%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET774+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:26:19 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET774+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:41:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(member_type, type, (
% 0.11/0.37 member: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_E_22_type, type, (
% 0.11/0.37 tptp_fun_E_22: $i)).
% 0.11/0.37 tff(tptp_fun_X_19_type, type, (
% 0.11/0.37 tptp_fun_X_19: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_R_20_type, type, (
% 0.11/0.37 tptp_fun_R_20: $i)).
% 0.11/0.37 tff(tptp_fun_X_21_type, type, (
% 0.11/0.37 tptp_fun_X_21: $i)).
% 0.11/0.37 tff(apply_type, type, (
% 0.11/0.37 apply: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_Z_17_type, type, (
% 0.11/0.37 tptp_fun_Z_17: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_Y_18_type, type, (
% 0.11/0.37 tptp_fun_Y_18: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_X_16_type, type, (
% 0.11/0.37 tptp_fun_X_16: ( $i * $i ) > $i)).
% 0.11/0.37 tff(pre_order_type, type, (
% 0.11/0.37 pre_order: ( $i * $i ) > $o)).
% 0.11/0.37 tff(subset_type, type, (
% 0.11/0.37 subset: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_X_0_type, type, (
% 0.11/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.11/0.37 tff(1,assumption,(~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))) | (~apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (~apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (^[R: $i, E: $i] : refl((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[9, 7])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))) <=> (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), rewrite((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))), rewrite((((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (^[R: $i, E: $i] : rewrite((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (^[R: $i, E: $i] : rewrite((pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.38 tff(18,axiom,(![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','pre_order')).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.38 tff(21,plain,(
% 0.11/0.38 ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[20])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[23, 10])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~((~member(tptp_fun_Z_17(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~((~member(tptp_fun_Z_17(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 ((~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))) <=> (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~((~member(tptp_fun_Z_17(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~((~member(tptp_fun_Z_17(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[27])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~((~member(tptp_fun_Z_17(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~((~member(tptp_fun_Z_17(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~((~member(tptp_fun_Z_17(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~((~member(tptp_fun_Z_17(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))) | ((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 ((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))) <=> (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~![E: $i, X: $i, R: $i] : ((pre_order(R, E) & subset(X, E)) => pre_order(R, X))) <=> (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(37,axiom,(~![E: $i, X: $i, R: $i] : ((pre_order(R, E) & subset(X, E)) => pre_order(R, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII10')).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.19/0.40 tff(42,plain,(
% 0.19/0.40 ~((~(pre_order(R!20, E!22) & subset(X!21, E!22))) | pre_order(R!20, X!21))),
% 0.19/0.40 inference(skolemize,[status(sab)],[41])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (pre_order(R!20, E!22) & subset(X!21, E!22)),
% 0.19/0.40 inference(or_elim,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (pre_order(R!20, E!22)),
% 0.19/0.40 inference(and_elim,[status(thm)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 ((~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))) | (~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 34])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))) | ![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | ((~member(tptp_fun_X_16(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) <=> ((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~member(tptp_fun_X_16(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | ((~member(tptp_fun_X_16(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~member(tptp_fun_X_16(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (~member(tptp_fun_X_16(X!21, R!20), E!22)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[52, 49, 3])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))) | member(tptp_fun_X_16(X!21, R!20), X!21)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (member(tptp_fun_X_16(X!21, R!20), X!21)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 1])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[59, 57])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.40 tff(66,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.40 tff(69,plain,(
% 0.19/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[68])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | (~(subset(X!21, E!22) | (~((~member(tptp_fun_X_0(E!22, X!21), X!21)) | member(tptp_fun_X_0(E!22, X!21), E!22)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (~((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | (~(subset(X!21, E!22) | (~((~member(tptp_fun_X_0(E!22, X!21), X!21)) | member(tptp_fun_X_0(E!22, X!21), E!22))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | (~(subset(X!21, E!22) | (~((~member(tptp_fun_X_0(E!22, X!21), X!21)) | member(tptp_fun_X_0(E!22, X!21), E!22)))))) | ((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (subset(X!21, E!22)),
% 0.19/0.40 inference(and_elim,[status(thm)],[43])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | (~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![X: $i] : ((~member(X, X!21)) | member(X, E!22))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_X_16(X!21, R!20), X!21)) | member(tptp_fun_X_16(X!21, R!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_X_16(X!21, R!20), X!21)) | member(tptp_fun_X_16(X!21, R!20), E!22))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_X_16(X!21, R!20), X!21)) | member(tptp_fun_X_16(X!21, R!20), E!22))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_X_16(X!21, R!20), X!21)) | member(tptp_fun_X_16(X!21, R!20), E!22)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 79, 55, 53])).
% 0.19/0.40 tff(84,plain,((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21)))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, X!21)) | (~member(Z, X!21)) | (~member(X, X!21)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))) <=> (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, X!21)) | (~member(Z, X!21)) | (~member(X, X!21)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21)))))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, X!21)) | (~member(Z, X!21)) | (~member(X, X!21)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21)))))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, X!21)) | (~member(Z, X!21)) | (~member(X, X!21)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21)))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[90, 25])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21))))))))) | (pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (~pre_order(R!20, X!21)),
% 0.19/0.42 inference(or_elim,[status(thm)],[42])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))))) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 ((~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (~((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[97, 84])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | member(tptp_fun_X_19(X!21, R!20), X!21)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (member(tptp_fun_X_19(X!21, R!20), X!21)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_X_19(X!21, R!20), X!21)) | member(tptp_fun_X_19(X!21, R!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | member(tptp_fun_X_19(X!21, R!20), E!22))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_X_19(X!21, R!20), X!21)) | member(tptp_fun_X_19(X!21, R!20), E!22))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | member(tptp_fun_X_19(X!21, R!20), E!22)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (member(tptp_fun_X_19(X!21, R!20), E!22)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[103, 79, 100])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | member(tptp_fun_Y_18(X!21, R!20), X!21)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (member(tptp_fun_Y_18(X!21, R!20), X!21)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 98])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_Y_18(X!21, R!20), X!21)) | member(tptp_fun_Y_18(X!21, R!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | member(tptp_fun_Y_18(X!21, R!20), E!22))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_Y_18(X!21, R!20), X!21)) | member(tptp_fun_Y_18(X!21, R!20), E!22))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | member(tptp_fun_Y_18(X!21, R!20), E!22)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (member(tptp_fun_Y_18(X!21, R!20), E!22)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[109, 79, 106])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | member(tptp_fun_Z_17(X!21, R!20), X!21)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (member(tptp_fun_Z_17(X!21, R!20), X!21)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[111, 98])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | member(tptp_fun_Z_17(X!21, R!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)) | member(tptp_fun_Z_17(X!21, R!20), E!22))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | member(tptp_fun_Z_17(X!21, R!20), E!22))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)) | member(tptp_fun_Z_17(X!21, R!20), E!22)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (member(tptp_fun_Z_17(X!21, R!20), E!22)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[115, 79, 112])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[117, 98])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[119, 98])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[121, 98])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))) | ![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[123, 47])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))) | ((~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 ((apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))) <=> ((~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))) | (apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))) | ((~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[126])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))) | (apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[127, 125])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))) | (apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 ((~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[130, 124, 122, 120, 118])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[131, 116, 110, 104])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------