%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET789+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n015.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 05:08:02 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Proof 0.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.21  % Problem  : SET789+4 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.22  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.43  % Computer : n015.cluster.edu
% 0.12/0.43  % Model    : x86_64 x86_64
% 0.12/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.43  % Memory   : 8042.1875MB
% 0.12/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.43  % CPULimit : 300
% 0.12/0.43  % WCLimit  : 300
% 0.12/0.43  % DateTime : Sat Sep  3 08:11:10 EDT 2022
% 0.12/0.43  % CPUTime  : 
% 0.12/0.43  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.43  Usage: tptp [options] [-file:]file
% 0.12/0.43    -h, -?       prints this message.
% 0.12/0.43    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.43    -m, -model   generate model.
% 0.12/0.43    -p, -proof   generate proof.
% 0.12/0.43    -c, -core    generate unsat core of named formulas.
% 0.12/0.43    -st, -statistics display statistics.
% 0.12/0.43    -t:timeout   set timeout (in second).
% 0.12/0.43    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.43    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.43    -<param>:<value> configuration parameter and value.
% 0.12/0.43    -o:<output-file> file to place output in.
% 0.20/0.49  % SZS status Theorem
% 0.20/0.49  % SZS output start Proof
% 0.20/0.49  tff(apply_type, type, (
% 0.20/0.49     apply: ( $i * $i * $i ) > $o)).
% 0.20/0.49  tff(tptp_fun_M_14_type, type, (
% 0.20/0.49     tptp_fun_M_14: $i)).
% 0.20/0.49  tff(tptp_fun_X_17_type, type, (
% 0.20/0.49     tptp_fun_X_17: $i)).
% 0.20/0.49  tff(tptp_fun_R_16_type, type, (
% 0.20/0.49     tptp_fun_R_16: $i)).
% 0.20/0.49  tff(member_type, type, (
% 0.20/0.49     member: ( $i * $i ) > $o)).
% 0.20/0.49  tff(tptp_fun_E_15_type, type, (
% 0.20/0.49     tptp_fun_E_15: $i)).
% 0.20/0.49  tff(greatest_type, type, (
% 0.20/0.49     greatest: ( $i * $i * $i ) > $o)).
% 0.20/0.49  tff(tptp_fun_X_8_type, type, (
% 0.20/0.49     tptp_fun_X_8: ( $i * $i * $i ) > $i)).
% 0.20/0.49  tff(order_type, type, (
% 0.20/0.49     order: ( $i * $i ) > $o)).
% 0.20/0.49  tff(tptp_fun_Z_3_type, type, (
% 0.20/0.49     tptp_fun_Z_3: ( $i * $i ) > $i)).
% 0.20/0.49  tff(tptp_fun_Y_4_type, type, (
% 0.20/0.49     tptp_fun_Y_4: ( $i * $i ) > $i)).
% 0.20/0.49  tff(tptp_fun_X_5_type, type, (
% 0.20/0.49     tptp_fun_X_5: ( $i * $i ) > $i)).
% 0.20/0.49  tff(tptp_fun_Y_1_type, type, (
% 0.20/0.49     tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.20/0.49  tff(tptp_fun_X_2_type, type, (
% 0.20/0.49     tptp_fun_X_2: ( $i * $i ) > $i)).
% 0.20/0.49  tff(tptp_fun_X_0_type, type, (
% 0.20/0.49     tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.49  tff(1,plain,
% 0.20/0.49      (^[R: $i, E: $i, M: $i] : rewrite((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(2,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[1])).
% 0.20/0.49  tff(3,plain,
% 0.20/0.49      (^[R: $i, E: $i, M: $i] : refl((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(4,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[3])).
% 0.20/0.49  tff(5,plain,
% 0.20/0.49      (^[R: $i, E: $i, M: $i] : rewrite((~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(6,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[5])).
% 0.20/0.49  tff(7,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.20/0.49      inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.49  tff(8,plain,
% 0.20/0.49      (^[R: $i, E: $i, M: $i] : trans(monotonicity(rewrite(((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) <=> ((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))), rewrite((greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))) <=> (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))), ((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))), rewrite((((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))), ((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(9,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) <=> ![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[8])).
% 0.20/0.49  tff(10,plain,
% 0.20/0.49      (^[R: $i, E: $i, M: $i] : rewrite((((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))) <=> (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(11,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))) <=> ![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[10])).
