%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU261+2 : 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 6.86s 7.03s
% Output : Proof 6.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU261+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % 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 06:30:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 6.86/7.03 % SZS status Theorem
% 6.86/7.03 % SZS output start Proof
% 6.86/7.03 tff(antisymmetric_type, type, (
% 6.86/7.03 antisymmetric: $i > $o)).
% 6.86/7.03 tff(tptp_fun_B_116_type, type, (
% 6.86/7.03 tptp_fun_B_116: $i)).
% 6.86/7.03 tff(connected_type, type, (
% 6.86/7.03 connected: $i > $o)).
% 6.86/7.03 tff(transitive_type, type, (
% 6.86/7.03 transitive: $i > $o)).
% 6.86/7.03 tff(reflexive_type, type, (
% 6.86/7.03 reflexive: $i > $o)).
% 6.86/7.03 tff(well_founded_relation_type, type, (
% 6.86/7.03 well_founded_relation: $i > $o)).
% 6.86/7.03 tff(well_ordering_type, type, (
% 6.86/7.03 well_ordering: $i > $o)).
% 6.86/7.03 tff(relation_type, type, (
% 6.86/7.03 relation: $i > $o)).
% 6.86/7.03 tff(relation_isomorphism_type, type, (
% 6.86/7.03 relation_isomorphism: ( $i * $i * $i ) > $o)).
% 6.86/7.03 tff(tptp_fun_C_117_type, type, (
% 6.86/7.03 tptp_fun_C_117: $i)).
% 6.86/7.03 tff(tptp_fun_A_115_type, type, (
% 6.86/7.03 tptp_fun_A_115: $i)).
% 6.86/7.03 tff(function_type, type, (
% 6.86/7.03 function: $i > $o)).
% 6.86/7.03 tff(1,plain,
% 6.86/7.03 ((relation(A!115) & (relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))))) <=> (relation(A!115) & relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))))),
% 6.86/7.03 inference(rewrite,[status(thm)],[])).
% 6.86/7.03 tff(2,plain,
% 6.86/7.03 ((~![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)))))))),
% 6.86/7.03 inference(rewrite,[status(thm)],[])).
% 6.86/7.03 tff(3,plain,
% 6.86/7.03 ((~![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)))))))),
% 6.86/7.03 inference(rewrite,[status(thm)],[])).
% 6.86/7.03 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')).
% 6.86/7.03 tff(5,plain,
% 6.86/7.03 (~![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))))))),
% 6.86/7.03 inference(modus_ponens,[status(thm)],[4, 3])).
% 6.86/7.03 tff(6,plain,
% 6.86/7.03 (~![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))))))),
% 6.86/7.03 inference(modus_ponens,[status(thm)],[5, 2])).
% 6.86/7.03 tff(7,plain,
% 6.86/7.03 (~![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))))))),
% 6.86/7.03 inference(modus_ponens,[status(thm)],[6, 2])).
% 6.86/7.03 tff(8,plain,
% 6.86/7.03 (~![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))))))),
% 6.86/7.03 inference(modus_ponens,[status(thm)],[7, 2])).
% 6.86/7.03 tff(9,plain,
% 6.86/7.03 (relation(A!115) & relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117)))))),
% 6.86/7.03 inference(modus_ponens,[status(thm)],[8, 1])).
% 6.86/7.03 tff(10,plain,
% 6.86/7.03 (relation(B!116)),
% 6.86/7.03 inference(and_elim,[status(thm)],[9])).
% 6.86/7.03 tff(11,plain,
% 6.86/7.03 (^[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)))))),
% 6.86/7.03 inference(bind,[status(th)],[])).
% 6.86/7.03 tff(12,plain,
% 6.86/7.03 (![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))))),
% 6.86/7.03 inference(quant_intro,[status(thm)],[11])).
% 6.86/7.03 tff(13,plain,
% 6.86/7.03 (^[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)))))),
% 6.86/7.03 inference(bind,[status(th)],[])).
