%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU261+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU261+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:30:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(well_founded_relation_type, type, (
% 0.12/0.38 well_founded_relation: $i > $o)).
% 0.12/0.38 tff(tptp_fun_B_2_type, type, (
% 0.12/0.38 tptp_fun_B_2: $i)).
% 0.12/0.38 tff(connected_type, type, (
% 0.12/0.38 connected: $i > $o)).
% 0.12/0.38 tff(transitive_type, type, (
% 0.12/0.38 transitive: $i > $o)).
% 0.12/0.38 tff(antisymmetric_type, type, (
% 0.12/0.38 antisymmetric: $i > $o)).
% 0.12/0.38 tff(reflexive_type, type, (
% 0.12/0.38 reflexive: $i > $o)).
% 0.12/0.38 tff(well_ordering_type, type, (
% 0.12/0.38 well_ordering: $i > $o)).
% 0.12/0.38 tff(relation_type, type, (
% 0.12/0.38 relation: $i > $o)).
% 0.12/0.38 tff(relation_isomorphism_type, type, (
% 0.12/0.38 relation_isomorphism: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_C_3_type, type, (
% 0.12/0.38 tptp_fun_C_3: $i)).
% 0.12/0.38 tff(tptp_fun_A_1_type, type, (
% 0.12/0.38 tptp_fun_A_1: $i)).
% 0.12/0.38 tff(function_type, type, (
% 0.12/0.38 function: $i > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((relation(A!1) & (relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))))) <=> (relation(A!1) & relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))) <=> (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((~![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => ((well_ordering(A) & relation_isomorphism(A, B, C)) => well_ordering(B)))))) <=> (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(~![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => ((well_ordering(A) & relation_isomorphism(A, B, C)) => well_ordering(B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t54_wellord1')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (relation(A!1) & relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (relation(B!2)),
% 0.12/0.38 inference(and_elim,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[A: $i] : refl(((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))) <=> ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))) <=> ![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.38 tff(13,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)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(14,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)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.38 tff(15,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(16,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(17,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)],[16])).
% 0.20/0.38 tff(18,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(19,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)],[18, 17])).
% 0.20/0.38 tff(20,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)],[19, 15])).
% 0.20/0.38 tff(21,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)],[20])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!2)) | (~(((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!2)) | (~(((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (((~relation(B!2)) | (~(((~reflexive(B!2)) | (~transitive(B!2)) | (~antisymmetric(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2)))) <=> ((~relation(B!2)) | (~(((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!2)) | (~(((~reflexive(B!2)) | (~transitive(B!2)) | (~antisymmetric(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!2)) | (~(((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!2)) | (~(((~reflexive(B!2)) | (~transitive(B!2)) | (~antisymmetric(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!2)) | (~(((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!2)) | (~(((~reflexive(B!2)) | (~transitive(B!2)) | (~antisymmetric(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!2)) | (~(((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (~(((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 23, 10])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))),
% 0.20/0.38 inference(and_elim,[status(thm)],[9])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (~well_ordering(B!2)),
% 0.20/0.38 inference(or_elim,[status(thm)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 ((((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2)) | ((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) | well_ordering(B!2)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 ((((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))) <=> well_ordering(B!2)) | ((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 ((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[34, 30])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (relation(A!1)),
% 0.20/0.38 inference(and_elim,[status(thm)],[9])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))))), rewrite((connected(A) => connected(B)) <=> (connected(B) | (~connected(A)))), ((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A)))) & (connected(B) | (~connected(A)))))), rewrite((((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A)))) & (connected(B) | (~connected(A)))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))))), ((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A)))))), rewrite((antisymmetric(A) => antisymmetric(B)) <=> (antisymmetric(B) | (~antisymmetric(A)))), (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A)))) & (antisymmetric(B) | (~antisymmetric(A)))))), rewrite((((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A)))) & (antisymmetric(B) | (~antisymmetric(A)))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))))), (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A)))))), rewrite((well_founded_relation(A) => well_founded_relation(B)) <=> (well_founded_relation(B) | (~well_founded_relation(A)))), ((((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A)))) & (well_founded_relation(B) | (~well_founded_relation(A)))))), rewrite((((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A)))) & (well_founded_relation(B) | (~well_founded_relation(A)))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A))))), ((((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))))), ((relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))) <=> (relation_isomorphism(A, B, C) => ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A))))))), rewrite((relation_isomorphism(A, B, C) => ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A))))) <=> ((~relation_isomorphism(A, B, C)) | ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))))), ((relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))) <=> ((~relation_isomorphism(A, B, C)) | ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A))))))), (((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))) <=> ((relation(C) & function(C)) => ((~relation_isomorphism(A, B, C)) | ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))))))), rewrite(((relation(C) & function(C)) => ((~relation_isomorphism(A, B, C)) | ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))), (![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))) <=> ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))), ((relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))))) <=> (relation(B) => ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))), rewrite((relation(B) => ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))) <=> ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))), ((relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))))) <=> ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))))), (![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))))) <=> ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))), ((relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))))), rewrite((relation(A) => ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))), ((relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.39 tff(47,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t53_wellord1')).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.39 tff(50,plain,(
