TSTP Solution File: SET765+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET765+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 : Tue Sep 20 05:07:55 EDT 2022
% Result : Theorem 0.11s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET765+4 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.35 % Computer : n023.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 3 08:10:03 EDT 2022
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.35 Usage: tptp [options] [-file:]file
% 0.11/0.35 -h, -? prints this message.
% 0.11/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.35 -m, -model generate model.
% 0.11/0.35 -p, -proof generate proof.
% 0.11/0.35 -c, -core generate unsat core of named formulas.
% 0.11/0.35 -st, -statistics display statistics.
% 0.11/0.35 -t:timeout set timeout (in second).
% 0.11/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.35 -<param>:<value> configuration parameter and value.
% 0.11/0.35 -o:<output-file> file to place output in.
% 0.11/0.40 % SZS status Theorem
% 0.11/0.40 % SZS output start Proof
% 0.11/0.40 tff(member_type, type, (
% 0.11/0.40 member: ( $i * $i ) > $o)).
% 0.11/0.40 tff(tptp_fun_E_22_type, type, (
% 0.11/0.40 tptp_fun_E_22: $i)).
% 0.11/0.40 tff(tptp_fun_Y_14_type, type, (
% 0.11/0.40 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.11/0.40 tff(tptp_fun_X_20_type, type, (
% 0.11/0.40 tptp_fun_X_20: $i)).
% 0.11/0.40 tff(tptp_fun_R_21_type, type, (
% 0.11/0.40 tptp_fun_R_21: $i)).
% 0.11/0.40 tff(tptp_fun_Z_13_type, type, (
% 0.11/0.40 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.11/0.40 tff(tptp_fun_X_15_type, type, (
% 0.11/0.40 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.11/0.40 tff(apply_type, type, (
% 0.11/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.11/0.40 tff(tptp_fun_X_10_type, type, (
% 0.11/0.40 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.11/0.40 tff(equivalence_type, type, (
% 0.11/0.40 equivalence: ( $i * $i ) > $o)).
% 0.11/0.40 tff(tptp_fun_Y_11_type, type, (
% 0.11/0.40 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.11/0.40 tff(tptp_fun_X_12_type, type, (
% 0.11/0.40 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.11/0.40 tff(subset_type, type, (
% 0.11/0.40 subset: ( $i * $i ) > $o)).
% 0.11/0.40 tff(tptp_fun_X_0_type, type, (
% 0.11/0.40 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.11/0.40 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)).
% 0.11/0.40 tff(2,plain,
% 0.11/0.40 (((~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)))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(3,plain,
% 0.11/0.40 (~apply(R!21, tptp_fun_X_10(R!21, X!20), tptp_fun_X_10(R!21, X!20))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.11/0.40 tff(4,plain,
% 0.11/0.40 (^[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)))))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(5,plain,
% 0.11/0.40 (![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))))))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.40 tff(6,plain,
% 0.11/0.40 (^[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)))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(7,plain,
% 0.11/0.40 (![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))))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.40 tff(8,plain,
% 0.11/0.40 (^[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)))))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(9,plain,
% 0.11/0.40 (![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))))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.11/0.41 tff(10,plain,
% 0.11/0.41 (![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))))))))),
% 0.11/0.41 inference(transitivity,[status(thm)],[9, 7])).
% 0.11/0.41 tff(11,plain,
% 0.11/0.41 (^[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))))))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(12,plain,
% 0.11/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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))))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.41 tff(13,plain,
% 0.11/0.41 (^[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) | (~(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))))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(14,plain,
% 0.11/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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)))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.41 tff(15,plain,
% 0.11/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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))))))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(16,plain,
% 0.11/0.41 (^[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)))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(17,plain,
% 0.11/0.41 (![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))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.41 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/sandbox/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.11/0.41 tff(19,plain,
% 0.11/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.41 tff(20,plain,
% 0.11/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.41 tff(21,plain,(
% 0.11/0.41 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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))))))))),
% 0.11/0.41 inference(skolemize,[status(sab)],[20])).
% 0.11/0.41 tff(22,plain,
% 0.11/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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)))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.41 tff(23,plain,
% 0.11/0.41 (![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))))))))),
% 0.11/0.42 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.11/0.42 tff(24,plain,
% 0.11/0.42 (![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))))))))),
% 0.11/0.42 inference(modus_ponens,[status(thm)],[23, 10])).