% 6.86/7.03 tff(14,plain,
% 6.86/7.03 (![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))))),
% 6.86/7.04 inference(quant_intro,[status(thm)],[13])).
% 6.86/7.04 tff(15,plain,
% 6.86/7.04 (![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))))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(16,plain,
% 6.86/7.04 (^[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))))))),
% 6.86/7.04 inference(bind,[status(th)],[])).
% 6.86/7.04 tff(17,plain,
% 6.86/7.04 (![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))))),
% 6.86/7.04 inference(quant_intro,[status(thm)],[16])).
% 6.86/7.04 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')).
% 6.86/7.04 tff(19,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[18, 17])).
% 6.86/7.04 tff(20,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[19, 15])).
% 6.86/7.04 tff(21,plain,(
% 6.86/7.04 ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 6.86/7.04 inference(skolemize,[status(sab)],[20])).
% 6.86/7.04 tff(22,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[21, 14])).
% 6.86/7.04 tff(23,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[22, 12])).
% 6.86/7.04 tff(24,plain,
% 6.86/7.04 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!116)) | (~(((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!116)) | (~(((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116))))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(25,plain,
% 6.86/7.04 (((~relation(B!116)) | (~(((~reflexive(B!116)) | (~connected(B!116)) | (~transitive(B!116)) | (~antisymmetric(B!116)) | (~well_founded_relation(B!116))) <=> well_ordering(B!116)))) <=> ((~relation(B!116)) | (~(((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116))))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(26,plain,
% 6.86/7.04 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!116)) | (~(((~reflexive(B!116)) | (~connected(B!116)) | (~transitive(B!116)) | (~antisymmetric(B!116)) | (~well_founded_relation(B!116))) <=> well_ordering(B!116))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!116)) | (~(((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116)))))),
% 6.86/7.04 inference(monotonicity,[status(thm)],[25])).
% 6.86/7.04 tff(27,plain,
% 6.86/7.04 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!116)) | (~(((~reflexive(B!116)) | (~connected(B!116)) | (~transitive(B!116)) | (~antisymmetric(B!116)) | (~well_founded_relation(B!116))) <=> well_ordering(B!116))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!116)) | (~(((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116))))),
% 6.86/7.04 inference(transitivity,[status(thm)],[26, 24])).
% 6.86/7.04 tff(28,plain,
% 6.86/7.04 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(B!116)) | (~(((~reflexive(B!116)) | (~connected(B!116)) | (~transitive(B!116)) | (~antisymmetric(B!116)) | (~well_founded_relation(B!116))) <=> well_ordering(B!116))))),
% 6.86/7.04 inference(quant_inst,[status(thm)],[])).
% 6.86/7.04 tff(29,plain,
% 6.86/7.04 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(B!116)) | (~(((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116)))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[28, 27])).
% 6.86/7.04 tff(30,plain,
% 6.86/7.04 (~(((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116))),
% 6.86/7.04 inference(unit_resolution,[status(thm)],[29, 23, 10])).
% 6.86/7.04 tff(31,plain,
% 6.86/7.04 (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))),
% 6.86/7.04 inference(and_elim,[status(thm)],[9])).
% 6.86/7.04 tff(32,plain,
% 6.86/7.04 (~well_ordering(B!116)),
% 6.86/7.04 inference(or_elim,[status(thm)],[31])).
% 6.86/7.04 tff(33,plain,
% 6.86/7.04 ((((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116)) | ((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) | well_ordering(B!116)),
% 6.86/7.04 inference(tautology,[status(thm)],[])).
% 6.86/7.04 tff(34,plain,
% 6.86/7.04 ((((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))) <=> well_ordering(B!116)) | ((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))),
% 6.86/7.04 inference(unit_resolution,[status(thm)],[33, 32])).
