%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PHI009+1 : TPTP v9.0.0. Released v7.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:22:44 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : PHI009+1 : TPTP v9.0.0. Released v7.2.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:18:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(object_type, type, (
% 0.11/0.36 object: $i > $o)).
% 0.11/0.36 tff(tptp_fun_Z_1_type, type, (
% 0.11/0.36 tptp_fun_Z_1: ( $i * $i ) > $i)).
% 0.11/0.36 tff(tptp_fun_F_2_type, type, (
% 0.11/0.36 tptp_fun_F_2: $i)).
% 0.11/0.36 tff(tptp_fun_Y_3_type, type, (
% 0.11/0.36 tptp_fun_Y_3: $i)).
% 0.11/0.36 tff(exemplifies_property_type, type, (
% 0.11/0.36 exemplifies_property: ( $i * $i ) > $o)).
% 0.11/0.36 tff(is_the_type, type, (
% 0.11/0.36 is_the: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.11/0.36 tptp_fun_Y_0: ( $i * $i ) > $i)).
% 0.11/0.36 tff(property_type, type, (
% 0.11/0.36 property: $i > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((![U: $i] : (~(object(U) & is_the(U, F!2))) & (object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))) & property(F!2)) <=> (![U: $i] : (~(object(U) & is_the(U, F!2))) & object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3)) & property(F!2))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((Z = Y!3) | (~object(Z)) | (~exemplifies_property(F!2, Z)))) <=> (object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 ((![U: $i] : (~(object(U) & is_the(U, F!2))) & (object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((Z = Y!3) | (~object(Z)) | (~exemplifies_property(F!2, Z)))) & property(F!2)) <=> (![U: $i] : (~(object(U) & is_the(U, F!2))) & (object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))) & property(F!2))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 ((![U: $i] : (~(object(U) & is_the(U, F!2))) & (object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((Z = Y!3) | (~object(Z)) | (~exemplifies_property(F!2, Z)))) & property(F!2)) <=> (![U: $i] : (~(object(U) & is_the(U, F!2))) & object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3)) & property(F!2))),
% 0.11/0.36 inference(transitivity,[status(thm)],[3, 1])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 ((~![F: $i] : (?[U: $i] : (object(U) & is_the(U, F)) | (~?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~object(Z)) | (~exemplifies_property(F, Z))))) | (~property(F)))) <=> (~![F: $i] : (?[U: $i] : (object(U) & is_the(U, F)) | (~?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~object(Z)) | (~exemplifies_property(F, Z))))) | (~property(F))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 ((~![F: $i] : (property(F) => (?[Y: $i] : ((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) => ?[U: $i] : (object(U) & is_the(U, F))))) <=> (~![F: $i] : (?[U: $i] : (object(U) & is_the(U, F)) | (~?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~object(Z)) | (~exemplifies_property(F, Z))))) | (~property(F))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(7,axiom,(~![F: $i] : (property(F) => (?[Y: $i] : ((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) => ?[U: $i] : (object(U) & is_the(U, F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','description_theorem_1')).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~![F: $i] : (?[U: $i] : (object(U) & is_the(U, F)) | (~?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~object(Z)) | (~exemplifies_property(F, Z))))) | (~property(F)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (~![F: $i] : (?[U: $i] : (object(U) & is_the(U, F)) | (~?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~object(Z)) | (~exemplifies_property(F, Z))))) | (~property(F)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (~![F: $i] : (?[U: $i] : (object(U) & is_the(U, F)) | (~?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~object(Z)) | (~exemplifies_property(F, Z))))) | (~property(F)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (~![F: $i] : (?[U: $i] : (object(U) & is_the(U, F)) | (~?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~object(Z)) | (~exemplifies_property(F, Z))))) | (~property(F)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![U: $i] : (~(object(U) & is_the(U, F!2))) & object(Y!3) & exemplifies_property(F!2, Y!3) & ![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3)) & property(F!2)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (property(F!2)),
% 0.11/0.36 inference(and_elim,[status(thm)],[12])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (object(Y!3)),
% 0.11/0.36 inference(and_elim,[status(thm)],[12])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (^[F: $i, G: $i, X: $i] : trans(monotonicity(rewrite((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))) <=> (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))))))))))), (((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))))))))))))), rewrite(((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))))))))))) <=> ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))), (((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (^[F: $i, G: $i, X: $i] : refl(((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (^[F: $i, G: $i, X: $i] : rewrite(((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[20, 18])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (^[F: $i, G: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((property(F) & property(G) & object(X)) <=> (~((~object(X)) | (~property(F)) | (~property(G))))), ((~(property(F) & property(G) & object(X))) <=> (~(~((~object(X)) | (~property(F)) | (~property(G))))))), rewrite((~(~((~object(X)) | (~property(F)) | (~property(G))))) <=> ((~object(X)) | (~property(F)) | (~property(G)))), ((~(property(F) & property(G) & object(X))) <=> ((~object(X)) | (~property(F)) | (~property(G))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((is_the(X, F) & exemplifies_property(G, X)) <=> (~((~is_the(X, F)) | (~exemplifies_property(G, X))))), ((~(is_the(X, F) & exemplifies_property(G, X))) <=> (~(~((~is_the(X, F)) | (~exemplifies_property(G, X))))))), rewrite((~(~((~is_the(X, F)) | (~exemplifies_property(G, X))))) <=> ((~is_the(X, F)) | (~exemplifies_property(G, X)))), ((~(is_the(X, F) & exemplifies_property(G, X))) <=> ((~is_the(X, F)) | (~exemplifies_property(G, X))))), rewrite((object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F))) <=> (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F)))))), (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) <=> (((~is_the(X, F)) | (~exemplifies_property(G, X))) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F)))))))), rewrite((((~is_the(X, F)) | (~exemplifies_property(G, X))) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F)))))) <=> ((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))), (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) <=> ((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F)))))))), rewrite(((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))) <=> ((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))), ((((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) <=> (((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F)))))) & ((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))), rewrite((((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F)))))) & ((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) <=> (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))), ((((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) <=> (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))), (((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))) <=> (((~object(X)) | (~property(F)) | (~property(G))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))))), rewrite((((~object(X)) | (~property(F)) | (~property(G))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))) <=> ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))), (((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))) <=> ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))) <=> ![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (^[F: $i, G: $i, X: $i] : rewrite(((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))) | (~exemplifies_property(G, Y)))))) <=> ((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))) | (~exemplifies_property(G, Y)))))) <=> ![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y)))) <=> ![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (^[F: $i, G: $i, X: $i] : trans(monotonicity(rewrite(((property(F) & property(G)) & object(X)) <=> (property(F) & property(G) & object(X))), rewrite(((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & exemplifies_property(G, Y))) <=> ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y)))), ((((property(F) & property(G)) & object(X)) => ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & exemplifies_property(G, Y)))) <=> ((property(F) & property(G) & object(X)) => ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y)))))), rewrite(((property(F) & property(G) & object(X)) => ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y)))) <=> ((~(property(F) & property(G) & object(X))) | ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y))))), ((((property(F) & property(G)) & object(X)) => ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & exemplifies_property(G, Y)))) <=> ((~(property(F) & property(G) & object(X))) | ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : (((property(F) & property(G)) & object(X)) => ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & exemplifies_property(G, Y)))) <=> ![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.37 tff(29,axiom,(![F: $i, G: $i, X: $i] : (((property(F) & property(G)) & object(X)) => ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & exemplifies_property(G, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','description_axiom_schema_instance')).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | ((is_the(X, F) & exemplifies_property(G, X)) <=> ?[Y: $i] : (object(Y) & exemplifies_property(F, Y) & ![Z: $i] : ((Z = Y) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.11/0.37 tff(32,plain,(
