%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET765+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:18 AM UTC 2025
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SET765+4 : TPTP v9.0.0. Released v2.2.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 05:41:09 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(member_type, type, (
% 0.14/0.41 member: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_E_22_type, type, (
% 0.14/0.41 tptp_fun_E_22: $i)).
% 0.14/0.41 tff(tptp_fun_Y_14_type, type, (
% 0.14/0.41 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_X_20_type, type, (
% 0.14/0.41 tptp_fun_X_20: $i)).
% 0.14/0.41 tff(tptp_fun_R_21_type, type, (
% 0.14/0.41 tptp_fun_R_21: $i)).
% 0.14/0.41 tff(apply_type, type, (
% 0.14/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_Z_13_type, type, (
% 0.14/0.41 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_X_15_type, type, (
% 0.14/0.41 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_X_10_type, type, (
% 0.14/0.41 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.14/0.41 tff(equivalence_type, type, (
% 0.14/0.41 equivalence: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_X_12_type, type, (
% 0.14/0.41 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_Y_11_type, type, (
% 0.14/0.41 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.14/0.41 tff(subset_type, type, (
% 0.14/0.41 subset: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_X_0_type, type, (
% 0.14/0.41 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.14/0.41 tff(1,assumption,(~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))), introduced(assumption)).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20))) | (~apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (~apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (^[A: $i, R: $i] : refl((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.14/0.42 tff(10,plain,
% 0.14/0.42 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[9, 7])).
% 0.14/0.42 tff(11,plain,
% 0.14/0.42 (^[A: $i, R: $i] : trans(monotonicity(rewrite(((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) <=> (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A))))), rewrite((~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))) <=> (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), rewrite((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))), rewrite((((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(12,plain,
% 0.14/0.42 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.14/0.42 tff(13,plain,
% 0.14/0.42 (^[A: $i, R: $i] : rewrite((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(14,plain,
% 0.14/0.42 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.14/0.42 tff(15,plain,
% 0.14/0.42 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(16,plain,
% 0.14/0.42 (^[A: $i, R: $i] : rewrite((equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(17,plain,
% 0.14/0.42 (![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.42 tff(18,axiom,(![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.14/0.42 tff(19,plain,
% 0.14/0.42 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.14/0.42 tff(20,plain,
% 0.14/0.42 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.14/0.42 tff(21,plain,(
% 0.14/0.42 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[20])).
% 0.14/0.42 tff(22,plain,
% 0.14/0.42 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.14/0.42 tff(23,plain,
% 0.14/0.42 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.14/0.43 tff(24,plain,
% 0.14/0.43 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[23, 10])).
% 0.14/0.43 tff(25,plain,
% 0.14/0.43 (![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.14/0.43 tff(26,plain,
% 0.14/0.43 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~((~member(tptp_fun_Y_11(R!21, E!22), E!22)) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)))) | (~((~member(tptp_fun_Z_13(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~((~member(tptp_fun_Y_11(R!21, E!22), E!22)) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)))) | (~((~member(tptp_fun_Z_13(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(27,plain,
% 0.14/0.43 ((~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))))) <=> (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~((~member(tptp_fun_Y_11(R!21, E!22), E!22)) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)))) | (~((~member(tptp_fun_Z_13(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(28,plain,
% 0.14/0.43 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~((~member(tptp_fun_Y_11(R!21, E!22), E!22)) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)))) | (~((~member(tptp_fun_Z_13(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[27])).
% 0.23/0.44 tff(29,plain,
% 0.23/0.44 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~((~member(tptp_fun_Y_11(R!21, E!22), E!22)) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)))) | (~((~member(tptp_fun_Z_13(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[28, 26])).