% 6.86/7.04 tff(35,plain,
% 6.86/7.04 ((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))),
% 6.86/7.04 inference(unit_resolution,[status(thm)],[34, 30])).
% 6.86/7.04 tff(36,plain,
% 6.86/7.04 (relation(A!115)),
% 6.86/7.04 inference(and_elim,[status(thm)],[9])).
% 6.86/7.04 tff(37,plain,
% 6.86/7.04 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))))),
% 6.86/7.04 inference(bind,[status(th)],[])).
% 6.86/7.04 tff(38,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 6.86/7.04 inference(quant_intro,[status(thm)],[37])).
% 6.86/7.04 tff(39,plain,
% 6.86/7.04 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))))),
% 6.86/7.04 inference(bind,[status(th)],[])).
% 6.86/7.04 tff(40,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 6.86/7.04 inference(quant_intro,[status(thm)],[39])).
% 6.86/7.04 tff(41,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 6.86/7.04 inference(transitivity,[status(thm)],[40, 38])).
% 6.86/7.04 tff(42,plain,
% 6.86/7.04 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))))),
% 6.86/7.04 inference(bind,[status(th)],[])).
% 6.86/7.04 tff(43,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 6.86/7.04 inference(quant_intro,[status(thm)],[42])).
% 6.86/7.04 tff(44,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(45,plain,
% 6.86/7.04 (^[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)))))) <=> ((~(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)))))), (((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)))))))), (![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] : ((~(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))))))), ((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] : ((~(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(B) => ![C: $i] : ((~(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)))))) <=> ((~relation(B)) | ![C: $i] : ((~(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))))))), ((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] : ((~(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))))))))), (![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] : ((~(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)))))))), ((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] : ((~(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(A) => ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))), ((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] : ((~(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)))))))))),
% 6.86/7.04 inference(bind,[status(th)],[])).
% 6.86/7.04 tff(46,plain,
% 6.86/7.04 (![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] : ((~(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)))))))),
% 6.86/7.04 inference(quant_intro,[status(thm)],[45])).
% 6.86/7.04 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')).
% 6.86/7.04 tff(48,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[47, 46])).
% 6.86/7.04 tff(49,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[48, 44])).
% 6.86/7.04 tff(50,plain,(
% 6.86/7.04 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))),
% 6.86/7.04 inference(skolemize,[status(sab)],[49])).
% 6.86/7.04 tff(51,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[50, 43])).
% 6.86/7.04 tff(52,plain,
% 6.86/7.04 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[51, 41])).
% 6.86/7.04 tff(53,plain,
% 6.86/7.04 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(54,plain,
% 6.86/7.04 (((~relation(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!115, B, C)) | (~function(C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) <=> ((~relation(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(55,plain,
% 6.86/7.04 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!115, B, C)) | (~function(C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))))),
% 6.86/7.04 inference(monotonicity,[status(thm)],[54])).
% 6.86/7.04 tff(56,plain,
% 6.86/7.04 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!115, B, C)) | (~function(C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))),
% 6.86/7.04 inference(transitivity,[status(thm)],[55, 53])).
% 6.86/7.04 tff(57,plain,
% 6.86/7.04 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!115, B, C)) | (~function(C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))),
% 6.86/7.04 inference(quant_inst,[status(thm)],[])).
% 6.86/7.04 tff(58,plain,
% 6.86/7.04 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[57, 56])).
% 6.86/7.04 tff(59,plain,
% 6.86/7.04 (![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))),
% 6.86/7.04 inference(unit_resolution,[status(thm)],[58, 52, 36])).
% 6.86/7.04 tff(60,plain,
% 6.86/7.04 (((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) | ((~relation(B!116)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))))) <=> ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) | (~relation(B!116)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(61,plain,
% 6.86/7.04 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) | ((~relation(B!116)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))))),
% 6.86/7.04 inference(quant_inst,[status(thm)],[])).