% 0.11/0.37 ![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)) | (~object(Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F))))) | (~exemplifies_property(G, Y))))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[31])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~(property(F) & property(G) & object(X))) | (((~(is_the(X, F) & exemplifies_property(G, X))) | (object(tptp_fun_Y_0(G, F)) & exemplifies_property(F, tptp_fun_Y_0(G, F)) & ![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z))) & exemplifies_property(G, tptp_fun_Y_0(G, F)))) & ((is_the(X, F) & exemplifies_property(G, X)) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))))))) | (~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[34, 21])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[35, 16])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (((~![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))) | ((~property(F!2)) | (~object(Y!3)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2)))))))))))) <=> ((~![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))) | (~property(F!2)) | (~object(Y!3)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2)))))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (((~object(Y!3)) | (~property(F!2)) | (~property(F!2)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2))))))))))) <=> ((~property(F!2)) | (~object(Y!3)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2)))))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 ((~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~object(tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(F!2, F!2)) | (~exemplifies_property(F!2, Z)))))))))) <=> (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2))))))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (((~object(Y!3)) | (~property(F!2)) | (~property(F!2)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~object(tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(F!2, F!2)) | (~exemplifies_property(F!2, Z))))))))))) <=> ((~object(Y!3)) | (~property(F!2)) | (~property(F!2)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2)))))))))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[39])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (((~object(Y!3)) | (~property(F!2)) | (~property(F!2)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~object(tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(F!2, F!2)) | (~exemplifies_property(F!2, Z))))))))))) <=> ((~property(F!2)) | (~object(Y!3)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2)))))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[40, 38])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (((~![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))) | ((~object(Y!3)) | (~property(F!2)) | (~property(F!2)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~object(tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(F!2, F!2)) | (~exemplifies_property(F!2, Z)))))))))))) <=> ((~![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))) | ((~property(F!2)) | (~object(Y!3)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2))))))))))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[41])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (((~![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))) | ((~object(Y!3)) | (~property(F!2)) | (~property(F!2)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~object(tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(F!2, F!2)) | (~exemplifies_property(F!2, Z)))))))))))) <=> ((~![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))) | (~property(F!2)) | (~object(Y!3)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2)))))))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[42, 37])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 ((~![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))) | ((~object(Y!3)) | (~property(F!2)) | (~property(F!2)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~object(tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(F!2, F!2)) | (~exemplifies_property(F!2, Z)))))))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 ((~![F: $i, G: $i, X: $i] : ((~object(X)) | (~property(F)) | (~property(G)) | (~((~((~((~is_the(X, F)) | (~exemplifies_property(G, X)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(G, Y)) | (~exemplifies_property(F, Y)) | (~((tptp_fun_Z_1(Y, F) = Y) | (~exemplifies_property(F, tptp_fun_Z_1(Y, F))) | (~object(tptp_fun_Z_1(Y, F)))))))) | (~((~is_the(X, F)) | (~exemplifies_property(G, X)) | (~((~object(tptp_fun_Y_0(G, F))) | (~exemplifies_property(F, tptp_fun_Y_0(G, F))) | (~exemplifies_property(G, tptp_fun_Y_0(G, F))) | (~![Z: $i] : ((~object(Z)) | (Z = tptp_fun_Y_0(G, F)) | (~exemplifies_property(F, Z)))))))))))) | (~property(F!2)) | (~object(Y!3)) | (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2))))))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 (~((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2)))))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[45, 36, 14, 13])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)) | (~((~exemplifies_property(F!2, tptp_fun_Y_0(F!2, F!2))) | (~object(tptp_fun_Y_0(F!2, F!2))) | (~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = tptp_fun_Y_0(F!2, F!2))))))))) | ((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 ((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (^[U: $i] : refl(((~object(U)) | (~is_the(U, F!2))) <=> ((~object(U)) | (~is_the(U, F!2))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (![U: $i] : ((~object(U)) | (~is_the(U, F!2))) <=> ![U: $i] : ((~object(U)) | (~is_the(U, F!2)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (^[U: $i] : trans(monotonicity(rewrite((object(U) & is_the(U, F!2)) <=> (~((~object(U)) | (~is_the(U, F!2))))), ((~(object(U) & is_the(U, F!2))) <=> (~(~((~object(U)) | (~is_the(U, F!2))))))), rewrite((~(~((~object(U)) | (~is_the(U, F!2))))) <=> ((~object(U)) | (~is_the(U, F!2)))), ((~(object(U) & is_the(U, F!2))) <=> ((~object(U)) | (~is_the(U, F!2)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (![U: $i] : (~(object(U) & is_the(U, F!2))) <=> ![U: $i] : ((~object(U)) | (~is_the(U, F!2)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (![U: $i] : (~(object(U) & is_the(U, F!2)))),
