%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU257+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:27:25 AM UTC 2025
% Result : Theorem 0.39s 0.54s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU257+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:29:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.39/0.54 % SZS status Theorem
% 0.39/0.54 % SZS output start Proof
% 0.39/0.54 tff(well_founded_relation_type, type, (
% 0.39/0.54 well_founded_relation: $i > $o)).
% 0.39/0.54 tff(relation_restriction_type, type, (
% 0.39/0.54 relation_restriction: ( $i * $i ) > $i)).
% 0.39/0.54 tff(tptp_fun_A_107_type, type, (
% 0.39/0.54 tptp_fun_A_107: $i)).
% 0.39/0.54 tff(tptp_fun_B_106_type, type, (
% 0.39/0.54 tptp_fun_B_106: $i)).
% 0.39/0.54 tff(antisymmetric_type, type, (
% 0.39/0.54 antisymmetric: $i > $o)).
% 0.39/0.54 tff(transitive_type, type, (
% 0.39/0.54 transitive: $i > $o)).
% 0.39/0.54 tff(connected_type, type, (
% 0.39/0.54 connected: $i > $o)).
% 0.39/0.54 tff(reflexive_type, type, (
% 0.39/0.54 reflexive: $i > $o)).
% 0.39/0.54 tff(well_ordering_type, type, (
% 0.39/0.54 well_ordering: $i > $o)).
% 0.39/0.54 tff(relation_type, type, (
% 0.39/0.54 relation: $i > $o)).
% 0.39/0.54 tff(1,plain,
% 0.39/0.54 ((~(well_ordering(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_ordering(B!106)))) <=> (~(well_ordering(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_ordering(B!106))))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(2,plain,
% 0.39/0.54 ((~![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))))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(3,plain,
% 0.39/0.54 ((~![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))))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(4,axiom,(~![A: $i, B: $i] : (relation(B) => (well_ordering(B) => well_ordering(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t32_wellord1')).
% 0.39/0.54 tff(5,plain,
% 0.39/0.54 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.39/0.54 tff(6,plain,
% 0.39/0.54 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.39/0.54 tff(7,plain,
% 0.39/0.54 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.39/0.54 tff(8,plain,
% 0.39/0.54 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.39/0.54 tff(9,plain,(
% 0.39/0.54 ~(well_ordering(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_ordering(B!106)))),
% 0.39/0.54 inference(skolemize,[status(sab)],[8])).
% 0.39/0.54 tff(10,plain,
% 0.39/0.54 (~(well_ordering(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_ordering(B!106)))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.39/0.54 tff(11,plain,
% 0.39/0.54 (relation(B!106)),
% 0.39/0.54 inference(or_elim,[status(thm)],[10])).
% 0.39/0.54 tff(12,plain,
% 0.39/0.54 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.39/0.54 inference(bind,[status(th)],[])).
% 0.39/0.54 tff(13,plain,
% 0.39/0.54 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.39/0.54 inference(quant_intro,[status(thm)],[12])).
% 0.39/0.54 tff(14,plain,
% 0.39/0.54 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(15,plain,
% 0.39/0.54 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.39/0.54 inference(bind,[status(th)],[])).
% 0.39/0.54 tff(16,plain,
% 0.39/0.54 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.39/0.54 inference(quant_intro,[status(thm)],[15])).
% 0.39/0.54 tff(17,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.39/0.54 tff(18,plain,
% 0.39/0.54 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.39/0.54 tff(19,plain,
% 0.39/0.54 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.39/0.54 tff(20,plain,(
% 0.39/0.54 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.39/0.54 inference(skolemize,[status(sab)],[19])).
% 0.39/0.54 tff(21,plain,
% 0.39/0.54 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.39/0.54 tff(22,plain,
% 0.39/0.54 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!106)) | relation(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!106)) | relation(relation_restriction(B!106, A!107)))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(23,plain,
% 0.39/0.54 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!106)) | relation(relation_restriction(B!106, A!107)))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(24,plain,
% 0.39/0.54 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!106)) | relation(relation_restriction(B!106, A!107))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.39/0.54 tff(25,plain,
% 0.39/0.54 (relation(relation_restriction(B!106, A!107))),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.39/0.54 tff(26,plain,
% 0.39/0.54 (^[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)))))),
% 0.39/0.54 inference(bind,[status(th)],[])).
% 0.39/0.54 tff(27,plain,
% 0.39/0.54 (![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))))),
% 0.39/0.54 inference(quant_intro,[status(thm)],[26])).
