, A!1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (relation(relation_restriction(B!0, A!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (^[A: $i] : refl(((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))) <=> ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))) <=> ![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (^[A: $i] : rewrite(((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![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)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (^[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))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.38 tff(33,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')).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.38 tff(36,plain,(
% 0.20/0.38 ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[35])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(relation_restriction(B!0, A!1))) | (~(((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) <=> well_ordering(relation_restriction(B!0, A!1)))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(relation_restriction(B!0, A!1))) | (~(((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) <=> well_ordering(relation_restriction(B!0, A!1)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(relation_restriction(B!0, A!1))) | (~(((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) <=> well_ordering(relation_restriction(B!0, A!1)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(relation_restriction(B!0, A!1))) | (~(((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) <=> well_ordering(relation_restriction(B!0, A!1))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 ((~relation(relation_restriction(B!0, A!1))) | (~(((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) <=> well_ordering(relation_restriction(B!0, A!1))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (~(((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) <=> well_ordering(relation_restriction(B!0, A!1)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[42, 25])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (~well_ordering(relation_restriction(B!0, A!1))),
% 0.20/0.38 inference(or_elim,[status(thm)],[10])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 ((((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) <=> well_ordering(relation_restriction(B!0, A!1))) | ((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) | well_ordering(relation_restriction(B!0, A!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 ((((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))) <=> well_ordering(relation_restriction(B!0, A!1))) | ((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 ((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!0)) | (~(((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) <=> well_ordering(B!0))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!0)) | (~(((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) <=> well_ordering(B!0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!0)) | (~(((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) <=> well_ordering(B!0))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!0)) | (~(((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) <=> well_ordering(B!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (~(((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) <=> well_ordering(B!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[50, 38, 11])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (well_ordering(B!0)),
% 0.20/0.38 inference(or_elim,[status(thm)],[10])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 ((((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) <=> well_ordering(B!0)) | (~((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0)))) | (~well_ordering(B!0))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 ((((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) <=> well_ordering(B!0)) | (~((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (~((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) | well_founded_relation(B!0)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (well_founded_relation(B!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl((well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B))) <=> (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B))) <=> ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B))) <=> ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite((well_founded_relation(B) => well_founded_relation(relation_restriction(B, A))) <=> ((~well_founded_relation(B)) | well_founded_relation(relation_restriction(B, A)))), ((relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A)))) <=> (relation(B) => ((~well_founded_relation(B)) | well_founded_relation(relation_restriction(B, A)))))), rewrite((relation(B) => ((~well_founded_relation(B)) | well_founded_relation(relation_restriction(B, A)))) <=> (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))), ((relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A)))) <=> (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 (![A: $i, B: $i] : (relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.38 tff(63,axiom,(![A: $i, B: $i] : (relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t31_wellord1')).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.39 tff(66,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[65])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | ((~relation(B!0)) | (~well_founded_relation(B!0)) | well_founded_relation(relation_restriction(B!0, A!1)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!0)) | (~well_founded_relation(B!0)) | well_founded_relation(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ((well_founded_relation(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~well_founded_relation(B!0))) <=> ((~relation(B!0)) | (~well_founded_relation(B!0)) | well_founded_relation(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~well_founded_relation(B!0)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | ((~relation(B!0)) | (~well_founded_relation(B!0)) | well_founded_relation(relation_restriction(B!0, A!1))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~well_founded_relation(B!0)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!0)) | (~well_founded_relation(B!0)) | well_founded_relation(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~well_founded_relation(B!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!0)) | (~well_founded_relation(B!0)) | well_founded_relation(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 ((~well_founded_relation(B!0)) | well_founded_relation(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[73, 67, 11])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (well_founded_relation(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[74, 57])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) | antisymmetric(B!