%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET774+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n017.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 05:07:58 EDT 2022

% Result   : Theorem 0.21s 0.41s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET774+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Sep  3 07:16:08 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.21/0.41  % SZS status Theorem
% 0.21/0.41  % SZS output start Proof
% 0.21/0.41  tff(member_type, type, (
% 0.21/0.41     member: ( $i * $i ) > $o)).
% 0.21/0.41  tff(tptp_fun_E_22_type, type, (
% 0.21/0.41     tptp_fun_E_22: $i)).
% 0.21/0.41  tff(tptp_fun_X_19_type, type, (
% 0.21/0.41     tptp_fun_X_19: ( $i * $i ) > $i)).
% 0.21/0.41  tff(tptp_fun_R_20_type, type, (
% 0.21/0.41     tptp_fun_R_20: $i)).
% 0.21/0.41  tff(tptp_fun_X_21_type, type, (
% 0.21/0.41     tptp_fun_X_21: $i)).
% 0.21/0.41  tff(tptp_fun_Z_17_type, type, (
% 0.21/0.41     tptp_fun_Z_17: ( $i * $i ) > $i)).
% 0.21/0.41  tff(tptp_fun_Y_18_type, type, (
% 0.21/0.41     tptp_fun_Y_18: ( $i * $i ) > $i)).
% 0.21/0.41  tff(apply_type, type, (
% 0.21/0.41     apply: ( $i * $i * $i ) > $o)).
% 0.21/0.41  tff(tptp_fun_X_16_type, type, (
% 0.21/0.41     tptp_fun_X_16: ( $i * $i ) > $i)).
% 0.21/0.41  tff(pre_order_type, type, (
% 0.21/0.41     pre_order: ( $i * $i ) > $o)).
% 0.21/0.41  tff(subset_type, type, (
% 0.21/0.41     subset: ( $i * $i ) > $o)).
% 0.21/0.41  tff(tptp_fun_X_0_type, type, (
% 0.21/0.41     tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.21/0.41  tff(1,assumption,(~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))), introduced(assumption)).
% 0.21/0.41  tff(2,plain,
% 0.21/0.41      (((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))) | (~apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))),
% 0.21/0.41      inference(tautology,[status(thm)],[])).
% 0.21/0.41  tff(3,plain,
% 0.21/0.41      (~apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))),
% 0.21/0.41      inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.41  tff(4,plain,
% 0.21/0.41      (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(5,plain,
% 0.21/0.41      (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[4])).
% 0.21/0.41  tff(6,plain,
% 0.21/0.41      (^[R: $i, E: $i] : refl((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(7,plain,
% 0.21/0.41      (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[6])).
% 0.21/0.41  tff(8,plain,
% 0.21/0.41      (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(9,plain,
% 0.21/0.41      (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[8])).
% 0.21/0.41  tff(10,plain,
% 0.21/0.41      (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.21/0.41      inference(transitivity,[status(thm)],[9, 7])).
% 0.21/0.41  tff(11,plain,
% 0.21/0.41      (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))) <=> (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), rewrite((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))), rewrite((((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(12,plain,
% 0.21/0.42      (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[11])).
% 0.21/0.42  tff(13,plain,
% 0.21/0.42      (^[R: $i, E: $i] : rewrite((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(14,plain,
% 0.21/0.42      (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[13])).
% 0.21/0.42  tff(15,plain,
% 0.21/0.42      (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.42      inference(rewrite,[status(thm)],[])).
% 0.21/0.42  tff(16,plain,
% 0.21/0.42      (^[R: $i, E: $i] : rewrite((pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(17,plain,
% 0.21/0.42      (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[16])).
% 0.21/0.42  tff(18,axiom,(![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax','pre_order')).
% 0.21/0.42  tff(19,plain,
% 0.21/0.42      (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.42  tff(20,plain,
% 0.21/0.42      (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.42  tff(21,plain,(
% 0.21/0.42      ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.21/0.42      inference(skolemize,[status(sab)],[20])).
% 0.21/0.42  tff(22,plain,
% 0.21/0.42      (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.42  tff(23,plain,
% 0.21/0.42      (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[22, 12])).
% 0.21/0.42  tff(24,plain,
% 0.21/0.42      (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[23, 10])).
% 0.21/0.42  tff(25,plain,
% 0.21/0.42      (![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[24, 5])).
% 0.21/0.42  tff(26,plain,
% 0.21/0.42      (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))))),
% 0.21/0.42      inference(rewrite,[status(thm)],[])).