% 0.23/0.44 tff(30,plain,
% 0.23/0.44 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~member(tptp_fun_Y_11(R!21, E!22), E!22)))) | (~(apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_Z_13(R!21, E!22), E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(31,plain,
% 0.23/0.44 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~((~member(tptp_fun_Y_11(R!21, E!22), E!22)) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)))) | (~((~member(tptp_fun_Z_13(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.23/0.44 tff(32,plain,
% 0.23/0.44 (~((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~((~member(tptp_fun_Y_11(R!21, E!22), E!22)) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)))) | (~((~member(tptp_fun_Z_13(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.23/0.44 tff(33,plain,
% 0.23/0.44 (((~(equivalence(R!21, E!22) | (~((~member(tptp_fun_X_10(R!21, E!22), E!22)) | apply(R!21, tptp_fun_X_10(R!21, E!22), tptp_fun_X_10(R!21, E!22)))) | (~((~member(tptp_fun_Y_11(R!21, E!22), E!22)) | (~member(tptp_fun_X_12(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_X_12(R!21, E!22), tptp_fun_Y_11(R!21, E!22))) | apply(R!21, tptp_fun_Y_11(R!21, E!22), tptp_fun_X_12(R!21, E!22)))) | (~((~member(tptp_fun_Z_13(R!21, E!22), E!22)) | (~member(tptp_fun_Y_14(R!21, E!22), E!22)) | (~member(tptp_fun_X_15(R!21, E!22), E!22)) | (~apply(R!21, tptp_fun_Y_14(R!21, E!22), tptp_fun_Z_13(R!21, E!22))) | (~apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Y_14(R!21, E!22))) | apply(R!21, tptp_fun_X_15(R!21, E!22), tptp_fun_Z_13(R!21, E!22)))))) | (~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))) | ((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(34,plain,
% 0.23/0.44 ((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.23/0.44 tff(35,plain,
% 0.23/0.44 ((~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))) <=> (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(36,plain,
% 0.23/0.45 ((~![E: $i, R: $i, X: $i] : ((equivalence(R, E) & subset(X, E)) => equivalence(R, X))) <=> (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(37,axiom,(~![E: $i, R: $i, X: $i] : ((equivalence(R, E) & subset(X, E)) => equivalence(R, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII01')).
% 0.23/0.45 tff(38,plain,
% 0.23/0.45 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.23/0.45 tff(39,plain,
% 0.23/0.45 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.23/0.45 tff(40,plain,
% 0.23/0.45 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.23/0.45 tff(41,plain,
% 0.23/0.45 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.23/0.45 tff(42,plain,(
% 0.23/0.45 ~((~(equivalence(R!21, E!22) & subset(X!20, E!22))) | equivalence(R!21, X!20))),
% 0.23/0.45 inference(skolemize,[status(sab)],[41])).
% 0.23/0.45 tff(43,plain,
% 0.23/0.45 (equivalence(R!21, E!22) & subset(X!20, E!22)),
% 0.23/0.45 inference(or_elim,[status(thm)],[42])).
% 0.23/0.45 tff(44,plain,
% 0.23/0.45 (equivalence(R!21, E!22)),
% 0.23/0.45 inference(and_elim,[status(thm)],[43])).
% 0.23/0.45 tff(45,plain,
% 0.23/0.45 ((~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))) | (~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(46,plain,
% 0.23/0.45 ((~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.23/0.45 tff(47,plain,
% 0.23/0.45 (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[46, 34])).
% 0.23/0.45 tff(48,plain,
% 0.23/0.45 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))) | ![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(49,plain,
% 0.23/0.45 (![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.23/0.45 tff(50,plain,
% 0.23/0.45 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | ((~member(tptp_fun_X_10(R!21, X!20), E!22)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) <=> ((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~member(tptp_fun_X_10(R!21, X!20), E!22)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(51,plain,
% 0.23/0.45 ((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | ((~member(tptp_fun_X_10(R!21, X!20), E!22)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(52,plain,
% 0.23/0.45 ((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~member(tptp_fun_X_10(R!21, X!20), E!22)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.23/0.45 tff(53,plain,
% 0.23/0.45 (~member(tptp_fun_X_10(R!21, X!20), E!22)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[52, 49, 3])).
% 0.23/0.45 tff(54,plain,
% 0.23/0.45 (((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20))) | member(tptp_fun_X_10(R!21, X!20), X!20)),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(55,plain,
% 0.23/0.45 (member(tptp_fun_X_10(R!21, X!20), X!20)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[54, 1])).
% 0.23/0.45 tff(56,plain,
% 0.23/0.45 (^[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))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(57,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[56])).
% 0.23/0.45 tff(58,plain,
% 0.23/0.45 (^[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))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(59,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[58])).
% 0.23/0.45 tff(60,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[59, 57])).
% 0.23/0.45 tff(61,plain,
% 0.23/0.45 (^[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)))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(62,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.23/0.45 tff(63,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(64,plain,
% 0.23/0.45 (^[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))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(65,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[64])).
% 0.23/0.45 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')).
% 0.23/0.45 tff(67,plain,
% 0.23/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.23/0.45 tff(68,plain,
% 0.23/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.23/0.45 tff(69,plain,(
% 0.23/0.45 ![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)))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[68])).