% 0.18/0.39 inference(and_elim,[status(thm)],[12])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (![U: $i] : ((~object(U)) | (~is_the(U, F!2)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (![U: $i] : ((~object(U)) | (~is_the(U, F!2)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (((~![U: $i] : ((~object(U)) | (~is_the(U, F!2)))) | ((~object(Y!3)) | (~is_the(Y!3, F!2)))) <=> ((~![U: $i] : ((~object(U)) | (~is_the(U, F!2)))) | (~object(Y!3)) | (~is_the(Y!3, F!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 ((~![U: $i] : ((~object(U)) | (~is_the(U, F!2)))) | ((~object(Y!3)) | (~is_the(Y!3, F!2)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 ((~![U: $i] : ((~object(U)) | (~is_the(U, F!2)))) | (~object(Y!3)) | (~is_the(Y!3, F!2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (~is_the(Y!3, F!2)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[58, 55, 14])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3))) | is_the(Y!3, F!2)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 ((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 ((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | (~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2))))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 ((~((~((~is_the(Y!3, F!2)) | (~exemplifies_property(F!2, Y!3)))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2)))))))) | ![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[63, 48])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (exemplifies_property(F!2, Y!3)),
% 0.18/0.39 inference(and_elim,[status(thm)],[12])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2))))))) | ((~object(Y!3)) | (~exemplifies_property(F!2, Y!3)) | (~((tptp_fun_Z_1(Y!3, F!2) = Y!3) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (~object(tptp_fun_Z_1(Y!3, F!2))))))) <=> ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2))))))) | (~object(Y!3)) | (~exemplifies_property(F!2, Y!3)) | (~((tptp_fun_Z_1(Y!3, F!2) = Y!3) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (~object(tptp_fun_Z_1(Y!3, F!2))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2))))))) | ((~object(Y!3)) | (~exemplifies_property(F!2, Y!3)) | (~((tptp_fun_Z_1(Y!3, F!2) = Y!3) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (~object(tptp_fun_Z_1(Y!3, F!2))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 ((~![Y: $i] : ((~object(Y)) | (~exemplifies_property(F!2, Y)) | (~((tptp_fun_Z_1(Y, F!2) = Y) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y, F!2))) | (~object(tptp_fun_Z_1(Y, F!2))))))) | (~object(Y!3)) | (~exemplifies_property(F!2, Y!3)) | (~((tptp_fun_Z_1(Y!3, F!2) = Y!3) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (~object(tptp_fun_Z_1(Y!3, F!2)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (~((tptp_fun_Z_1(Y!3, F!2) = Y!3) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (~object(tptp_fun_Z_1(Y!3, F!2))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[68, 14, 65, 64])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (((tptp_fun_Z_1(Y!3, F!2) = Y!3) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (~object(tptp_fun_Z_1(Y!3, F!2)))) | object(tptp_fun_Z_1(Y!3, F!2))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (object(tptp_fun_Z_1(Y!3, F!2))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (((tptp_fun_Z_1(Y!3, F!2) = Y!3) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (~object(tptp_fun_Z_1(Y!3, F!2)))) | exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 (exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (((tptp_fun_Z_1(Y!3, F!2) = Y!3) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (~object(tptp_fun_Z_1(Y!3, F!2)))) | (~(tptp_fun_Z_1(Y!3, F!2) = Y!3))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (~(tptp_fun_Z_1(Y!3, F!2) = Y!3)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[74, 69])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (^[Z: $i] : refl(((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3)) <=> ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3)) <=> ![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))),
% 0.18/0.39 inference(and_elim,[status(thm)],[12])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (((~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))) | ((~object(tptp_fun_Z_1(Y!3, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (tptp_fun_Z_1(Y!3, F!2) = Y!3))) <=> ((~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))) | (~object(tptp_fun_Z_1(Y!3, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (tptp_fun_Z_1(Y!3, F!2) = Y!3))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 ((~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))) | ((~object(tptp_fun_Z_1(Y!3, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (tptp_fun_Z_1(Y!3, F!2) = Y!3))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 ((~![Z: $i] : ((~object(Z)) | (~exemplifies_property(F!2, Z)) | (Z = Y!3))) | (~object(tptp_fun_Z_1(Y!3, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_1(Y!3, F!2))) | (tptp_fun_Z_1(Y!3, F!2) = Y!3)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[82, 79, 75, 73, 71])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------