%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PHI010+1 : TPTP v9.0.0. Released v7.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PHI010+1 : TPTP v9.0.0. Released v7.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n016.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 02:18:47 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(exemplifies_property_type, type, (
% 0.19/0.36 exemplifies_property: ( $i * $i ) > $o)).
% 0.19/0.36 tff(tptp_fun_F_2_type, type, (
% 0.19/0.36 tptp_fun_F_2: $i)).
% 0.19/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.36 tptp_fun_Y_1: $i)).
% 0.19/0.36 tff(object_type, type, (
% 0.19/0.36 object: $i > $o)).
% 0.19/0.36 tff(is_the_type, type, (
% 0.19/0.36 is_the: ( $i * $i ) > $o)).
% 0.19/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.36 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.19/0.36 tff(property_type, type, (
% 0.19/0.36 property: $i > $o)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 ((~(exemplifies_property(F!2, Y!1) | (~object(Y!1)) | (~is_the(Y!1, F!2)) | (~property(F!2)))) <=> (~(exemplifies_property(F!2, Y!1) | (~object(Y!1)) | (~is_the(Y!1, F!2)) | (~property(F!2))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 ((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~is_the(Y, F)) | (~property(F)))) <=> (~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~is_the(Y, F)) | (~property(F))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 ((~![X: $i, F: $i, Y: $i] : (((object(X) & property(F)) & object(Y)) => ((is_the(X, F) & (X = Y)) => exemplifies_property(F, Y)))) <=> (~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~is_the(Y, F)) | (~property(F))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(4,axiom,(~![X: $i, F: $i, Y: $i] : (((object(X) & property(F)) & object(Y)) => ((is_the(X, F) & (X = Y)) => exemplifies_property(F, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_1')).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~is_the(Y, F)) | (~property(F)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~is_the(Y, F)) | (~property(F)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~is_the(Y, F)) | (~property(F)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~is_the(Y, F)) | (~property(F)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.36 tff(9,plain,(
% 0.19/0.36 ~(exemplifies_property(F!2, Y!1) | (~object(Y!1)) | (~is_the(Y!1, F!2)) | (~property(F!2)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[8])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (~(exemplifies_property(F!2, Y!1) | (~object(Y!1)) | (~is_the(Y!1, F!2)) | (~property(F!2)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (~exemplifies_property(F!2, Y!1)),
% 0.19/0.36 inference(or_elim,[status(thm)],[10])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))) | exemplifies_property(F!2, Y!1)),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 ((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (is_the(Y!1, F!2)),
% 0.19/0.36 inference(or_elim,[status(thm)],[10])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 ((~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))) | (~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))))))) | ((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 ((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (property(F!2)),
% 0.19/0.37 inference(or_elim,[status(thm)],[10])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (object(Y!1)),
% 0.19/0.37 inference(or_elim,[status(thm)],[10])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (^[F: $i, X: $i, W: $i] : rewrite(((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))) <=> ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))) <=> ![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (^[F: $i, X: $i, W: $i] : refl(((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))) <=> ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))) <=> ![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (^[F: $i, X: $i, W: $i] : rewrite(((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))) <=> ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))) <=> ![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))) <=> ![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (^[F: $i, X: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((property(F) & object(X) & object(W)) <=> (~((~object(W)) | (~object(X)) | (~property(F))))), ((~(property(F) & object(X) & object(W))) <=> (~(~((~object(W)) | (~object(X)) | (~property(F))))))), rewrite((~(~((~object(W)) | (~object(X)) | (~property(F))))) <=> ((~object(W)) | (~object(X)) | (~property(F)))), ((~(property(F) & object(X) & object(W))) <=> ((~object(W)) | (~object(X)) | (~property(F))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((is_the(X, F) & (X = W)) <=> (~((~is_the(X, F)) | (~(X = W))))), ((~(is_the(X, F) & (X = W))) <=> (~(~((~is_the(X, F)) | (~(X = W))))))), rewrite((~(~((~is_the(X, F)) | (~(X = W))))) <=> ((~is_the(X, F)) | (~(X = W)))), ((~(is_the(X, F) & (X = W))) <=> ((~is_the(X, F)) | (~(X = W))))), rewrite((object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))) <=> (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))), (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) <=> (((~is_the(X, F)) | (~(X = W))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))))), rewrite((((~is_the(X, F)) | (~(X = W))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))) <=> ((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))), (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) <=> ((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))))), trans(monotonicity(rewrite((is_the(X, F) & (X = W)) <=> (~((~is_the(X, F)) | (~(X = W))))), rewrite((~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) <=> (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))), (((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))) <=> ((~((~is_the(X, F)) | (~(X = W)))) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))))), rewrite(((~((~is_the(X, F)) | (~(X = W)))) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))) <=> ((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))), (((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))) <=> ((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))), ((((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))))) <=> (((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))) & ((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))), rewrite((((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))) & ((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) <=> (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))), ((((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))))) <=> (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))), (((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))))) <=> (((~object(W)) | (~object(X)) | (~property(F))) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))))), rewrite((((~object(W)) | (~object(X)) | (~property(F))) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W))))))))) <=> ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))), (((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))))) <=> ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))))) <=> ![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (^[F: $i, X: $i, W: $i] : rewrite(((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | ((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))))))) <=> ((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | ((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))))))) <=> ![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))) <=> ![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (^[F: $i, X: $i, W: $i] : trans(monotonicity(rewrite(((property(F) & object(X)) & object(W)) <=> (property(F) & object(X) & object(W))), rewrite(((is_the(X, F) & (X = W)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & (Y = W))) <=> ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))), ((((property(F) & object(X)) & object(W)) => ((is_the(X, F) & (X = W)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & (Y = W)))) <=> ((property(F) & object(X) & object(W)) => ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))), rewrite(((property(F) & object(X) & object(W)) => ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))) <=> ((~(property(F) & object(X) & object(W))) | ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))), ((((property(F) & object(X)) & object(W)) => ((is_the(X, F) & (X = W)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & (Y = W)))) <=> ((~(property(F) & object(X) & object(W))) | ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : (((property(F) & object(X)) & object(W)) => ((is_the(X, F) & (X = W)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & (Y = W)))) <=> ![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.37 tff(35,axiom,(![F: $i, X: $i, W: $i] : (((property(F) & object(X)) & object(W)) => ((is_the(X, F) & (X = W)) <=> ?[Y: $i] : (((object(Y) & exemplifies_property(F, Y)) & ![Z: $i] : (object(Z) => (exemplifies_property(F, Z) => (Z = Y)))) & (Y = W))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','description_axiom_identity_instance')).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | ((is_the(X, F) & (X = W)) <=> (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.37 tff(38,plain,(
% 0.19/0.37 ![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | ((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F)))))))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[37])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~(property(F) & object(X) & object(W))) | (((~(is_the(X, F) & (X = W))) | (object(W) & exemplifies_property(F, W) & ![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z))))) & ((is_the(X, F) & (X = W)) | (~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[40, 27])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[41, 22])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (((~![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))) | ((~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))))))) <=> ((~![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (((~object(Y!1)) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))))))))) <=> ((~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((tptp_fun_Z_0(Y!1, F!2) = Y!1) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((Z = Y!1) | (~object(Z)) | (~exemplifies_property(F!2, Z)))))))))) <=> (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (((~object(Y!1)) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((tptp_fun_Z_0(Y!1, F!2) = Y!1) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((Z = Y!1) | (~object(Z)) | (~exemplifies_property(F!2, Z))))))))))) <=> ((~object(Y!1)) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (((~object(Y!1)) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((tptp_fun_Z_0(Y!1, F!2) = Y!1) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((Z = Y!1) | (~object(Z)) | (~exemplifies_property(F!2, Z))))))))))) <=> ((~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (((~![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))) | ((~object(Y!1)) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((tptp_fun_Z_0(Y!1, F!2) = Y!1) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((Z = Y!1) | (~object(Z)) | (~exemplifies_property(F!2, Z)))))))))))) <=> ((~![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))) | ((~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))))))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (((~![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))) | ((~object(Y!1)) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((tptp_fun_Z_0(Y!1, F!2) = Y!1) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((Z = Y!1) | (~object(Z)) | (~exemplifies_property(F!2, Z)))))))))))) <=> ((~![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z)))))))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[48, 43])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 ((~![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))) | ((~object(Y!1)) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((tptp_fun_Z_0(Y!1, F!2) = Y!1) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)))))) | (~((~is_the(Y!1, F!2)) | (~(Y!1 = Y!1)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((Z = Y!1) | (~object(Z)) | (~exemplifies_property(F!2, Z)))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ((~![F: $i, X: $i, W: $i] : ((~object(W)) | (~object(X)) | (~property(F)) | (~((~((~object(W)) | (~exemplifies_property(F, W)) | (~((tptp_fun_Z_0(W, F) = W) | (~object(tptp_fun_Z_0(W, F))) | (~exemplifies_property(F, tptp_fun_Z_0(W, F))))) | (~((~is_the(X, F)) | (~(X = W)))))) | (~((~is_the(X, F)) | (~(X = W)) | (~((~object(W)) | (~exemplifies_property(F, W)) | (~![Z: $i] : ((Z = W) | (~object(Z)) | (~exemplifies_property(F, Z)))))))))))) | (~object(Y!1)) | (~property(F!2)) | (~((~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~((~exemplifies_property(F!2, tptp_fun_Z_0(Y!1, F!2))) | (~object(tptp_fun_Z_0(Y!1, F!2))) | (tptp_fun_Z_0(Y!1, F!2) = Y!1))) | is_the(Y!1, F!2))) | (~((~is_the(Y!1, F!2)) | (~((~object(Y!1)) | (~exemplifies_property(F!2, Y!1)) | (~![Z: $i] : ((~object(Z)) | (Z = Y!1) | (~exemplifies_property(F!2, Z))))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[51, 42, 20, 19, 18])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------