% 0.39/0.54 tff(28,plain,
% 0.39/0.54 (^[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)))))),
% 0.39/0.54 inference(bind,[status(th)],[])).
% 0.39/0.54 tff(29,plain,
% 0.39/0.54 (![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))))),
% 0.39/0.54 inference(quant_intro,[status(thm)],[28])).
% 0.39/0.54 tff(30,plain,
% 0.39/0.54 (![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))))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(31,plain,
% 0.39/0.54 (^[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))))))),
% 0.39/0.54 inference(bind,[status(th)],[])).
% 0.39/0.54 tff(32,plain,
% 0.39/0.54 (![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))))),
% 0.39/0.54 inference(quant_intro,[status(thm)],[31])).
% 0.39/0.54 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/sandbox/benchmark/theBenchmark.p','d4_wellord1')).
% 0.39/0.54 tff(34,plain,
% 0.39/0.54 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.39/0.54 tff(35,plain,
% 0.39/0.54 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.39/0.54 tff(36,plain,(
% 0.39/0.54 ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.39/0.54 inference(skolemize,[status(sab)],[35])).
% 0.39/0.54 tff(37,plain,
% 0.39/0.54 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.39/0.54 tff(38,plain,
% 0.39/0.54 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.39/0.54 tff(39,plain,
% 0.39/0.54 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(relation_restriction(B!106, A!107))) | (~(((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) <=> well_ordering(relation_restriction(B!106, A!107)))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(relation_restriction(B!106, A!107))) | (~(((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) <=> well_ordering(relation_restriction(B!106, A!107)))))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(40,plain,
% 0.39/0.54 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(relation_restriction(B!106, A!107))) | (~(((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) <=> well_ordering(relation_restriction(B!106, A!107)))))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(41,plain,
% 0.39/0.54 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(relation_restriction(B!106, A!107))) | (~(((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) <=> well_ordering(relation_restriction(B!106, A!107))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.39/0.55 tff(42,plain,
% 0.39/0.55 ((~relation(relation_restriction(B!106, A!107))) | (~(((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) <=> well_ordering(relation_restriction(B!106, A!107))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.39/0.55 tff(43,plain,
% 0.39/0.55 (~(((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) <=> well_ordering(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[42, 25])).
% 0.39/0.55 tff(44,plain,
% 0.39/0.55 (~well_ordering(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(or_elim,[status(thm)],[10])).
% 0.39/0.55 tff(45,plain,
% 0.39/0.55 ((((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) <=> well_ordering(relation_restriction(B!106, A!107))) | ((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) | well_ordering(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(46,plain,
% 0.39/0.55 ((((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))) <=> well_ordering(relation_restriction(B!106, A!107))) | ((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.39/0.55 tff(47,plain,
% 0.39/0.55 ((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.39/0.55 tff(48,plain,
% 0.39/0.55 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!106)) | (~(((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!106)) | (~(((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(49,plain,
% 0.39/0.55 (((~relation(B!106)) | (~(((~reflexive(B!106)) | (~connected(B!106)) | (~transitive(B!106)) | (~antisymmetric(B!106)) | (~well_founded_relation(B!106))) <=> well_ordering(B!106)))) <=> ((~relation(B!106)) | (~(((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(50,plain,
% 0.39/0.55 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!106)) | (~(((~reflexive(B!106)) | (~connected(B!106)) | (~transitive(B!106)) | (~antisymmetric(B!106)) | (~well_founded_relation(B!106))) <=> well_ordering(B!106))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!106)) | (~(((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106)))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[49])).
% 0.39/0.55 tff(51,plain,
% 0.39/0.55 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!106)) | (~(((~reflexive(B!106)) | (~connected(B!106)) | (~transitive(B!106)) | (~antisymmetric(B!106)) | (~well_founded_relation(B!106))) <=> well_ordering(B!106))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!106)) | (~(((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106))))),
% 0.39/0.55 inference(transitivity,[status(thm)],[50, 48])).
% 0.39/0.55 tff(52,plain,
% 0.39/0.55 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!106)) | (~(((~reflexive(B!106)) | (~connected(B!106)) | (~transitive(B!106)) | (~antisymmetric(B!106)) | (~well_founded_relation(B!106))) <=> well_ordering(B!106))))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(53,plain,
% 0.39/0.55 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!106)) | (~(((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.39/0.55 tff(54,plain,
% 0.39/0.55 (~(((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[53, 38, 11])).
% 0.39/0.55 tff(55,plain,
% 0.39/0.55 (well_ordering(B!106)),
% 0.39/0.55 inference(or_elim,[status(thm)],[10])).
