%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PHI012+1 : TPTP v9.0.0. Released v7.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:22:45 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PHI012+1 : TPTP v9.0.0. Released v7.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:18:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(exemplifies_relation_type, type, (
% 0.12/0.38 exemplifies_relation: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.38 tptp_fun_Y_2: $i > $i)).
% 0.12/0.38 tff(tptp_fun_X_1_type, type, (
% 0.12/0.38 tptp_fun_X_1: $i)).
% 0.12/0.38 tff(greater_than_type, type, (
% 0.12/0.38 greater_than: $i)).
% 0.12/0.38 tff(exemplifies_property_type, type, (
% 0.12/0.38 exemplifies_property: ( $i * $i ) > $o)).
% 0.12/0.38 tff(conceivable_type, type, (
% 0.12/0.38 conceivable: $i)).
% 0.12/0.38 tff(object_type, type, (
% 0.12/0.38 object: $i > $o)).
% 0.12/0.38 tff(none_greater_type, type, (
% 0.12/0.38 none_greater: $i)).
% 0.12/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.38 tptp_fun_Y_0: $i > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $i] : refl(((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X)))))) <=> ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X)))))) <=> ![X: $i] : ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((~?[X: $i] : (object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y))))) <=> (~?[X: $i] : (object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((~(?[X: $i] : (object(X) & exemplifies_property(none_greater, X)) => ?[X: $i] : ((object(X) & exemplifies_property(none_greater, X)) & ![Y: $i] : (object(Y) => (exemplifies_property(none_greater, Y) => (Y = X)))))) <=> (~((~?[X: $i] : (object(X) & exemplifies_property(none_greater, X))) | ?[X: $i] : (object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,axiom,(~(?[X: $i] : (object(X) & exemplifies_property(none_greater, X)) => ?[X: $i] : ((object(X) & exemplifies_property(none_greater, X)) & ![Y: $i] : (object(Y) => (exemplifies_property(none_greater, Y) => (Y = X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma_2')).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~((~?[X: $i] : (object(X) & exemplifies_property(none_greater, X))) | ?[X: $i] : (object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~?[X: $i] : (object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y))))),
% 0.12/0.38 inference(or_elim,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~?[X: $i] : (object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~?[X: $i] : (object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~?[X: $i] : (object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[X: $i] : nnf_neg(refl($oeq((~object(X)), (~object(X)))), refl($oeq((~exemplifies_property(none_greater, X)), (~exemplifies_property(none_greater, X)))), sk($oeq((~![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y)))), (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))), $oeq((~(object(X) & exemplifies_property(none_greater, X) & ![Y: $i] : ((Y = X) | (~object(Y)) | (~exemplifies_property(none_greater, Y))))), ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,(
% 0.12/0.38 ![X: $i] : ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))),
% 0.12/0.38 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (?[X: $i] : (object(X) & exemplifies_property(none_greater, X)) <=> ?[X: $i] : (object(X) & exemplifies_property(none_greater, X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (?[X: $i] : (object(X) & exemplifies_property(none_greater, X))),
% 0.12/0.38 inference(or_elim,[status(thm)],[6])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (?[X: $i] : (object(X) & exemplifies_property(none_greater, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.38 tff(17,plain,(
% 0.12/0.38 object(X!1) & exemplifies_property(none_greater, X!1)),
% 0.12/0.38 inference(skolemize,[status(sab)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (exemplifies_property(none_greater, X!1)),
% 0.12/0.38 inference(and_elim,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (object(X!1)),
% 0.12/0.38 inference(and_elim,[status(thm)],[17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (((~![X: $i] : ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))) | ((~object(X!1)) | (~exemplifies_property(none_greater, X!1)) | (~((tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))))))) <=> ((~![X: $i] : ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))) | (~object(X!1)) | (~exemplifies_property(none_greater, X!1)) | (~((tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((~![X: $i] : ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))) | ((~object(X!1)) | (~exemplifies_property(none_greater, X!1)) | (~((tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![X: $i] : ((~object(X)) | (~exemplifies_property(none_greater, X)) | (~((tptp_fun_Y_2(X) = X) | (~object(tptp_fun_Y_2(X))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X))))))) | (~object(X!1)) | (~exemplifies_property(none_greater, X!1)) | (~((tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (~((tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[22, 19, 18, 13])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (((tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1)))) | object(tptp_fun_Y_2(X!1))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (object(tptp_fun_Y_2(X!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))) <=> ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X))))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))) <=> ![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (^[X: $i] : refl(((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))) <=> ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))) <=> ![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))) <=> ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))) <=> ![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))) <=> ![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[31, 29])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~object(X)) | (((~exemplifies_property(none_greater, X)) | (exemplifies_property(conceivable, X) & ![Y: $i] : (~(object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))) & (exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (object(tptp_fun_Y_0(X)) & exemplifies_relation(greater_than, tptp_fun_Y_0(X), X) & exemplifies_property(conceivable, tptp_fun_Y_0(X)))))) <=> ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (((~exemplifies_property(none_greater, X)) | (exemplifies_property(conceivable, X) & ![Y: $i] : (~(object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))) & (exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (object(tptp_fun_Y_0(X)) & exemplifies_relation(greater_than, tptp_fun_Y_0(X), X) & exemplifies_property(conceivable, tptp_fun_Y_0(X)))))) <=> ![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~object(X)) | (((~exemplifies_property(none_greater, X)) | (exemplifies_property(conceivable, X) & ![Y: $i] : (~(object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))) & (exemplifies_property(none_greater, X) | ((~exemplifies_property(conceivable, X)) | (object(tptp_fun_Y_0(X)) & exemplifies_relation(greater_than, tptp_fun_Y_0(X), X) & exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) <=> ((~object(X)) | (((~exemplifies_property(none_greater, X)) | (exemplifies_property(conceivable, X) & ![Y: $i] : (~(object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))) & (exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (object(tptp_fun_Y_0(X)) & exemplifies_relation(greater_than, tptp_fun_Y_0(X), X) & exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (((~exemplifies_property(none_greater, X)) | (exemplifies_property(conceivable, X) & ![Y: $i] : (~(object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))) & (exemplifies_property(none_greater, X) | ((~exemplifies_property(conceivable, X)) | (object(tptp_fun_Y_0(X)) & exemplifies_relation(greater_than, tptp_fun_Y_0(X), X) & exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) <=> ![X: $i] : ((~object(X)) | (((~exemplifies_property(none_greater, X)) | (exemplifies_property(conceivable, X) & ![Y: $i] : (~(object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))) & (exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (object(tptp_fun_Y_0(X)) & exemplifies_relation(greater_than, tptp_fun_Y_0(X), X) & exemplifies_property(conceivable, tptp_fun_Y_0(X))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![X: $i] : ((~object(X)) | (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y)))))) <=> ![X: $i] : ((~object(X)) | (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (^[X: $i] : trans(monotonicity(rewrite((exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : ((object(Y) & exemplifies_relation(greater_than, Y, X)) & exemplifies_property(conceivable, Y))))) <=> (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y)))))), ((object(X) => (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : ((object(Y) & exemplifies_relation(greater_than, Y, X)) & exemplifies_property(conceivable, Y)))))) <=> (object(X) => (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y)))))))), rewrite((object(X) => (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y)))))) <=> ((~object(X)) | (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))))), ((object(X) => (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : ((object(Y) & exemplifies_relation(greater_than, Y, X)) & exemplifies_property(conceivable, Y)))))) <=> ((~object(X)) | (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (![X: $i] : (object(X) => (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : ((object(Y) & exemplifies_relation(greater_than, Y, X)) & exemplifies_property(conceivable, Y)))))) <=> ![X: $i] : ((~object(X)) | (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.39 tff(40,axiom,(![X: $i] : (object(X) => (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : ((object(Y) & exemplifies_relation(greater_than, Y, X)) & exemplifies_property(conceivable, Y))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','definition_none_greater')).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![X: $i] : ((~object(X)) | (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![X: $i] : ((~object(X)) | (exemplifies_property(none_greater, X) <=> (exemplifies_property(conceivable, X) & (~?[Y: $i] : (object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.12/0.39 tff(43,plain,(
% 0.12/0.39 ![X: $i] : ((~object(X)) | (((~exemplifies_property(none_greater, X)) | (exemplifies_property(conceivable, X) & ![Y: $i] : (~(object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))) & (exemplifies_property(none_greater, X) | ((~exemplifies_property(conceivable, X)) | (object(tptp_fun_Y_0(X)) & exemplifies_relation(greater_than, tptp_fun_Y_0(X), X) & exemplifies_property(conceivable, tptp_fun_Y_0(X)))))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[42])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![X: $i] : ((~object(X)) | (((~exemplifies_property(none_greater, X)) | (exemplifies_property(conceivable, X) & ![Y: $i] : (~(object(Y) & exemplifies_relation(greater_than, Y, X) & exemplifies_property(conceivable, Y))))) & (exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (object(tptp_fun_Y_0(X)) & exemplifies_relation(greater_than, tptp_fun_Y_0(X), X) & exemplifies_property(conceivable, tptp_fun_Y_0(X))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![X: $i] : ((~object(X)) | (~((~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))) | (~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 32])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[46, 27])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))))))) <=> ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | (~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (((~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))))))))) <=> ((~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))))))) <=> ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))))))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))))))) <=> ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | (~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[50, 48])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | (~object(tptp_fun_Y_2(X!1))) | (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (~((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[53, 47, 25])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.40 (((~(exemplifies_property(none_greater, tptp_fun_Y_2(X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(tptp_fun_Y_2(X!1)))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(tptp_fun_Y_2(X!1)), tptp_fun_Y_2(X!1))) | (~object(tptp_fun_Y_0(tptp_fun_Y_2(X!1)))))))) | (~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))))))) | ((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 ((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (((tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1)))) | exemplifies_property(none_greater, tptp_fun_Y_2(X!1))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (exemplifies_property(none_greater, tptp_fun_Y_2(X!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[57, 23])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~((~exemplifies_property(none_greater, tptp_fun_Y_2(X!1))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))))) | (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (~((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))) | exemplifies_property(conceivable, tptp_fun_Y_2(X!1))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (exemplifies_property(conceivable, tptp_fun_Y_2(X!