% 0.20/0.49  tff(12,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) <=> ![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(13,plain,
% 0.20/0.49      (^[R: $i, E: $i, M: $i] : rewrite((greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M)))) <=> (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(14,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M)))) <=> ![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[13])).
% 0.20/0.49  tff(15,axiom,(![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : (member(X, E) => apply(R, X, M))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax','greatest')).
% 0.20/0.49  tff(16,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.49  tff(17,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (greatest(M, R, E) <=> (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.49  tff(18,plain,(
% 0.20/0.49      ![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | ((~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))))),
% 0.20/0.49      inference(skolemize,[status(sab)],[17])).
% 0.20/0.49  tff(19,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (((~greatest(M, R, E)) | (member(M, E) & ![X: $i] : ((~member(X, E)) | apply(R, X, M)))) & (greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.49  tff(20,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[19, 9])).
% 0.20/0.49  tff(21,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (~((~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M))))))) | (~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M)))))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[20, 7])).
% 0.20/0.49  tff(22,plain,
% 0.20/0.49      (![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[21, 2])).
% 0.20/0.49  tff(23,plain,
% 0.20/0.49      ((~![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))) | (~((~(greatest(X!17, R!16, E!15) | (~member(X!17, E!15)) | (~((~member(tptp_fun_X_8(X!17, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(X!17, E!15, R!16), X!17))))) | (~((~greatest(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17)))))))))),
% 0.20/0.49      inference(quant_inst,[status(thm)],[])).
% 0.20/0.49  tff(24,plain,
% 0.20/0.49      (~((~(greatest(X!17, R!16, E!15) | (~member(X!17, E!15)) | (~((~member(tptp_fun_X_8(X!17, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(X!17, E!15, R!16), X!17))))) | (~((~greatest(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))))))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.50  tff(25,plain,
% 0.20/0.50      (((~(greatest(X!17, R!16, E!15) | (~member(X!17, E!15)) | (~((~member(tptp_fun_X_8(X!17, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(X!17, E!15, R!16), X!17))))) | (~((~greatest(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17)))))))) | ((~greatest(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(26,plain,
% 0.20/0.50      ((~greatest(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17)))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.50  tff(27,plain,
% 0.20/0.50      (((order(R!16, E!15) & greatest(M!14, R!16, E!15)) & (~((~greatest(X!17, R!16, E!15)) | (M!14 = X!17)))) <=> (order(R!16, E!15) & greatest(M!14, R!16, E!15) & (~((~greatest(X!17, R!16, E!15)) | (M!14 = X!17))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(28,plain,
% 0.20/0.50      ((~(~(order(R!16, E!15) & greatest(M!14, R!16, E!15)))) <=> (order(R!16, E!15) & greatest(M!14, R!16, E!15))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(29,plain,
% 0.20/0.50      (((~(~(order(R!16, E!15) & greatest(M!14, R!16, E!15)))) & (~((~greatest(X!17, R!16, E!15)) | (M!14 = X!17)))) <=> ((order(R!16, E!15) & greatest(M!14, R!16, E!15)) & (~((~greatest(X!17, R!16, E!15)) | (M!14 = X!17))))),
% 0.20/0.50      inference(monotonicity,[status(thm)],[28])).
% 0.20/0.50  tff(30,plain,
% 0.20/0.50      (((~(~(order(R!16, E!15) & greatest(M!14, R!16, E!15)))) & (~((~greatest(X!17, R!16, E!15)) | (M!14 = X!17)))) <=> (order(R!16, E!15) & greatest(M!14, R!16, E!15) & (~((~greatest(X!17, R!16, E!15)) | (M!14 = X!17))))),
% 0.20/0.50      inference(transitivity,[status(thm)],[29, 27])).
% 0.20/0.50  tff(31,plain,
% 0.20/0.50      ((~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X)))) <=> (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(32,plain,
% 0.20/0.50      ((~![R: $i, E: $i, M: $i] : ((order(R, E) & greatest(M, R, E)) => ![X: $i] : (greatest(X, R, E) => (M = X)))) <=> (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(33,axiom,(~![R: $i, E: $i, M: $i] : ((order(R, E) & greatest(M, R, E)) => ![X: $i] : (greatest(X, R, E) => (M = X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIV1')).
% 0.20/0.50  tff(34,plain,
% 0.20/0.50      (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.50  tff(35,plain,
% 0.20/0.50      (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[34, 31])).
% 0.20/0.50  tff(36,plain,
% 0.20/0.50      (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.50  tff(37,plain,
% 0.20/0.50      (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[36, 31])).