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (antisymmetric(B!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[76, 55])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))) <=> (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))) <=> ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))) <=> ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((antisymmetric(B) => antisymmetric(relation_restriction(B, A))) <=> (antisymmetric(relation_restriction(B, A)) | (~antisymmetric(B)))), ((relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A)))) <=> (relation(B) => (antisymmetric(relation_restriction(B, A)) | (~antisymmetric(B)))))), rewrite((relation(B) => (antisymmetric(relation_restriction(B, A)) | (~antisymmetric(B)))) <=> (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))), ((relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A)))) <=> (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (![A: $i, B: $i] : (relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.39 tff(83,axiom,(![A: $i, B: $i] : (relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t25_wellord1')).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.39 tff(86,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[85])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | ((~relation(B!0)) | (~antisymmetric(B!0)) | antisymmetric(relation_restriction(B!0, A!1)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!0)) | (~antisymmetric(B!0)) | antisymmetric(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 ((antisymmetric(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~antisymmetric(B!0))) <=> ((~relation(B!0)) | (~antisymmetric(B!0)) | antisymmetric(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~antisymmetric(B!0)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | ((~relation(B!0)) | (~antisymmetric(B!0)) | antisymmetric(relation_restriction(B!0, A!1))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~antisymmetric(B!0)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!0)) | (~antisymmetric(B!0)) | antisymmetric(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[90, 88])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~antisymmetric(B!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!0)) | (~antisymmetric(B!0)) | antisymmetric(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 ((~antisymmetric(B!0)) | antisymmetric(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[93, 87, 11])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (antisymmetric(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[94, 77])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) | transitive(B!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (transitive(B!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[96, 55])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))) <=> (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))) <=> ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))) <=> ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((transitive(B) => transitive(relation_restriction(B, A))) <=> ((~transitive(B)) | transitive(relation_restriction(B, A)))), ((relation(B) => (transitive(B) => transitive(relation_restriction(B, A)))) <=> (relation(B) => ((~transitive(B)) | transitive(relation_restriction(B, A)))))), rewrite((relation(B) => ((~transitive(B)) | transitive(relation_restriction(B, A)))) <=> (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))), ((relation(B) => (transitive(B) => transitive(relation_restriction(B, A)))) <=> (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.39 tff(103,axiom,(![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_wellord1')).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.39 tff(106,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[105])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | ((~relation(B!0)) | (~transitive(B!0)) | transitive(relation_restriction(B!0, A!1)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!0)) | (~transitive(B!0)) | transitive(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 ((transitive(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~transitive(B!0))) <=> ((~relation(B!0)) | (~transitive(B!0)) | transitive(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~transitive(B!0)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | ((~relation(B!0)) | (~transitive(B!0)) | transitive(relation_restriction(B!0, A!1))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~transitive(B!0)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!0)) | (~transitive(B!0)) | transitive(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~transitive(B!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!0)) | (~transitive(B!0)) | transitive(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 ((~transitive(B!0)) | transitive(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[113, 107, 11])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 (transitive(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[114, 97])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 (((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) | reflexive(B!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(117,plain,
% 0.20/0.39 (reflexive(B!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[116, 55])).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))) <=> (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))) <=> ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.39 tff(120,plain,
% 0.20/0.39 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))) <=> ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(121,plain,
% 0.20/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((reflexive(B) => reflexive(relation_restriction(B, A))) <=> ((~reflexive(B)) | reflexive(relation_restriction(B, A)))), ((relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A)))) <=> (relation(B) => ((~reflexive(B)) | reflexive(relation_restriction(B, A)))))), rewrite((relation(B) => ((~reflexive(B)) | reflexive(relation_restriction(B, A)))) <=> (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))), ((relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A)))) <=> (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(122,plain,
% 0.20/0.39 (![A: $i, B: $i] : (relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.39 tff(123,axiom,(![A: $i, B: $i] : (relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_wellord1')).
% 0.20/0.39 tff(124,plain,
% 0.20/0.39 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.20/0.39 tff(126,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[125])).