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~object(tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))))))) <=> ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | (~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~object(tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (((~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~object(tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))))))))) <=> ((~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~object(tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~object(tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))))))) <=> ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~object(tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))))))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[65])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~object(tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))))))) <=> ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | (~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~object(tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[66, 64])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | ((~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~object(tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 ((~![X: $i] : ((~object(X)) | (~((~(exemplifies_property(none_greater, X) | (~exemplifies_property(conceivable, X)) | (~((~object(tptp_fun_Y_0(X))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X), X)) | (~exemplifies_property(conceivable, tptp_fun_Y_0(X))))))) | (~((~exemplifies_property(none_greater, X)) | (~((~exemplifies_property(conceivable, X)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X)))))))))))) | (~object(X!1)) | (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~object(tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (~((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~object(tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[69, 47, 19])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (((~(exemplifies_property(none_greater, X!1) | (~exemplifies_property(conceivable, X!1)) | (~((~exemplifies_property(conceivable, tptp_fun_Y_0(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_0(X!1), X!1)) | (~object(tptp_fun_Y_0(X!1))))))) | (~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))))))) | ((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 ((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 ((~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))) | (~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 ((~((~exemplifies_property(none_greater, X!1)) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))))) | (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[73, 18])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (~((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[74, 72])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))) | ((~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1)))) <=> ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(79,plain,
% 0.12/0.41 ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))) | ((~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(80,plain,
% 0.12/0.41 ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1)))) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.12/0.41 tff(81,plain,
% 0.12/0.41 ((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[80, 77, 25])).
% 0.12/0.41 tff(82,plain,
% 0.12/0.41 (~exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[81, 63])).
% 0.12/0.41 tff(83,plain,
% 0.12/0.41 (((tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | (~exemplifies_property(none_greater, tptp_fun_Y_2(X!1)))) | (~(tptp_fun_Y_2(X!1) = X!1))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(84,plain,
% 0.12/0.41 (~(tptp_fun_Y_2(X!1) = X!1)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[83, 23])).
% 0.12/0.41 tff(85,plain,
% 0.12/0.41 (^[X: $i, Y: $i] : refl(((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X))) <=> ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(86,plain,
% 0.12/0.41 (![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X))) <=> ![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.12/0.41 tff(87,plain,
% 0.12/0.41 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((object(X) & object(Y)) <=> (~((~object(Y)) | (~object(X))))), ((~(object(X) & object(Y))) <=> (~(~((~object(Y)) | (~object(X))))))), rewrite((~(~((~object(Y)) | (~object(X))))) <=> ((~object(Y)) | (~object(X)))), ((~(object(X) & object(Y))) <=> ((~object(Y)) | (~object(X))))), (((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y)))) <=> ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | ((~object(Y)) | (~object(X)))))), rewrite(((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | ((~object(Y)) | (~object(X)))) <=> ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))), (((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y)))) <=> ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(88,plain,
% 0.12/0.41 (![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y)))) <=> ![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.12/0.41 tff(89,plain,
% 0.12/0.41 (![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y)))) <=> ![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(90,plain,
% 0.12/0.41 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((exemplifies_relation(greater_than, X, Y) | exemplifies_relation(greater_than, Y, X)) <=> (exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y))), (((exemplifies_relation(greater_than, X, Y) | exemplifies_relation(greater_than, Y, X)) | (X = Y)) <=> ((exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y)) | (X = Y)))), rewrite(((exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y)) | (X = Y)) <=> ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y))), (((exemplifies_relation(greater_than, X, Y) | exemplifies_relation(greater_than, Y, X)) | (X = Y)) <=> ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y)))), (((object(X) & object(Y)) => ((exemplifies_relation(greater_than, X, Y) | exemplifies_relation(greater_than, Y, X)) | (X = Y))) <=> ((object(X) & object(Y)) => ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y))))), rewrite(((object(X) & object(Y)) => ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y))) <=> ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y))))), (((object(X) & object(Y)) => ((exemplifies_relation(greater_than, X, Y) | exemplifies_relation(greater_than, Y, X)) | (X = Y))) <=> ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(91,plain,
% 0.12/0.41 (![X: $i, Y: $i] : ((object(X) & object(Y)) => ((exemplifies_relation(greater_than, X, Y) | exemplifies_relation(greater_than, Y, X)) | (X = Y))) <=> ![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.12/0.41 tff(92,axiom,(![X: $i, Y: $i] : ((object(X) & object(Y)) => ((exemplifies_relation(greater_than, X, Y) | exemplifies_relation(greater_than, Y, X)) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','connectedness_of_greater_than')).