% 0.11/0.42 tff(25,plain,
% 0.11/0.42 (![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))))))))))),
% 0.11/0.42 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.11/0.42 tff(26,plain,
% 0.11/0.42 (((~![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] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, 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)))) | (~(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] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))))))),
% 0.11/0.42 inference(rewrite,[status(thm)],[])).
% 0.11/0.42 tff(27,plain,
% 0.11/0.42 ((~((~(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)))) | (~(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] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))))))),
% 0.11/0.42 inference(rewrite,[status(thm)],[])).
% 0.11/0.42 tff(28,plain,
% 0.11/0.42 (((~![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)))) | (~(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] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))))))),
% 0.11/0.43 inference(monotonicity,[status(thm)],[27])).
% 0.11/0.43 tff(29,plain,
% 0.11/0.43 (((~![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)))) | (~(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] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))))))),
% 0.11/0.43 inference(transitivity,[status(thm)],[28, 26])).
% 0.11/0.43 tff(30,plain,
% 0.11/0.43 ((~![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))))))))))),
% 0.11/0.43 inference(quant_inst,[status(thm)],[])).
% 0.11/0.43 tff(31,plain,
% 0.11/0.43 ((~![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] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))))))),
% 0.11/0.43 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.43 tff(32,plain,
% 0.11/0.43 (~((~(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] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))))),
% 0.11/0.43 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.11/0.43 tff(33,plain,
% 0.11/0.43 (((~(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] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))))) | ((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))),
% 0.11/0.43 inference(tautology,[status(thm)],[])).
% 0.11/0.43 tff(34,plain,
% 0.11/0.43 ((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))),
% 0.11/0.43 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.11/0.43 tff(35,plain,
% 0.11/0.43 ((~![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)))),
% 0.11/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(36,plain,
% 0.18/0.43 ((~![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(37,axiom,(~![E: $i, R: $i, X: $i] : ((equivalence(R, E) & subset(X, E)) => equivalence(R, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIII01')).
% 0.18/0.43 tff(38,plain,
% 0.18/0.43 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.43 tff(39,plain,
% 0.18/0.43 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.18/0.43 tff(40,plain,
% 0.18/0.43 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.18/0.43 tff(41,plain,
% 0.18/0.43 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.18/0.43 tff(42,plain,
% 0.18/0.43 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.18/0.43 tff(43,plain,
% 0.18/0.43 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.18/0.43 tff(44,plain,
% 0.18/0.43 (~![E: $i, R: $i, X: $i] : ((~(equivalence(R, E) & subset(X, E))) | equivalence(R, X))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[43, 35])).
% 0.18/0.43 tff(45,plain,(
% 0.18/0.43 ~((~(equivalence(R!21, E!22) & subset(X!20, E!22))) | equivalence(R!21, X!20))),
% 0.18/0.43 inference(skolemize,[status(sab)],[44])).
% 0.18/0.43 tff(46,plain,
% 0.18/0.43 (equivalence(R!21, E!22) & subset(X!20, E!22)),
% 0.18/0.43 inference(or_elim,[status(thm)],[45])).
% 0.18/0.43 tff(47,plain,
% 0.18/0.43 (equivalence(R!21, E!22)),
% 0.18/0.43 inference(and_elim,[status(thm)],[46])).
% 0.18/0.43 tff(48,plain,
% 0.18/0.43 ((~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))) | (~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(49,plain,
% 0.18/0.43 ((~((~equivalence(R!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))))) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.18/0.43 tff(50,plain,
% 0.18/0.43 (~((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[49, 34])).
% 0.18/0.43 tff(51,plain,
% 0.18/0.43 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))) | ![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(52,plain,
% 0.18/0.44 (![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.18/0.44 tff(53,plain,
% 0.18/0.44 (((~![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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(54,plain,
% 0.18/0.44 ((~![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)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(55,plain,
% 0.18/0.44 ((~![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))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.44 tff(56,plain,
% 0.18/0.44 (~member(tptp_fun_X_10(R!21, X!20), E!22)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[55, 52, 3])).