% 0.20/0.39 tff(127,plain,
% 0.20/0.39 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.20/0.39 tff(128,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | ((~relation(B!0)) | (~reflexive(B!0)) | reflexive(relation_restriction(B!0, A!1)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!0)) | (~reflexive(B!0)) | reflexive(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(129,plain,
% 0.20/0.39 ((reflexive(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~reflexive(B!0))) <=> ((~relation(B!0)) | (~reflexive(B!0)) | reflexive(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(130,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~reflexive(B!0)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | ((~relation(B!0)) | (~reflexive(B!0)) | reflexive(relation_restriction(B!0, A!1))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.39 tff(131,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~reflexive(B!0)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!0)) | (~reflexive(B!0)) | reflexive(relation_restriction(B!0, A!1)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[130, 128])).
% 0.20/0.39 tff(132,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~reflexive(B!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(133,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!0)) | (~reflexive(B!0)) | reflexive(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.39 tff(134,plain,
% 0.20/0.39 ((~reflexive(B!0)) | reflexive(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[133, 127, 11])).
% 0.20/0.39 tff(135,plain,
% 0.20/0.39 (reflexive(relation_restriction(B!0, A!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[134, 117])).
% 0.20/0.39 tff(136,plain,
% 0.20/0.39 (((~reflexive(B!0)) | (~connected(B!0)) | (~transitive(B!0)) | (~antisymmetric(B!0)) | (~well_founded_relation(B!0))) | connected(B!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(137,plain,
% 0.20/0.39 (connected(B!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[136, 55])).
% 0.20/0.39 tff(138,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))) <=> (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(139,plain,
% 0.20/0.39 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))) <=> ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.39 tff(140,plain,
% 0.20/0.39 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))) <=> ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(141,plain,
% 0.20/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((connected(B) => connected(relation_restriction(B, A))) <=> (connected(relation_restriction(B, A)) | (~connected(B)))), ((relation(B) => (connected(B) => connected(relation_restriction(B, A)))) <=> (relation(B) => (connected(relation_restriction(B, A)) | (~connected(B)))))), rewrite((relation(B) => (connected(relation_restriction(B, A)) | (~connected(B)))) <=> (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))), ((relation(B) => (connected(B) => connected(relation_restriction(B, A)))) <=> (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(142,plain,
% 0.20/0.39 (![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.39 tff(143,axiom,(![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_wellord1')).
% 0.20/0.39 tff(144,plain,
% 0.20/0.39 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.39 tff(145,plain,
% 0.20/0.39 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.20/0.39 tff(146,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[145])).
% 0.20/0.39 tff(147,plain,
% 0.20/0.39 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.20/0.39 tff(148,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | ((~relation(B!0)) | (~connected(B!0)) | connected(relation_restriction(B!0, A!1)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!0)) | (~connected(B!0)) | connected(relation_restriction(B!0, A!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(149,plain,
% 0.20/0.40 ((connected(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~connected(B!0))) <=> ((~relation(B!0)) | (~connected(B!0)) | connected(relation_restriction(B!0, A!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(150,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~connected(B!0)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | ((~relation(B!0)) | (~connected(B!0)) | connected(relation_restriction(B!0, A!1))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.40 tff(151,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~connected(B!0)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!0)) | (~connected(B!0)) | connected(relation_restriction(B!0, A!1)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[150, 148])).
% 0.20/0.40 tff(152,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!0, A!1)) | (~relation(B!0)) | (~connected(B!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(153,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!0)) | (~connected(B!0)) | connected(relation_restriction(B!0, A!1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.40 tff(154,plain,
% 0.20/0.40 ((~connected(B!0)) | connected(relation_restriction(B!0, A!1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[153, 147, 11])).
% 0.20/0.40 tff(155,plain,
% 0.20/0.40 (connected(relation_restriction(B!0, A!1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[154, 137])).
% 0.20/0.40 tff(156,plain,
% 0.20/0.40 ((~((~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1))))) | (~reflexive(relation_restriction(B!0, A!1))) | (~connected(relation_restriction(B!0, A!1))) | (~transitive(relation_restriction(B!0, A!1))) | (~antisymmetric(relation_restriction(B!0, A!1))) | (~well_founded_relation(relation_restriction(B!0, A!1)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(157,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[156, 155, 135, 115, 95, 75, 47])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------