% 0.12/0.41 tff(93,plain,
% 0.12/0.41 (![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.12/0.41 tff(94,plain,
% 0.12/0.41 (![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.12/0.41 tff(95,plain,(
% 0.12/0.41 ![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~(object(X) & object(Y))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[94])).
% 0.12/0.41 tff(96,plain,
% 0.12/0.41 (![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.12/0.41 tff(97,plain,
% 0.12/0.41 (![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.12/0.41 tff(98,plain,
% 0.12/0.41 (((~![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))) | ((~object(X!1)) | (tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))) | (~object(X!1)) | (tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(99,plain,
% 0.12/0.41 (((tptp_fun_Y_2(X!1) = X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | (~object(X!1)) | (~object(tptp_fun_Y_2(X!1)))) <=> ((~object(X!1)) | (tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(100,plain,
% 0.12/0.41 (((~![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))) | ((tptp_fun_Y_2(X!1) = X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | (~object(X!1)) | (~object(tptp_fun_Y_2(X!1))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))) | ((~object(X!1)) | (tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[99])).
% 0.12/0.41 tff(101,plain,
% 0.12/0.41 (((~![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))) | ((tptp_fun_Y_2(X!1) = X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | (~object(X!1)) | (~object(tptp_fun_Y_2(X!1))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))) | (~object(X!1)) | (tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[100, 98])).
% 0.12/0.41 tff(102,plain,
% 0.12/0.41 ((~![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))) | ((tptp_fun_Y_2(X!1) = X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | (~object(X!1)) | (~object(tptp_fun_Y_2(X!1))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(103,plain,
% 0.12/0.41 ((~![X: $i, Y: $i] : ((X = Y) | exemplifies_relation(greater_than, Y, X) | exemplifies_relation(greater_than, X, Y) | (~object(Y)) | (~object(X)))) | (~object(X!1)) | (tptp_fun_Y_2(X!1) = X!1) | (~object(tptp_fun_Y_2(X!1))) | exemplifies_relation(greater_than, tptp_fun_Y_2(X!1), X!1) | exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.12/0.41 tff(104,plain,
% 0.12/0.41 (exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[103, 97, 19, 84, 25, 82])).
% 0.12/0.41 tff(105,plain,
% 0.12/0.41 (((~exemplifies_property(conceivable, tptp_fun_Y_2(X!1))) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1)))))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(106,plain,
% 0.12/0.41 (![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[105, 61])).
% 0.12/0.41 tff(107,plain,
% 0.12/0.41 (((~exemplifies_property(conceivable, X!1)) | (~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, X!1))))) | exemplifies_property(conceivable, X!1)),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(108,plain,
% 0.12/0.41 (exemplifies_property(conceivable, X!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[107, 75])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))) | ((~object(X!1)) | (~exemplifies_property(conceivable, X!1)) | (~exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1))))) <=> ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))) | (~object(X!1)) | (~exemplifies_property(conceivable, X!1)) | (~exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))) | ((~object(X!1)) | (~exemplifies_property(conceivable, X!1)) | (~exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(conceivable, Y)) | (~exemplifies_relation(greater_than, Y, tptp_fun_Y_2(X!1))))) | (~object(X!1)) | (~exemplifies_property(conceivable, X!1)) | (~exemplifies_relation(greater_than, X!1, tptp_fun_Y_2(X!1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[111, 19, 108, 106, 104])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------