% 0.18/0.44 tff(57,plain,
% 0.18/0.44 (((~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)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(58,plain,
% 0.18/0.44 (member(tptp_fun_X_10(R!21, X!20), X!20)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[57, 1])).
% 0.18/0.44 tff(59,plain,
% 0.18/0.44 (^[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))))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(60,plain,
% 0.18/0.44 (![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)))))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.44 tff(61,plain,
% 0.18/0.44 (^[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))))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(62,plain,
% 0.18/0.44 (![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)))))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 (![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)))))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[62, 60])).
% 0.18/0.44 tff(64,plain,
% 0.18/0.44 (^[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)))))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(65,plain,
% 0.18/0.44 (![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)))))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[64])).
% 0.18/0.44 tff(66,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(67,plain,
% 0.18/0.44 (^[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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(68,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[67])).
% 0.18/0.44 tff(69,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.18/0.44 tff(70,plain,
% 0.18/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.44 tff(71,plain,
% 0.18/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.18/0.44 tff(72,plain,(
% 0.18/0.44 ![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)))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[71])).
% 0.18/0.44 tff(73,plain,
% 0.18/0.44 (![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)))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.18/0.44 tff(74,plain,
% 0.18/0.44 (![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)))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.18/0.44 tff(75,plain,
% 0.18/0.44 ((~![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)))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(76,plain,
% 0.18/0.44 (~((~((~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))))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.18/0.44 tff(77,plain,
% 0.18/0.44 (((~((~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)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(78,plain,
% 0.18/0.44 ((~subset(X!20, E!22)) | ![X: $i] : ((~member(X, X!20)) | member(X, E!22))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.18/0.44 tff(79,plain,
% 0.18/0.44 (subset(X!20, E!22)),
% 0.18/0.44 inference(and_elim,[status(thm)],[46])).
% 0.18/0.44 tff(80,plain,
% 0.18/0.44 ((~((~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))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(81,plain,
% 0.18/0.44 ((~((~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))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.18/0.44 tff(82,plain,
% 0.18/0.44 (![X: $i] : ((~member(X, X!20)) | member(X, E!22))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[81, 78])).
% 0.18/0.44 tff(83,plain,
% 0.18/0.44 (((~![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))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(84,plain,
% 0.18/0.44 ((~![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))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(85,plain,
% 0.18/0.44 ((~![X: $i] : ((~member(X, X!20)) | member(X, E!22))) | (~member(tptp_fun_X_10(R!21, X!20), X!20)) | member(tptp_fun_X_10(R!21, X!20), E!22)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.18/0.44 tff(86,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[85, 82, 58, 56])).
% 0.18/0.44 tff(87,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,[]))).
% 0.18/0.44 tff(88,assumption,(~(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)))), introduced(assumption)).
% 0.18/0.44 tff(89,plain,
% 0.18/0.44 ((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))) | member(tptp_fun_Y_11(R!21, X!20), X!20)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(90,plain,
% 0.18/0.44 (member(tptp_fun_Y_11(R!21, X!20), X!20)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.18/0.44 tff(91,plain,
% 0.18/0.44 (((~![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))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(92,plain,
% 0.18/0.44 ((~![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))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(93,plain,
% 0.18/0.44 ((~![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)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.18/0.44 tff(94,plain,
% 0.18/0.44 (member(tptp_fun_Y_11(R!21, X!20), E!22)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[93, 82, 90])).
% 0.18/0.44 tff(95,plain,
% 0.18/0.44 ((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))) | member(tptp_fun_X_12(R!21, X!20), X!20)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(96,plain,
% 0.18/0.44 (member(tptp_fun_X_12(R!21, X!20), X!20)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[95, 88])).
% 0.18/0.44 tff(97,plain,
% 0.18/0.44 (((~![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))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(98,plain,
% 0.18/0.44 ((~![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))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(99,plain,
% 0.18/0.44 ((~![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)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.44 tff(100,plain,
% 0.18/0.44 (member(tptp_fun_X_12(R!21, X!20), E!22)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[99, 82, 96])).
% 0.18/0.44 tff(101,plain,
% 0.18/0.44 ((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_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(102,plain,
% 0.18/0.44 (apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[101, 88])).
% 0.18/0.44 tff(103,plain,
% 0.18/0.44 ((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_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(104,plain,
% 0.18/0.44 (~apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[103, 88])).