% 0.21/0.42  tff(27,plain,
% 0.21/0.42      ((~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))) <=> (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))),
% 0.21/0.42      inference(rewrite,[status(thm)],[])).
% 0.21/0.42  tff(28,plain,
% 0.21/0.42      (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))))),
% 0.21/0.43      inference(monotonicity,[status(thm)],[27])).
% 0.21/0.43  tff(29,plain,
% 0.21/0.43      (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))))),
% 0.21/0.43      inference(transitivity,[status(thm)],[28, 26])).
% 0.21/0.43  tff(30,plain,
% 0.21/0.43      ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))),
% 0.21/0.43      inference(quant_inst,[status(thm)],[])).
% 0.21/0.43  tff(31,plain,
% 0.21/0.43      ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.43  tff(32,plain,
% 0.21/0.43      (~((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[31, 25])).
% 0.21/0.43  tff(33,plain,
% 0.21/0.43      (((~(pre_order(R!20, E!22) | (~((~member(tptp_fun_X_16(E!22, R!20), E!22)) | apply(R!20, tptp_fun_X_16(E!22, R!20), tptp_fun_X_16(E!22, R!20)))) | (~(apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Z_17(E!22, R!20)) | (~apply(R!20, tptp_fun_X_19(E!22, R!20), tptp_fun_Y_18(E!22, R!20))) | (~apply(R!20, tptp_fun_Y_18(E!22, R!20), tptp_fun_Z_17(E!22, R!20))) | (~member(tptp_fun_X_19(E!22, R!20), E!22)) | (~member(tptp_fun_Y_18(E!22, R!20), E!22)) | (~member(tptp_fun_Z_17(E!22, R!20), E!22)))))) | (~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))) | ((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))),
% 0.21/0.43      inference(tautology,[status(thm)],[])).
% 0.21/0.43  tff(34,plain,
% 0.21/0.43      ((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))),
% 0.21/0.43      inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.44  tff(35,plain,
% 0.21/0.44      ((~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))) <=> (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X)))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(36,plain,
% 0.21/0.44      ((~![E: $i, X: $i, R: $i] : ((pre_order(R, E) & subset(X, E)) => pre_order(R, X))) <=> (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X)))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(37,axiom,(~![E: $i, X: $i, R: $i] : ((pre_order(R, E) & subset(X, E)) => pre_order(R, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIII10')).
% 0.21/0.44  tff(38,plain,
% 0.21/0.44      (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.44  tff(39,plain,
% 0.21/0.44      (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[38, 35])).
% 0.21/0.44  tff(40,plain,
% 0.21/0.44      (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.44  tff(41,plain,
% 0.21/0.44      (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[40, 35])).
% 0.21/0.44  tff(42,plain,
% 0.21/0.44      (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[41, 35])).
% 0.21/0.44  tff(43,plain,
% 0.21/0.44      (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.44  tff(44,plain,
% 0.21/0.44      (~![E: $i, X: $i, R: $i] : ((~(pre_order(R, E) & subset(X, E))) | pre_order(R, X))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[43, 35])).
% 0.21/0.44  tff(45,plain,(
% 0.21/0.44      ~((~(pre_order(R!20, E!22) & subset(X!21, E!22))) | pre_order(R!20, X!21))),
% 0.21/0.44      inference(skolemize,[status(sab)],[44])).
% 0.21/0.44  tff(46,plain,
% 0.21/0.44      (pre_order(R!20, E!22) & subset(X!21, E!22)),
% 0.21/0.44      inference(or_elim,[status(thm)],[45])).
% 0.21/0.44  tff(47,plain,
% 0.21/0.44      (pre_order(R!20, E!22)),
% 0.21/0.44      inference(and_elim,[status(thm)],[46])).
% 0.21/0.44  tff(48,plain,
% 0.21/0.44      ((~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))) | (~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(49,plain,
% 0.21/0.44      ((~((~pre_order(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.44  tff(50,plain,
% 0.21/0.44      (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[49, 34])).
% 0.21/0.44  tff(51,plain,
% 0.21/0.44      (((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))) | ![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(52,plain,
% 0.21/0.44      (![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.44  tff(53,plain,
% 0.21/0.44      (((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | ((~member(tptp_fun_X_16(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) <=> ((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~member(tptp_fun_X_16(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(54,plain,
% 0.21/0.44      ((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | ((~member(tptp_fun_X_16(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))),
% 0.21/0.44      inference(quant_inst,[status(thm)],[])).