% 0.20/0.50  tff(38,plain,
% 0.20/0.50      (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[37, 31])).
% 0.20/0.50  tff(39,plain,
% 0.20/0.50      (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.50  tff(40,plain,
% 0.20/0.50      (~![R: $i, E: $i, M: $i] : ((~(order(R, E) & greatest(M, R, E))) | ![X: $i] : ((~greatest(X, R, E)) | (M = X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[39, 31])).
% 0.20/0.50  tff(41,plain,
% 0.20/0.50      (order(R!16, E!15) & greatest(M!14, R!16, E!15) & (~((~greatest(X!17, R!16, E!15)) | (M!14 = X!17)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[40, 30])).
% 0.20/0.50  tff(42,plain,
% 0.20/0.50      (~((~greatest(X!17, R!16, E!15)) | (M!14 = X!17))),
% 0.20/0.50      inference(and_elim,[status(thm)],[41])).
% 0.20/0.50  tff(43,plain,
% 0.20/0.50      (greatest(X!17, R!16, E!15)),
% 0.20/0.50      inference(or_elim,[status(thm)],[42])).
% 0.20/0.50  tff(44,plain,
% 0.20/0.50      ((~((~greatest(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))))))) | (~greatest(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17)))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(45,plain,
% 0.20/0.50      ((~((~greatest(X!17, R!16, E!15)) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))))))) | (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17)))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.50  tff(46,plain,
% 0.20/0.50      (~((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[45, 26])).
% 0.20/0.50  tff(47,plain,
% 0.20/0.50      (((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17)))) | member(X!17, E!15)),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(48,plain,
% 0.20/0.50      (member(X!17, E!15)),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.50  tff(49,plain,
% 0.20/0.50      ((~![R: $i, E: $i, M: $i] : (~((~(greatest(M, R, E) | (~member(M, E)) | (~((~member(tptp_fun_X_8(M, E, R), E)) | apply(R, tptp_fun_X_8(M, E, R), M))))) | (~((~greatest(M, R, E)) | (~((~member(M, E)) | (~![X: $i] : ((~member(X, E)) | apply(R, X, M)))))))))) | (~((~(greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))) | (~((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))))))))),
% 0.20/0.50      inference(quant_inst,[status(thm)],[])).
% 0.20/0.50  tff(50,plain,
% 0.20/0.50      (~((~(greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))) | (~((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))))))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[49, 22])).
% 0.20/0.50  tff(51,plain,
% 0.20/0.50      (((~(greatest(M!14, R!16, E!15) | (~member(M!14, E!15)) | (~((~member(tptp_fun_X_8(M!14, E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_8(M!14, E!15, R!16), M!14))))) | (~((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))))))) | ((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(52,plain,
% 0.20/0.50      ((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.50  tff(53,plain,
% 0.20/0.50      (greatest(M!14, R!16, E!15)),
% 0.20/0.50      inference(and_elim,[status(thm)],[41])).
% 0.20/0.50  tff(54,plain,
% 0.20/0.50      ((~((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))))))) | (~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(55,plain,
% 0.20/0.50      ((~((~greatest(M!14, R!16, E!15)) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))))))) | (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.50  tff(56,plain,
% 0.20/0.50      (~((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[55, 52])).
% 0.20/0.50  tff(57,plain,
% 0.20/0.50      (((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))) | ![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(58,plain,
% 0.20/0.50      (![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.50  tff(59,plain,
% 0.20/0.50      (((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))) | ((~member(X!17, E!15)) | apply(R!16, X!17, M!14))) <=> ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))) | (~member(X!17, E!15)) | apply(R!16, X!17, M!14))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(60,plain,
% 0.20/0.50      ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))) | ((~member(X!17, E!15)) | apply(R!16, X!17, M!14))),
% 0.20/0.50      inference(quant_inst,[status(thm)],[])).
% 0.20/0.50  tff(61,plain,
% 0.20/0.50      ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14))) | (~member(X!17, E!15)) | apply(R!16, X!17, M!14)),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.50  tff(62,plain,
% 0.20/0.50      (apply(R!16, X!17, M!14)),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.20/0.50  tff(63,plain,
% 0.20/0.50      (((~member(X!17, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17)))) | ![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(64,plain,
% 0.20/0.50      (![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[63, 46])).