% 0.39/0.55 tff(56,plain,
% 0.39/0.55 ((((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106)) | (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106)))) | (~well_ordering(B!106))),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(57,plain,
% 0.39/0.55 ((((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) <=> well_ordering(B!106)) | (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.39/0.55 tff(58,plain,
% 0.39/0.55 (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.39/0.55 tff(59,plain,
% 0.39/0.55 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | well_founded_relation(B!106)),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(60,plain,
% 0.39/0.55 (well_founded_relation(B!106)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.39/0.55 tff(61,plain,
% 0.39/0.55 (^[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))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(62,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[61])).
% 0.39/0.55 tff(63,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(64,plain,
% 0.39/0.55 (^[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)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(65,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[64])).
% 0.39/0.55 tff(66,axiom,(![A: $i, B: $i] : (relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t31_wellord1')).
% 0.39/0.55 tff(67,plain,
% 0.39/0.55 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.39/0.55 tff(68,plain,
% 0.39/0.55 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.39/0.55 tff(69,plain,(
% 0.39/0.55 ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.39/0.55 inference(skolemize,[status(sab)],[68])).
% 0.39/0.55 tff(70,plain,
% 0.39/0.55 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.39/0.55 tff(71,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | ((~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(72,plain,
% 0.39/0.55 ((well_founded_relation(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_founded_relation(B!106))) <=> ((~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(73,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_founded_relation(B!106)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | ((~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[72])).
% 0.39/0.55 tff(74,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_founded_relation(B!106)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(transitivity,[status(thm)],[73, 71])).
% 0.39/0.55 tff(75,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_founded_relation(B!106)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(76,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.39/0.55 tff(77,plain,
% 0.39/0.55 ((~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[76, 70, 11])).
% 0.39/0.55 tff(78,plain,
% 0.39/0.55 (well_founded_relation(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[77, 60])).
% 0.39/0.55 tff(79,plain,
% 0.39/0.55 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | antisymmetric(B!106)),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(80,plain,
% 0.39/0.55 (antisymmetric(B!106)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[79, 58])).
% 0.39/0.55 tff(81,plain,
% 0.39/0.55 (^[A: $i, B: $i] : refl((antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))) <=> (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(82,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[81])).
% 0.39/0.55 tff(83,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(84,plain,
% 0.39/0.55 (^[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)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(85,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[84])).
% 0.39/0.55 tff(86,axiom,(![A: $i, B: $i] : (relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_wellord1')).
% 0.39/0.55 tff(87,plain,
% 0.39/0.55 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.39/0.55 tff(88,plain,
% 0.39/0.55 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.39/0.55 tff(89,plain,(
% 0.39/0.55 ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.39/0.55 inference(skolemize,[status(sab)],[88])).
% 0.39/0.55 tff(90,plain,
% 0.39/0.55 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.39/0.55 tff(91,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | ((~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(92,plain,
% 0.39/0.55 ((antisymmetric(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~antisymmetric(B!106))) <=> ((~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(93,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~antisymmetric(B!106)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | ((~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[92])).
% 0.39/0.55 tff(94,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~antisymmetric(B!106)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(transitivity,[status(thm)],[93, 91])).
% 0.39/0.55 tff(95,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~antisymmetric(B!106)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(96,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.39/0.55 tff(97,plain,
% 0.39/0.55 ((~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[96, 90, 11])).
% 0.39/0.55 tff(98,plain,
% 0.39/0.55 (antisymmetric(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[97, 80])).
% 0.39/0.55 tff(99,plain,
% 0.39/0.55 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | transitive(B!106)),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(100,plain,
% 0.39/0.55 (transitive(B!106)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[99, 58])).
% 0.39/0.55 tff(101,plain,
% 0.39/0.55 (^[A: $i, B: $i] : refl((transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))) <=> (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(102,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[101])).
% 0.39/0.55 tff(103,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(104,plain,
% 0.39/0.55 (^[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)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(105,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[104])).
% 0.39/0.55 tff(106,axiom,(![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_wellord1')).
% 0.39/0.55 tff(107,plain,
% 0.39/0.55 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.39/0.55 tff(108,plain,
% 0.39/0.55 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.39/0.55 tff(109,plain,(
% 0.39/0.55 ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.39/0.55 inference(skolemize,[status(sab)],[108])).
% 0.39/0.55 tff(110,plain,
% 0.39/0.55 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.39/0.55 tff(111,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | ((~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(112,plain,
% 0.39/0.55 ((transitive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~transitive(B!106))) <=> ((~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(113,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~transitive(B!106)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | ((~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[112])).