% 0.21/0.44  tff(55,plain,
% 0.21/0.44      ((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~member(tptp_fun_X_16(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.44  tff(56,plain,
% 0.21/0.44      (~member(tptp_fun_X_16(X!21, R!20), E!22)),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[55, 52, 3])).
% 0.21/0.44  tff(57,plain,
% 0.21/0.44      (((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))) | member(tptp_fun_X_16(X!21, R!20), X!21)),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(58,plain,
% 0.21/0.44      (member(tptp_fun_X_16(X!21, R!20), X!21)),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[57, 1])).
% 0.21/0.44  tff(59,plain,
% 0.21/0.44      (^[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))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(60,plain,
% 0.21/0.44      (![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)))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[59])).
% 0.21/0.44  tff(61,plain,
% 0.21/0.44      (^[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))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(62,plain,
% 0.21/0.44      (![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)))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[61])).
% 0.21/0.44  tff(63,plain,
% 0.21/0.44      (![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)))))))),
% 0.21/0.44      inference(transitivity,[status(thm)],[62, 60])).
% 0.21/0.44  tff(64,plain,
% 0.21/0.44      (^[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)))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(65,plain,
% 0.21/0.44      (![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)))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[64])).
% 0.21/0.44  tff(66,plain,
% 0.21/0.44      (![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)))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(67,plain,
% 0.21/0.44      (^[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))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(68,plain,
% 0.21/0.44      (![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)))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[67])).
% 0.21/0.44  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')).
% 0.21/0.44  tff(70,plain,
% 0.21/0.44      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.44  tff(71,plain,
% 0.21/0.44      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[70, 66])).
% 0.21/0.44  tff(72,plain,(
% 0.21/0.44      ![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)))))),
% 0.21/0.44      inference(skolemize,[status(sab)],[71])).
% 0.21/0.44  tff(73,plain,
% 0.21/0.44      (![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)))))))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[72, 65])).
% 0.21/0.44  tff(74,plain,
% 0.21/0.44      (![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)))))))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[73, 63])).
% 0.21/0.44  tff(75,plain,
% 0.21/0.44      ((~![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!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | (~(subset(X!21, E!22) | (~((~member(tptp_fun_X_0(E!22, X!21), X!21)) | member(tptp_fun_X_0(E!22, X!21), E!22)))))))),
% 0.21/0.44      inference(quant_inst,[status(thm)],[])).
% 0.21/0.44  tff(76,plain,
% 0.21/0.44      (~((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | (~(subset(X!21, E!22) | (~((~member(tptp_fun_X_0(E!22, X!21), X!21)) | member(tptp_fun_X_0(E!22, X!21), E!22))))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.44  tff(77,plain,
% 0.21/0.44      (((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | (~(subset(X!21, E!22) | (~((~member(tptp_fun_X_0(E!22, X!21), X!21)) | member(tptp_fun_X_0(E!22, X!21), E!22)))))) | ((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(78,plain,
% 0.21/0.44      ((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[77, 76])).
% 0.21/0.44  tff(79,plain,
% 0.21/0.44      (subset(X!21, E!22)),
% 0.21/0.44      inference(and_elim,[status(thm)],[46])).
% 0.21/0.44  tff(80,plain,
% 0.21/0.44      ((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | (~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(81,plain,
% 0.21/0.44      ((~((~subset(X!21, E!22)) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22)))) | ![X: $i] : ((~member(X, X!21)) | member(X, E!22))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.44  tff(82,plain,
% 0.21/0.44      (![X: $i] : ((~member(X, X!21)) | member(X, E!22))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[81, 78])).
% 0.21/0.44  tff(83,plain,
% 0.21/0.44      (((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_X_16(X!21, R!20), X!21)) | member(tptp_fun_X_16(X!21, R!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_X_16(X!21, R!20), X!21)) | member(tptp_fun_X_16(X!21, R!20), E!22))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(84,plain,
% 0.21/0.44      ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_X_16(X!21, R!20), X!21)) | member(tptp_fun_X_16(X!21, R!20), E!22))),
% 0.21/0.44      inference(quant_inst,[status(thm)],[])).
% 0.21/0.44  tff(85,plain,
% 0.21/0.44      ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_X_16(X!21, R!20), X!21)) | member(tptp_fun_X_16(X!21, R!20), E!22)),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.44  tff(86,plain,
% 0.21/0.44      ($false),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[85, 82, 58, 56])).