% 0.18/0.44 tff(105,plain,
% 0.18/0.44 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))) | ![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(106,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[105, 50])).
% 0.18/0.44 tff(107,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(108,plain,
% 0.18/0.44 (((~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))) | (~member(tptp_fun_X_12(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))) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(109,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_X_12(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | (~member(tptp_fun_X_12(R!21, X!20), E!22))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[108])).
% 0.18/0.44 tff(110,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_X_12(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | (~member(tptp_fun_X_12(R!21, X!20), E!22)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[109, 107])).
% 0.18/0.44 tff(111,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_X_12(R!21, X!20), E!22)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(112,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | apply(R!21, tptp_fun_Y_11(R!21, X!20), tptp_fun_X_12(R!21, X!20)) | (~apply(R!21, tptp_fun_X_12(R!21, X!20), tptp_fun_Y_11(R!21, X!20))) | (~member(tptp_fun_Y_11(R!21, X!20), E!22)) | (~member(tptp_fun_X_12(R!21, X!20), E!22))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.18/0.44 tff(113,plain,
% 0.18/0.44 ((~member(tptp_fun_Y_11(R!21, X!20), E!22)) | (~member(tptp_fun_X_12(R!21, X!20), E!22))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[112, 106, 104, 102])).
% 0.18/0.44 tff(114,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[113, 100, 94])).
% 0.18/0.44 tff(115,plain,(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))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(116,plain,
% 0.18/0.44 (((~![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, 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] : ((~member(Y, X!20)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | (~apply(R!21, Y, Z)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(Y, X!20)) | (~member(X, 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)))) | (~(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] : ((~member(Y, X!20)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | (~apply(R!21, Y, Z)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(Y, X!20)) | (~member(X, X!20)))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(117,plain,
% 0.18/0.44 ((~((~(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)))) | (~(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] : ((~member(Y, X!20)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | (~apply(R!21, Y, Z)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(Y, X!20)) | (~member(X, X!20))))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(118,plain,
% 0.18/0.45 (((~![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)))) | (~(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] : ((~member(Y, X!20)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | (~apply(R!21, Y, Z)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(Y, X!20)) | (~member(X, X!20)))))))))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[117])).
% 0.18/0.45 tff(119,plain,
% 0.18/0.45 (((~![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)))) | (~(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] : ((~member(Y, X!20)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | (~apply(R!21, Y, Z)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(Y, X!20)) | (~member(X, X!20)))))))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[118, 116])).
% 0.18/0.45 tff(120,plain,
% 0.18/0.45 ((~![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))))))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(121,plain,
% 0.18/0.45 ((~![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] : ((~member(Y, X!20)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | (~apply(R!21, Y, Z)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(Y, X!20)) | (~member(X, X!20))))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.18/0.45 tff(122,plain,
% 0.18/0.45 (~((~(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] : ((~member(Y, X!20)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | (~apply(R!21, Y, Z)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(Y, X!20)) | (~member(X, X!20)))))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[121, 25])).
% 0.18/0.45 tff(123,plain,
% 0.18/0.45 (((~(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] : ((~member(Y, X!20)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, X!20)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!20)) | (~apply(R!21, Y, Z)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(Y, X!20)) | (~member(X, 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)))) | (~(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)))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(124,plain,
% 0.18/0.45 (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))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.18/0.45 tff(125,plain,
% 0.18/0.45 (~equivalence(R!21, X!20)),
% 0.18/0.45 inference(or_elim,[status(thm)],[45])).
% 0.18/0.45 tff(126,plain,
% 0.18/0.45 ((~(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) | (~((~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))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(127,plain,
% 0.18/0.45 ((~(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)))))) | (~((~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))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.18/0.46 tff(128,plain,
% 0.18/0.46 ((~((~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))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[127, 124])).
% 0.18/0.46 tff(129,plain,
% 0.18/0.46 (~(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)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[128, 115, 87])).
% 0.18/0.46 tff(130,plain,
% 0.18/0.46 ((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))) | member(tptp_fun_Y_14(R!21, X!20), X!20)),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(131,plain,
% 0.18/0.46 (member(tptp_fun_Y_14(R!21, X!20), X!20)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.18/0.46 tff(132,plain,
% 0.18/0.46 (((~![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))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(133,plain,
% 0.18/0.46 ((~![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))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(134,plain,
% 0.18/0.46 ((~![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)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.18/0.46 tff(135,plain,
% 0.18/0.46 (member(tptp_fun_Y_14(R!21, X!20), E!22)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[134, 82, 131])).