% 0.23/0.45 tff(70,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.23/0.45 tff(71,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.23/0.45 tff(72,plain,
% 0.23/0.45 ((~![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!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22)))) | (~(subset(X!20, E!22) | (~((~member(tptp_fun_X_0(E!22, X!20), X!20)) | member(tptp_fun_X_0(E!22, X!20), E!22)))))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(73,plain,
% 0.23/0.45 (~((~((~subset(X!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22)))) | (~(subset(X!20, E!22) | (~((~member(tptp_fun_X_0(E!22, X!20), X!20)) | member(tptp_fun_X_0(E!22, X!20), E!22))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.23/0.45 tff(74,plain,
% 0.23/0.45 (((~((~subset(X!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22)))) | (~(subset(X!20, E!22) | (~((~member(tptp_fun_X_0(E!22, X!20), X!20)) | member(tptp_fun_X_0(E!22, X!20), E!22)))))) | ((~subset(X!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22)))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(75,plain,
% 0.23/0.45 ((~subset(X!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.23/0.45 tff(76,plain,
% 0.23/0.45 (subset(X!20, E!22)),
% 0.23/0.45 inference(and_elim,[status(thm)],[43])).
% 0.23/0.45 tff(77,plain,
% 0.23/0.45 ((~((~subset(X!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22)))) | (~subset(X!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(78,plain,
% 0.23/0.45 ((~((~subset(X!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22)))) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.23/0.45 tff(79,plain,
% 0.23/0.45 (![X: $i] : ((~member(X, X!20)) | member(X, E!22))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.23/0.45 tff(80,plain,
% 0.23/0.45 (((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_X_10(R!21, X!20), X!20)) | member(tptp_fun_X_10(R!21, X!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_X_10(R!21, X!20), X!20)) | member(tptp_fun_X_10(R!21, X!20), E!22))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(81,plain,
% 0.23/0.46 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_X_10(R!21, X!20), X!20)) | member(tptp_fun_X_10(R!21, X!20), E!22))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(82,plain,
% 0.23/0.46 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_X_10(R!21, X!20), X!20)) | member(tptp_fun_X_10(R!21, X!20), E!22)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.23/0.46 tff(83,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[82, 79, 55, 53])).
% 0.23/0.46 tff(84,plain,((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(85,assumption,(~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))), introduced(assumption)).
% 0.23/0.46 tff(86,plain,
% 0.23/0.46 (((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20))) | member(tptp_fun_X_12(R!21, X!20), X!20)),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(87,plain,
% 0.23/0.46 (member(tptp_fun_X_12(R!21, X!20), X!20)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.23/0.46 tff(88,plain,
% 0.23/0.46 (((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_X_12(R!21, X!20), X!20)) | member(tptp_fun_X_12(R!21, X!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | member(tptp_fun_X_12(R!21, X!20), E!22))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(89,plain,
% 0.23/0.46 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_X_12(R!21, X!20), X!20)) | member(tptp_fun_X_12(R!21, X!20), E!22))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(90,plain,
% 0.23/0.46 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | member(tptp_fun_X_12(R!21, X!20), E!22)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.23/0.46 tff(91,plain,
% 0.23/0.46 (member(tptp_fun_X_12(R!21, X!20), E!22)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[90, 79, 87])).
% 0.23/0.46 tff(92,plain,
% 0.23/0.46 (((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20))) | member(tptp_fun_Y_11(R!21, X!20), X!20)),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(93,plain,
% 0.23/0.46 (member(tptp_fun_Y_11(R!21, X!20), X!20)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[92, 85])).
% 0.23/0.46 tff(94,plain,
% 0.23/0.46 (((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | member(tptp_fun_Y_11(R!21, X!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_Y_11(R!21, X!20), X!20)) | member(tptp_fun_Y_11(R!21, X!20), E!22))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(95,plain,
% 0.23/0.46 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | member(tptp_fun_Y_11(R!21, X!20), E!22))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(96,plain,
% 0.23/0.46 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_Y_11(R!21, X!20), X!20)) | member(tptp_fun_Y_11(R!21, X!20), E!22)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.23/0.46 tff(97,plain,
% 0.23/0.46 (member(tptp_fun_Y_11(R!21, X!20), E!22)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[96, 79, 93])).
% 0.23/0.46 tff(98,plain,
% 0.23/0.46 (((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(99,plain,
% 0.23/0.46 (~apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[98, 85])).
% 0.23/0.46 tff(100,plain,
% 0.23/0.46 (((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20))) | apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(101,plain,
% 0.23/0.46 (apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[100, 85])).