% 0.39/0.55 tff(114,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~transitive(B!106)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(transitivity,[status(thm)],[113, 111])).
% 0.39/0.55 tff(115,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~transitive(B!106)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(116,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.39/0.55 tff(117,plain,
% 0.39/0.55 ((~transitive(B!106)) | transitive(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[116, 110, 11])).
% 0.39/0.55 tff(118,plain,
% 0.39/0.55 (transitive(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[117, 100])).
% 0.39/0.55 tff(119,plain,
% 0.39/0.55 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | connected(B!106)),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(120,plain,
% 0.39/0.55 (connected(B!106)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[119, 58])).
% 0.39/0.55 tff(121,plain,
% 0.39/0.55 (^[A: $i, B: $i] : refl((connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))) <=> (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(122,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[121])).
% 0.39/0.55 tff(123,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(124,plain,
% 0.39/0.55 (^[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)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(125,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[124])).
% 0.39/0.55 tff(126,axiom,(![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_wellord1')).
% 0.39/0.55 tff(127,plain,
% 0.39/0.55 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.39/0.55 tff(128,plain,
% 0.39/0.55 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.39/0.55 tff(129,plain,(
% 0.39/0.55 ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.39/0.55 inference(skolemize,[status(sab)],[128])).
% 0.39/0.55 tff(130,plain,
% 0.39/0.55 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.39/0.55 tff(131,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | ((~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(132,plain,
% 0.39/0.55 ((connected(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~connected(B!106))) <=> ((~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(133,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~connected(B!106)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | ((~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[132])).
% 0.39/0.55 tff(134,plain,
% 0.39/0.55 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~connected(B!106)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107)))),
% 0.39/0.55 inference(transitivity,[status(thm)],[133, 131])).
% 0.39/0.55 tff(135,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~connected(B!106)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(136,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.39/0.55 tff(137,plain,
% 0.39/0.55 ((~connected(B!106)) | connected(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[136, 130, 11])).
% 0.39/0.55 tff(138,plain,
% 0.39/0.55 (connected(relation_restriction(B!106, A!107))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[137, 120])).
% 0.39/0.55 tff(139,plain,
% 0.39/0.55 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | reflexive(B!106)),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(140,plain,
% 0.39/0.55 (reflexive(B!106)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[139, 58])).
% 0.39/0.55 tff(141,plain,
% 0.39/0.55 (^[A: $i, B: $i] : refl((reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))) <=> (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(142,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[141])).
% 0.39/0.55 tff(143,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(144,plain,
% 0.39/0.55 (^[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)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(145,plain,
% 0.39/0.55 (![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)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[144])).
% 0.39/0.55 tff(146,axiom,(![A: $i, B: $i] : (relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t22_wellord1')).
% 0.39/0.55 tff(147,plain,
% 0.39/0.55 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.39/0.57 tff(148,plain,
% 0.39/0.57 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.39/0.57 tff(149,plain,(
% 0.39/0.57 ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.39/0.57 inference(skolemize,[status(sab)],[148])).
% 0.39/0.57 tff(150,plain,
% 0.39/0.57 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.39/0.57 tff(151,plain,
% 0.39/0.57 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | ((~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107)))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(152,plain,
% 0.39/0.57 ((reflexive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~reflexive(B!106))) <=> ((~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107)))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(153,plain,
% 0.39/0.57 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~reflexive(B!106)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | ((~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107))))),
% 0.39/0.57 inference(monotonicity,[status(thm)],[152])).
% 0.39/0.57 tff(154,plain,
% 0.39/0.57 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~reflexive(B!106)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107)))),
% 0.39/0.57 inference(transitivity,[status(thm)],[153, 151])).
% 0.39/0.57 tff(155,plain,
% 0.39/0.57 ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~reflexive(B!106)))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(156,plain,
% 0.39/0.57 ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.39/0.57 tff(157,plain,
% 0.39/0.57 ((~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[156, 150, 11])).
% 0.39/0.57 tff(158,plain,
% 0.39/0.57 (reflexive(relation_restriction(B!106, A!107))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[157, 140])).
% 0.39/0.57 tff(159,plain,
% 0.39/0.57 ((~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))) | (~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.39/0.57 inference(tautology,[status(thm)],[])).
% 0.39/0.57 tff(160,plain,
% 0.39/0.57 ($false),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[159, 158, 138, 118, 98, 78, 47])).
% 0.39/0.57 % SZS output end Proof
% 0.39/0.57 % E exiting
%------------------------------------------------------------------------------