% 0.18/0.46 tff(136,plain,
% 0.18/0.46 ((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))) | member(tptp_fun_Z_13(R!21, X!20), X!20)),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(137,plain,
% 0.18/0.46 (member(tptp_fun_Z_13(R!21, X!20), X!20)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[136, 129])).
% 0.18/0.46 tff(138,plain,
% 0.18/0.46 (((~![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))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(139,plain,
% 0.18/0.46 ((~![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))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(140,plain,
% 0.18/0.46 ((~![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)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.18/0.46 tff(141,plain,
% 0.18/0.46 (member(tptp_fun_Z_13(R!21, X!20), E!22)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[140, 82, 137])).
% 0.18/0.46 tff(142,plain,
% 0.18/0.46 ((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))) | member(tptp_fun_X_15(R!21, X!20), X!20)),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(143,plain,
% 0.18/0.46 (member(tptp_fun_X_15(R!21, X!20), X!20)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[142, 129])).
% 0.18/0.46 tff(144,plain,
% 0.18/0.46 (((~![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))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(145,plain,
% 0.18/0.46 ((~![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))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(146,plain,
% 0.18/0.46 ((~![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)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.18/0.46 tff(147,plain,
% 0.18/0.46 (member(tptp_fun_X_15(R!21, X!20), E!22)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[146, 82, 143])).
% 0.18/0.46 tff(148,plain,
% 0.18/0.46 ((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))) | apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(149,plain,
% 0.18/0.46 (apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[148, 129])).
% 0.18/0.46 tff(150,plain,
% 0.18/0.46 ((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))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(151,plain,
% 0.18/0.46 (apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[150, 129])).
% 0.18/0.46 tff(152,plain,
% 0.18/0.46 ((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))) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(153,plain,
% 0.18/0.46 (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[152, 129])).
% 0.18/0.46 tff(154,plain,
% 0.18/0.46 (((~![X: $i] : ((~member(X, E!22)) | apply(R!21, X, X))) | (~![X: $i, Y: $i] : ((~member(Y, E!22)) | apply(R!21, Y, X) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22))))) | ![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(155,plain,
% 0.18/0.46 (![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[154, 50])).
% 0.18/0.46 tff(156,plain,
% 0.18/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, 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_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, 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_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(157,plain,
% 0.18/0.46 (((~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))) | (~member(tptp_fun_Y_14(R!21, X!20), 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))) | (~member(tptp_fun_X_15(R!21, X!20), 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_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(158,plain,
% 0.18/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_Y_14(R!21, X!20), 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))) | (~member(tptp_fun_X_15(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, 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_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[157])).
% 0.18/0.46 tff(159,plain,
% 0.18/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_Y_14(R!21, X!20), 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))) | (~member(tptp_fun_X_15(R!21, X!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, 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_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[158, 156])).
% 0.18/0.46 tff(160,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, 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))) | (~member(tptp_fun_Y_14(R!21, X!20), 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))) | (~member(tptp_fun_X_15(R!21, X!20), E!22)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(161,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | (~apply(R!21, Y, Z)) | (~member(Y, E!22)) | apply(R!21, X, Z) | (~apply(R!21, X, Y)) | (~member(X, E!22)))) | apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Z_13(R!21, X!20)) | (~apply(R!21, tptp_fun_X_15(R!21, X!20), tptp_fun_Y_14(R!21, X!20))) | (~apply(R!21, tptp_fun_Y_14(R!21, X!20), tptp_fun_Z_13(R!21, X!20))) | (~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.46 tff(162,plain,
% 0.18/0.46 ((~member(tptp_fun_X_15(R!21, X!20), E!22)) | (~member(tptp_fun_Z_13(R!21, X!20), E!22)) | (~member(tptp_fun_Y_14(R!21, X!20), E!22))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[161, 155, 153, 151, 149])).
% 0.18/0.46 tff(163,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[162, 147, 141, 135])).
% 0.18/0.46 % SZS output end Proof
%------------------------------------------------------------------------------