% 0.23/0.46 tff(102,plain,
% 0.23/0.46 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))) | ![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(103,plain,
% 0.23/0.46 (![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[102, 47])).
% 0.23/0.46 tff(104,plain,
% 0.23/0.46 (((~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | ((~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(105,plain,
% 0.23/0.46 (((~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20))) <=> ((~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(106,plain,
% 0.23/0.46 (((~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | ((~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) <=> ((~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | ((~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[105])).
% 0.23/0.46 tff(107,plain,
% 0.23/0.46 (((~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | ((~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) <=> ((~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[106, 104])).
% 0.23/0.46 tff(108,plain,
% 0.23/0.46 ((~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | ((~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(109,plain,
% 0.23/0.46 ((~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.23/0.46 tff(110,plain,
% 0.23/0.46 ((~member(tptp_fun_X_12(R!21, X!20), E!22)) | (~member(tptp_fun_Y_11(R!21, X!20), E!22))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[109, 103, 101, 99])).
% 0.23/0.46 tff(111,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[110, 97, 91])).
% 0.23/0.46 tff(112,plain,((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(113,plain,
% 0.23/0.46 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, X!20)) | (~apply(R!21, X, Y)) | apply(R!21, Y, X) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, X!20)) | (~apply(R!21, X, Y)) | apply(R!21, Y, X) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20)))))))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(114,plain,
% 0.23/0.47 ((~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~member(tptp_fun_Y_11(R!21, X!20), X!20)))) | (~(apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)) | (~member(Y, X!20)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20)) | (~member(Z, X!20)))))))))) <=> (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, X!20)) | (~apply(R!21, X, Y)) | apply(R!21, Y, X) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20))))))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(115,plain,
% 0.23/0.47 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~member(tptp_fun_Y_11(R!21, X!20), X!20)))) | (~(apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)) | (~member(Y, X!20)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20)) | (~member(Z, X!20))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, X!20)) | (~apply(R!21, X, Y)) | apply(R!21, Y, X) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20)))))))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[114])).
% 0.23/0.47 tff(116,plain,
% 0.23/0.47 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~member(tptp_fun_Y_11(R!21, X!20), X!20)))) | (~(apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)) | (~member(Y, X!20)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20)) | (~member(Z, X!20))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, X!20)) | (~apply(R!21, X, Y)) | apply(R!21, Y, X) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20)))))))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[115, 113])).
% 0.23/0.48 tff(117,plain,
% 0.23/0.48 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~(apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~member(tptp_fun_Y_11(R!21, X!20), X!20)))) | (~(apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : (apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)) | (~member(Y, X!20)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20)) | (~member(Z, X!20))))))))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(118,plain,
% 0.23/0.48 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, X!20)) | (~apply(R!21, X, Y)) | apply(R!21, Y, X) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20))))))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.23/0.48 tff(119,plain,
% 0.23/0.48 (~((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, X!20)) | (~apply(R!21, X, Y)) | apply(R!21, Y, X) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20)))))))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[118, 25])).
% 0.23/0.48 tff(120,plain,
% 0.23/0.48 (((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~equivalence(R!21, X!20)) | (~((~![X: $i] : ((~member(X, X!20)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, X!20)) | (~apply(R!21, X, Y)) | apply(R!21, Y, X) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, X!20)) | (~member(Y, X!20))))))))) | (equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(121,plain,
% 0.23/0.48 (equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.23/0.48 tff(122,plain,
% 0.23/0.48 (~equivalence(R!21, X!20)),
% 0.23/0.48 inference(or_elim,[status(thm)],[42])).
% 0.23/0.48 tff(123,plain,
% 0.23/0.48 ((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(124,plain,
% 0.23/0.48 ((~(equivalence(R!21, X!20) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))))) | (~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.23/0.48 tff(125,plain,
% 0.23/0.48 ((~((~member(tptp_fun_X_10(R!21, X!20), X!20)) | apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20)))) | (~((~member(tptp_fun_Y_11(R!21, X!20), X!20)) | (~member(tptp_fun_X_12(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))) | (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.23/0.49 tff(126,plain,
% 0.23/0.49 (~((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[125, 112, 84])).