% 6.86/7.04 tff(62,plain,
% 6.86/7.04 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) | (~relation(B!116)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))),
% 6.86/7.04 inference(modus_ponens,[status(thm)],[61, 60])).
% 6.86/7.04 tff(63,plain,
% 6.86/7.04 (![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))),
% 6.86/7.04 inference(unit_resolution,[status(thm)],[62, 10, 59])).
% 6.86/7.04 tff(64,plain,
% 6.86/7.04 (well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117)),
% 6.86/7.04 inference(or_elim,[status(thm)],[31])).
% 6.86/7.04 tff(65,plain,
% 6.86/7.04 (relation_isomorphism(A!115, B!116, C!117)),
% 6.86/7.04 inference(and_elim,[status(thm)],[64])).
% 6.86/7.04 tff(66,plain,
% 6.86/7.04 (relation(C!117) & function(C!117)),
% 6.86/7.04 inference(or_elim,[status(thm)],[31])).
% 6.86/7.04 tff(67,plain,
% 6.86/7.04 (function(C!117)),
% 6.86/7.04 inference(and_elim,[status(thm)],[66])).
% 6.86/7.04 tff(68,plain,
% 6.86/7.04 (relation(C!117)),
% 6.86/7.04 inference(and_elim,[status(thm)],[66])).
% 6.86/7.04 tff(69,plain,
% 6.86/7.04 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | (~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(70,plain,
% 6.86/7.04 (((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))) <=> ((~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(71,plain,
% 6.86/7.04 ((~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) <=> (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))),
% 6.86/7.04 inference(rewrite,[status(thm)],[])).
% 6.86/7.04 tff(72,plain,
% 6.86/7.04 (((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))) <=> ((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))),
% 6.86/7.04 inference(monotonicity,[status(thm)],[71])).
% 6.86/7.04 tff(73,plain,
% 6.86/7.04 (((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))) <=> ((~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))),
% 6.86/7.04 inference(transitivity,[status(thm)],[72, 70])).
% 6.86/7.04 tff(74,plain,
% 6.86/7.04 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117))))),
% 6.86/7.04 inference(monotonicity,[status(thm)],[73])).
% 6.86/7.04 tff(75,plain,
% 6.86/7.04 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | (~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))),
% 6.86/7.05 inference(transitivity,[status(thm)],[74, 69])).
% 6.86/7.05 tff(76,plain,
% 6.86/7.05 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))),
% 6.86/7.05 inference(quant_inst,[status(thm)],[])).
% 6.86/7.05 tff(77,plain,
% 6.86/7.05 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | (~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117))),
% 6.86/7.05 inference(modus_ponens,[status(thm)],[76, 75])).
% 6.86/7.05 tff(78,plain,
% 6.86/7.05 (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[77, 68, 67, 65, 63])).
% 6.86/7.05 tff(79,plain,
% 6.86/7.05 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (reflexive(B!116) | (~reflexive(A!115)))),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(80,plain,
% 6.86/7.05 (reflexive(B!116) | (~reflexive(A!115))),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[79, 78])).
% 6.86/7.05 tff(81,plain,
% 6.86/7.05 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!115)) | (~(((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!115)) | (~(((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115))))),
% 6.86/7.05 inference(rewrite,[status(thm)],[])).
% 6.86/7.05 tff(82,plain,
% 6.86/7.05 (((~relation(A!115)) | (~(((~reflexive(A!115)) | (~connected(A!115)) | (~transitive(A!115)) | (~antisymmetric(A!115)) | (~well_founded_relation(A!115))) <=> well_ordering(A!115)))) <=> ((~relation(A!115)) | (~(((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115))))),
% 6.86/7.05 inference(rewrite,[status(thm)],[])).
% 6.86/7.05 tff(83,plain,
% 6.86/7.05 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!115)) | (~(((~reflexive(A!115)) | (~connected(A!115)) | (~transitive(A!115)) | (~antisymmetric(A!115)) | (~well_founded_relation(A!115))) <=> well_ordering(A!115))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!115)) | (~(((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115)))))),
% 6.86/7.05 inference(monotonicity,[status(thm)],[82])).