% 0.21/0.44  tff(87,plain,((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44  tff(88,plain,
% 0.21/0.44      (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21)))))))))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(89,plain,
% 0.21/0.45      ((~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, X!21)) | (~member(Z, X!21)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, X!21)))))))))) <=> (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21))))))))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(90,plain,
% 0.21/0.45      (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, X!21)) | (~member(Z, X!21)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, X!21))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21)))))))))))),
% 0.21/0.45      inference(monotonicity,[status(thm)],[89])).
% 0.21/0.45  tff(91,plain,
% 0.21/0.45      (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, X!21)) | (~member(Z, X!21)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, X!21))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21)))))))))))),
% 0.21/0.45      inference(transitivity,[status(thm)],[90, 88])).
% 0.21/0.45  tff(92,plain,
% 0.21/0.45      ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~member(Y, X!21)) | (~member(Z, X!21)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, X!21))))))))))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(93,plain,
% 0.21/0.45      ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21))))))))))),
% 0.21/0.46      inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.46  tff(94,plain,
% 0.21/0.46      (~((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21)))))))))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[93, 25])).
% 0.21/0.46  tff(95,plain,
% 0.21/0.46      (((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~pre_order(R!20, X!21)) | (~((~![X: $i] : ((~member(X, X!21)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, X!21)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(Y, X!21)) | (~member(X, X!21))))))))) | (pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))),
% 0.21/0.46      inference(tautology,[status(thm)],[])).
% 0.21/0.46  tff(96,plain,
% 0.21/0.46      (pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.46  tff(97,plain,
% 0.21/0.46      (~pre_order(R!20, X!21)),
% 0.21/0.46      inference(or_elim,[status(thm)],[45])).
% 0.21/0.46  tff(98,plain,
% 0.21/0.46      ((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))))),
% 0.21/0.46      inference(tautology,[status(thm)],[])).
% 0.21/0.46  tff(99,plain,
% 0.21/0.46      ((~(pre_order(R!20, X!21) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))))) | (~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[98, 97])).
% 0.21/0.46  tff(100,plain,
% 0.21/0.46      ((~((~member(tptp_fun_X_16(X!21, R!20), X!21)) | apply(R!20, tptp_fun_X_16(X!21, R!20), tptp_fun_X_16(X!21, R!20)))) | (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[99, 96])).
% 0.21/0.46  tff(101,plain,
% 0.21/0.46      (~(apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)))),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[100, 87])).
% 0.21/0.46  tff(102,plain,
% 0.21/0.46      ((apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))) | member(tptp_fun_X_19(X!21, R!20), X!21)),
% 0.21/0.46      inference(tautology,[status(thm)],[])).
% 0.21/0.46  tff(103,plain,
% 0.21/0.46      (member(tptp_fun_X_19(X!21, R!20), X!21)),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.46  tff(104,plain,
% 0.21/0.46      (((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_X_19(X!21, R!20), X!21)) | member(tptp_fun_X_19(X!21, R!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | member(tptp_fun_X_19(X!21, R!20), E!22))),
% 0.21/0.46      inference(rewrite,[status(thm)],[])).
% 0.21/0.46  tff(105,plain,
% 0.21/0.46      ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_X_19(X!21, R!20), X!21)) | member(tptp_fun_X_19(X!21, R!20), E!22))),
% 0.21/0.46      inference(quant_inst,[status(thm)],[])).
% 0.21/0.46  tff(106,plain,
% 0.21/0.46      ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | member(tptp_fun_X_19(X!21, R!20), E!22)),
% 0.21/0.46      inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.46  tff(107,plain,
% 0.21/0.46      (member(tptp_fun_X_19(X!21, R!20), E!22)),
% 0.21/0.46      inference(unit_resolution,[status(thm)],[106, 82, 103])).
% 0.21/0.46  tff(108,plain,
% 0.21/0.46      ((apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))) | member(tptp_fun_Z_17(X!21, R!20), X!21)),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(109,plain,
% 0.21/0.47      (member(tptp_fun_Z_17(X!21, R!20), X!21)),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[108, 101])).
% 0.21/0.47  tff(110,plain,
% 0.21/0.47      (((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | member(tptp_fun_Z_17(X!21, R!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)) | member(tptp_fun_Z_17(X!21, R!20), E!22))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(111,plain,
% 0.21/0.47      ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_Z_17(X!21, R!20), X!21)) | member(tptp_fun_Z_17(X!21, R!20), E!22))),
% 0.21/0.47      inference(quant_inst,[status(thm)],[])).