% 0.23/0.49 tff(127,plain,
% 0.23/0.49 (((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | member(tptp_fun_Y_14(R!21, X!20), X!20)),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(128,plain,
% 0.23/0.49 (member(tptp_fun_Y_14(R!21, X!20), X!20)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.23/0.49 tff(129,plain,
% 0.23/0.49 (((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_Y_14(R!21, X!20), X!20)) | member(tptp_fun_Y_14(R!21, X!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | member(tptp_fun_Y_14(R!21, X!20), E!22))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(130,plain,
% 0.23/0.49 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_Y_14(R!21, X!20), X!20)) | member(tptp_fun_Y_14(R!21, X!20), E!22))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(131,plain,
% 0.23/0.49 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | member(tptp_fun_Y_14(R!21, X!20), E!22)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.23/0.49 tff(132,plain,
% 0.23/0.49 (member(tptp_fun_Y_14(R!21, X!20), E!22)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[131, 79, 128])).
% 0.23/0.49 tff(133,plain,
% 0.23/0.49 (((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | member(tptp_fun_X_15(R!21, X!20), X!20)),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(134,plain,
% 0.23/0.49 (member(tptp_fun_X_15(R!21, X!20), X!20)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[133, 126])).
% 0.23/0.49 tff(135,plain,
% 0.23/0.49 (((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_X_15(R!21, X!20), X!20)) | member(tptp_fun_X_15(R!21, X!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | member(tptp_fun_X_15(R!21, X!20), E!22))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(136,plain,
% 0.23/0.49 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_X_15(R!21, X!20), X!20)) | member(tptp_fun_X_15(R!21, X!20), E!22))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(137,plain,
% 0.23/0.49 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | member(tptp_fun_X_15(R!21, X!20), E!22)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.23/0.49 tff(138,plain,
% 0.23/0.49 (member(tptp_fun_X_15(R!21, X!20), E!22)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[137, 79, 134])).
% 0.23/0.49 tff(139,plain,
% 0.23/0.49 (((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | member(tptp_fun_Z_13(R!21, X!20), X!20)),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(140,plain,
% 0.23/0.49 (member(tptp_fun_Z_13(R!21, X!20), X!20)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[139, 126])).
% 0.23/0.49 tff(141,plain,
% 0.23/0.49 (((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | member(tptp_fun_Z_13(R!21, X!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_Z_13(R!21, X!20), X!20)) | member(tptp_fun_Z_13(R!21, X!20), E!22))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(142,plain,
% 0.23/0.49 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | ((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | member(tptp_fun_Z_13(R!21, X!20), E!22))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(143,plain,
% 0.23/0.49 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_Z_13(R!21, X!20), X!20)) | member(tptp_fun_Z_13(R!21, X!20), E!22)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.23/0.49 tff(144,plain,
% 0.23/0.49 (member(tptp_fun_Z_13(R!21, X!20), E!22)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[143, 79, 140])).
% 0.23/0.49 tff(145,plain,
% 0.23/0.49 (((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(146,plain,
% 0.23/0.49 (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[145, 126])).
% 0.23/0.49 tff(147,plain,
% 0.23/0.49 (((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(148,plain,
% 0.23/0.49 (apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[147, 126])).
% 0.23/0.49 tff(149,plain,
% 0.23/0.49 (((~member(tptp_fun_Z_13(R!21, X!20), X!20)) | (~member(tptp_fun_Y_14(R!21, X!20), X!20)) | (~member(tptp_fun_X_15(R!21, X!20), X!20)) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(150,plain,
% 0.23/0.49 (apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[149, 126])).
% 0.23/0.49 tff(151,plain,
% 0.23/0.49 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R!21, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)) | apply(R!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))) | ![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(152,plain,
% 0.23/0.49 (![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[151, 47])).
% 0.23/0.49 tff(153,plain,
% 0.23/0.49 (((~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))) | ((~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(154,plain,
% 0.23/0.49 ((apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22))) <=> ((~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(155,plain,
% 0.23/0.49 (((~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))) | (apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))) | ((~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[154])).
% 0.23/0.49 tff(156,plain,
% 0.23/0.49 (((~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))) | (apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[155, 153])).
% 0.23/0.49 tff(157,plain,
% 0.23/0.49 ((~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))) | (apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(158,plain,
% 0.23/0.50 ((~![X: $i, Y: $i, Z: $i] : (apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~apply(R!21, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.23/0.50 tff(159,plain,
% 0.23/0.50 ((~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[158, 152, 150, 148, 146])).
% 0.23/0.50 tff(160,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[159, 144, 138, 132])).
% 0.23/0.50 % SZS output end Proof
% 0.23/0.50 % E exiting
%------------------------------------------------------------------------------