% 0.20/0.39 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[49])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))) | (~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1)))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1)))))) | (~function(C))))) <=> ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1)))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1)))))) | (~function(C)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1))))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1)))))) | (~function(C)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))) | (~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1)))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[55, 53])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1)))))) | (~function(C)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))) | (~(reflexive(B) | (~reflexive(A)))))) | (~function(C)))))) | (~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[58, 52, 36])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1))))))))) | ((~relation(B!2)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))))))) <=> ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1))))))))) | (~relation(B!2)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1))))))))) | ((~relation(B!2)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))) | (~(reflexive(B) | (~reflexive(A!1))))))))) | (~relation(B!2)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[62, 10, 59])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3)),
% 0.20/0.40 inference(or_elim,[status(thm)],[31])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (relation_isomorphism(A!1, B!2, C!3)),
% 0.20/0.40 inference(and_elim,[status(thm)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (relation(C!3) & function(C!3)),
% 0.20/0.40 inference(or_elim,[status(thm)],[31])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (function(C!3)),
% 0.20/0.40 inference(and_elim,[status(thm)],[66])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (relation(C!3)),
% 0.20/0.40 inference(and_elim,[status(thm)],[66])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) | ((~relation(C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) | (~relation(C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))))) <=> ((~relation(C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))) <=> (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))))) <=> ((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))))) <=> ((~relation(C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) | ((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) | ((~relation(C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) | ((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) | (~relation(C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[74, 69])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) | ((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))))) | (~relation(C!3)) | (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (~((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[77, 68, 67, 65, 63])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))) | (well_founded_relation(B!2) | (~well_founded_relation(A!1)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (well_founded_relation(B!2) | (~well_founded_relation(A!1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!1)) | (~(((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!1)) | (~(((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (((~relation(A!1)) | (~(((~reflexive(A!1)) | (~transitive(A!1)) | (~antisymmetric(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1)))) <=> ((~relation(A!1)) | (~(((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!1)) | (~(((~reflexive(A!1)) | (~transitive(A!1)) | (~antisymmetric(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!1)) | (~(((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!1)) | (~(((~reflexive(A!1)) | (~transitive(A!1)) | (~antisymmetric(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!1)) | (~(((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!1)) | (~(((~reflexive(A!1)) | (~transitive(A!1)) | (~antisymmetric(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!1)) | (~(((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (~(((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[86, 23, 36])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (well_ordering(A!1)),
% 0.20/0.40 inference(and_elim,[status(thm)],[64])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 ((((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1)) | (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1)))) | (~well_ordering(A!1))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 ((((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) <=> well_ordering(A!1)) | (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | well_founded_relation(A!1)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (well_founded_relation(A!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 ((~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | well_founded_relation(B!2) | (~well_founded_relation(A!1))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 ((~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | well_founded_relation(B!2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 (well_founded_relation(B!2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[95, 80])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))) | (connected(B!2) | (~connected(A!1)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (connected(B!2) | (~connected(A!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 78])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | connected(A!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (connected(A!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[99, 91])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~(connected(B!2) | (~connected(A!1)))) | connected(B!2) | (~connected(A!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 ((~(connected(B!2) | (~connected(A!1)))) | connected(B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (connected(B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[102, 98])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))) | (transitive(B!2) | (~transitive(A!1)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (transitive(B!2) | (~transitive(A!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[104, 78])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | transitive(A!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (transitive(A!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[106, 91])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 ((~(transitive(B!2) | (~transitive(A!1)))) | transitive(B!2) | (~transitive(A!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 ((~(transitive(B!2) | (~transitive(A!1)))) | transitive(B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (transitive(B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))) | (antisymmetric(B!2) | (~antisymmetric(A!1)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (antisymmetric(B!2) | (~antisymmetric(A!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[111, 78])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | antisymmetric(A!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (antisymmetric(A!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[113, 91])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | antisymmetric(B!2) | (~antisymmetric(A!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 ((~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | antisymmetric(B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (antisymmetric(B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 112])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (((~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | (~(reflexive(B!2) | (~reflexive(A!1))))) | (reflexive(B!2) | (~reflexive(A!1)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (reflexive(B!2) | (~reflexive(A!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[118, 78])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | reflexive(A!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (reflexive(A!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[120, 91])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ((~(reflexive(B!2) | (~reflexive(A!1)))) | reflexive(B!2) | (~reflexive(A!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ((~(reflexive(B!2) | (~reflexive(A!1)))) | reflexive(B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (reflexive(B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[123, 119])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 ((~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))) | (~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[125, 124, 117, 110, 103, 96, 35])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------