% 6.86/7.05 tff(84,plain,
% 6.86/7.05 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!115)) | (~(((~reflexive(A!115)) | (~connected(A!115)) | (~transitive(A!115)) | (~antisymmetric(A!115)) | (~well_founded_relation(A!115))) <=> well_ordering(A!115))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!115)) | (~(((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115))))),
% 6.86/7.05 inference(transitivity,[status(thm)],[83, 81])).
% 6.86/7.05 tff(85,plain,
% 6.86/7.05 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(A!115)) | (~(((~reflexive(A!115)) | (~connected(A!115)) | (~transitive(A!115)) | (~antisymmetric(A!115)) | (~well_founded_relation(A!115))) <=> well_ordering(A!115))))),
% 6.86/7.05 inference(quant_inst,[status(thm)],[])).
% 6.86/7.05 tff(86,plain,
% 6.86/7.05 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(A!115)) | (~(((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115)))),
% 6.86/7.05 inference(modus_ponens,[status(thm)],[85, 84])).
% 6.86/7.05 tff(87,plain,
% 6.86/7.05 (~(((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115))),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[86, 23, 36])).
% 6.86/7.05 tff(88,plain,
% 6.86/7.05 (well_ordering(A!115)),
% 6.86/7.05 inference(and_elim,[status(thm)],[64])).
% 6.86/7.05 tff(89,plain,
% 6.86/7.05 ((((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115)) | (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115)))) | (~well_ordering(A!115))),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(90,plain,
% 6.86/7.05 ((((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) <=> well_ordering(A!115)) | (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))))),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[89, 88])).
% 6.86/7.05 tff(91,plain,
% 6.86/7.05 (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115)))),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[90, 87])).
% 6.86/7.05 tff(92,plain,
% 6.86/7.05 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | reflexive(A!115)),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(93,plain,
% 6.86/7.05 (reflexive(A!115)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[92, 91])).
% 6.86/7.05 tff(94,plain,
% 6.86/7.05 ((~(reflexive(B!116) | (~reflexive(A!115)))) | reflexive(B!116) | (~reflexive(A!115))),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(95,plain,
% 6.86/7.05 ((~(reflexive(B!116) | (~reflexive(A!115)))) | reflexive(B!116)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[94, 93])).
% 6.86/7.05 tff(96,plain,
% 6.86/7.05 (reflexive(B!116)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[95, 80])).
% 6.86/7.05 tff(97,plain,
% 6.86/7.05 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (transitive(B!116) | (~transitive(A!115)))),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(98,plain,
% 6.86/7.05 (transitive(B!116) | (~transitive(A!115))),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[97, 78])).
% 6.86/7.05 tff(99,plain,
% 6.86/7.05 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | transitive(A!115)),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(100,plain,
% 6.86/7.05 (transitive(A!115)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[99, 91])).
% 6.86/7.05 tff(101,plain,
% 6.86/7.05 ((~(transitive(B!116) | (~transitive(A!115)))) | transitive(B!116) | (~transitive(A!115))),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(102,plain,
% 6.86/7.05 ((~(transitive(B!116) | (~transitive(A!115)))) | transitive(B!116)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[101, 100])).
% 6.86/7.05 tff(103,plain,
% 6.86/7.05 (transitive(B!116)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[102, 98])).
% 6.86/7.05 tff(104,plain,
% 6.86/7.05 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (antisymmetric(B!116) | (~antisymmetric(A!115)))),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(105,plain,
% 6.86/7.05 (antisymmetric(B!116) | (~antisymmetric(A!115))),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[104, 78])).
% 6.86/7.05 tff(106,plain,
% 6.86/7.05 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | antisymmetric(A!115)),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(107,plain,
% 6.86/7.05 (antisymmetric(A!115)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[106, 91])).