% 0.21/0.47  tff(112,plain,
% 0.21/0.47      ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_Z_17(X!21, R!20), X!21)) | member(tptp_fun_Z_17(X!21, R!20), E!22)),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.47  tff(113,plain,
% 0.21/0.47      (member(tptp_fun_Z_17(X!21, R!20), E!22)),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[112, 82, 109])).
% 0.21/0.47  tff(114,plain,
% 0.21/0.47      ((apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))) | member(tptp_fun_Y_18(X!21, R!20), X!21)),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(115,plain,
% 0.21/0.47      (member(tptp_fun_Y_18(X!21, R!20), X!21)),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[114, 101])).
% 0.21/0.47  tff(116,plain,
% 0.21/0.47      (((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_Y_18(X!21, R!20), X!21)) | member(tptp_fun_Y_18(X!21, R!20), E!22))) <=> ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | member(tptp_fun_Y_18(X!21, R!20), E!22))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(117,plain,
% 0.21/0.47      ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | ((~member(tptp_fun_Y_18(X!21, R!20), X!21)) | member(tptp_fun_Y_18(X!21, R!20), E!22))),
% 0.21/0.47      inference(quant_inst,[status(thm)],[])).
% 0.21/0.47  tff(118,plain,
% 0.21/0.47      ((~![X: $i] : ((~member(X, X!21)) | member(X, E!22))) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | member(tptp_fun_Y_18(X!21, R!20), E!22)),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.47  tff(119,plain,
% 0.21/0.47      (member(tptp_fun_Y_18(X!21, R!20), E!22)),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[118, 82, 115])).
% 0.21/0.47  tff(120,plain,
% 0.21/0.47      ((apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))) | apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(121,plain,
% 0.21/0.47      (apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[120, 101])).
% 0.21/0.47  tff(122,plain,
% 0.21/0.47      ((apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(123,plain,
% 0.21/0.47      (apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[122, 101])).
% 0.21/0.47  tff(124,plain,
% 0.21/0.47      ((apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), X!21)) | (~member(tptp_fun_Y_18(X!21, R!20), X!21)) | (~member(tptp_fun_Z_17(X!21, R!20), X!21))) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(125,plain,
% 0.21/0.47      (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[124, 101])).
% 0.21/0.47  tff(126,plain,
% 0.21/0.47      (((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))) | ![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(127,plain,
% 0.21/0.47      (![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[126, 50])).
% 0.21/0.47  tff(128,plain,
% 0.21/0.47      (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))) | (apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(129,plain,
% 0.21/0.47      (((~member(tptp_fun_Z_17(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), E!22))) <=> (apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(130,plain,
% 0.21/0.47      (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))) | ((~member(tptp_fun_Z_17(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))) | (apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22))))),
% 0.21/0.47      inference(monotonicity,[status(thm)],[129])).
% 0.21/0.47  tff(131,plain,
% 0.21/0.47      (((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))) | ((~member(tptp_fun_Z_17(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))),
% 0.21/0.48      inference(transitivity,[status(thm)],[130, 128])).
% 0.21/0.48  tff(132,plain,
% 0.21/0.48      ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))) | ((~member(tptp_fun_Z_17(X!21, R!20), E!22)) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_X_19(X!21, R!20), E!22)))),
% 0.21/0.48      inference(quant_inst,[status(thm)],[])).
% 0.21/0.48  tff(133,plain,
% 0.21/0.48      ((~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!22)) | apply(R!20, X, Z) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))) | apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Z_17(X!21, R!20)) | (~apply(R!20, tptp_fun_X_19(X!21, R!20), tptp_fun_Y_18(X!21, R!20))) | (~apply(R!20, tptp_fun_Y_18(X!21, R!20), tptp_fun_Z_17(X!21, R!20))) | (~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.48  tff(134,plain,
% 0.21/0.48      ((~member(tptp_fun_Z_17(X!21, R!20), E!22)) | (~member(tptp_fun_Y_18(X!21, R!20), E!22)) | (~member(tptp_fun_X_19(X!21, R!20), E!22))),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[133, 127, 125, 123, 121])).
% 0.21/0.48  tff(135,plain,
% 0.21/0.48      ($false),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[134, 119, 113, 107])).
% 0.21/0.48  % SZS output end Proof
%------------------------------------------------------------------------------