% 6.86/7.05 tff(108,plain,
% 6.86/7.05 ((~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | antisymmetric(B!116) | (~antisymmetric(A!115))),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(109,plain,
% 6.86/7.05 ((~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | antisymmetric(B!116)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[108, 107])).
% 6.86/7.05 tff(110,plain,
% 6.86/7.05 (antisymmetric(B!116)),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[109, 105])).
% 6.86/7.05 tff(111,plain,
% 6.86/7.05 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (connected(B!116) | (~connected(A!115)))),
% 6.86/7.05 inference(tautology,[status(thm)],[])).
% 6.86/7.05 tff(112,plain,
% 6.86/7.05 (connected(B!116) | (~connected(A!115))),
% 6.86/7.05 inference(unit_resolution,[status(thm)],[111, 78])).
% 6.86/7.05 tff(113,plain,
% 6.86/7.05 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | connected(A!115)),
% 6.86/7.07 inference(tautology,[status(thm)],[])).
% 6.86/7.07 tff(114,plain,
% 6.86/7.07 (connected(A!115)),
% 6.86/7.07 inference(unit_resolution,[status(thm)],[113, 91])).
% 6.86/7.07 tff(115,plain,
% 6.86/7.07 ((~(connected(B!116) | (~connected(A!115)))) | connected(B!116) | (~connected(A!115))),
% 6.86/7.07 inference(tautology,[status(thm)],[])).
% 6.86/7.07 tff(116,plain,
% 6.86/7.07 ((~(connected(B!116) | (~connected(A!115)))) | connected(B!116)),
% 6.86/7.07 inference(unit_resolution,[status(thm)],[115, 114])).
% 6.86/7.07 tff(117,plain,
% 6.86/7.07 (connected(B!116)),
% 6.86/7.07 inference(unit_resolution,[status(thm)],[116, 112])).
% 6.86/7.07 tff(118,plain,
% 6.86/7.07 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (well_founded_relation(B!116) | (~well_founded_relation(A!115)))),
% 6.86/7.07 inference(tautology,[status(thm)],[])).
% 6.86/7.07 tff(119,plain,
% 6.86/7.07 (well_founded_relation(B!116) | (~well_founded_relation(A!115))),
% 6.86/7.07 inference(unit_resolution,[status(thm)],[118, 78])).
% 6.86/7.07 tff(120,plain,
% 6.86/7.07 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | well_founded_relation(A!115)),
% 6.86/7.07 inference(tautology,[status(thm)],[])).
% 6.86/7.07 tff(121,plain,
% 6.86/7.07 (well_founded_relation(A!115)),
% 6.86/7.07 inference(unit_resolution,[status(thm)],[120, 91])).
% 6.86/7.07 tff(122,plain,
% 6.86/7.07 ((~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))) | well_founded_relation(B!116) | (~well_founded_relation(A!115))),
% 6.86/7.07 inference(tautology,[status(thm)],[])).
% 6.86/7.07 tff(123,plain,
% 6.86/7.07 ((~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))) | well_founded_relation(B!116)),
% 6.86/7.07 inference(unit_resolution,[status(thm)],[122, 121])).
% 6.86/7.07 tff(124,plain,
% 6.86/7.07 (well_founded_relation(B!116)),
% 6.86/7.07 inference(unit_resolution,[status(thm)],[123, 119])).
% 6.86/7.07 tff(125,plain,
% 6.86/7.07 ((~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))) | (~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))),
% 6.86/7.07 inference(tautology,[status(thm)],[])).
% 6.86/7.07 tff(126,plain,
% 6.86/7.07 ($false),
% 6.86/7.07 inference(unit_resolution,[status(thm)],[125, 124, 117, 110, 103, 96, 35])).
% 6.86/7.07 % SZS output end Proof
% 6.86/7.09 % E exiting
%------------------------------------------------------------------------------