% 0.20/0.50  tff(65,plain,
% 0.20/0.50      (((~member(M!14, E!15)) | (~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, M!14)))) | member(M!14, E!15)),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(66,plain,
% 0.20/0.50      (member(M!14, E!15)),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[65, 56])).
% 0.20/0.50  tff(67,plain,
% 0.20/0.50      (((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))) | ((~member(M!14, E!15)) | apply(R!16, M!14, X!17))) <=> ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))) | (~member(M!14, E!15)) | apply(R!16, M!14, X!17))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(68,plain,
% 0.20/0.50      ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))) | ((~member(M!14, E!15)) | apply(R!16, M!14, X!17))),
% 0.20/0.50      inference(quant_inst,[status(thm)],[])).
% 0.20/0.50  tff(69,plain,
% 0.20/0.50      ((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X!17))) | (~member(M!14, E!15)) | apply(R!16, M!14, X!17)),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.50  tff(70,plain,
% 0.20/0.50      (apply(R!16, M!14, X!17)),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[69, 66, 64])).
% 0.20/0.50  tff(71,plain,
% 0.20/0.50      (^[R: $i, E: $i] : rewrite((~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(72,plain,
% 0.20/0.51      (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[71])).
% 0.20/0.51  tff(73,plain,
% 0.20/0.51      (^[R: $i, E: $i] : refl((~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(74,plain,
% 0.20/0.51      (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[73])).
% 0.20/0.51  tff(75,plain,
% 0.20/0.51      (^[R: $i, E: $i] : rewrite((~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(76,plain,
% 0.20/0.51      (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[75])).
% 0.20/0.51  tff(77,plain,
% 0.20/0.51      (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.20/0.51      inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.51  tff(78,plain,
% 0.20/0.51      (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) <=> ((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))), trans(monotonicity(rewrite((~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) <=> (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E))))), rewrite((~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))) <=> (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))), ((order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))) <=> (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))), rewrite((order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))) <=> (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))), ((order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))) <=> (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))), ((((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))) <=> (((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))))), rewrite((((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) <=> (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))), ((((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))) <=> (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(79,plain,
% 0.20/0.51      (![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[78])).
% 0.20/0.51  tff(80,plain,
% 0.20/0.51      (^[R: $i, E: $i] : rewrite((((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | ((~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))))) <=> (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(81,plain,
% 0.20/0.51      (![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | ((~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[80])).
% 0.20/0.51  tff(82,plain,
% 0.20/0.51      (![R: $i, E: $i] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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))))))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(83,plain,
% 0.20/0.52      (^[R: $i, E: $i] : rewrite((order(R, E) <=> ((![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => ((apply(R, X, Y) & apply(R, Y, X)) => (X = Y)))) & ![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))))) <=> (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))))),
% 0.20/0.52      inference(bind,[status(th)],[])).
% 0.20/0.52  tff(84,plain,
% 0.20/0.52      (![R: $i, E: $i] : (order(R, E) <=> ((![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => ((apply(R, X, Y) & apply(R, Y, X)) => (X = Y)))) & ![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] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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))))))),
% 0.20/0.52      inference(quant_intro,[status(thm)],[83])).
% 0.20/0.52  tff(85,axiom,(![R: $i, E: $i] : (order(R, E) <=> ((![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => ((apply(R, X, Y) & apply(R, Y, X)) => (X = Y)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax','order')).
% 0.20/0.52  tff(86,plain,
% 0.20/0.52      (![R: $i, E: $i] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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))))))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.52  tff(87,plain,
% 0.20/0.52      (![R: $i, E: $i] : (order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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))))))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.52  tff(88,plain,(
% 0.20/0.52      ![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | ((~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E))))))))),
% 0.20/0.52      inference(skolemize,[status(sab)],[87])).
% 0.20/0.52  tff(89,plain,
% 0.20/0.52      (![R: $i, E: $i] : (((~order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i] : ((X = Y) | (~(apply(R, X, Y) & apply(R, Y, X))) | (~(member(X, E) & member(Y, E)))) & ![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)))))) & (order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~(apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R)) & apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R)))) | (~(member(tptp_fun_X_2(E, R), E) & member(tptp_fun_Y_1(E, R), E))))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R)) & apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R)))) | (~(member(tptp_fun_X_5(E, R), E) & member(tptp_fun_Y_4(E, R), E) & member(tptp_fun_Z_3(E, R), E)))))))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.52  tff(90,plain,
% 0.20/0.52      (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[89, 79])).
% 0.20/0.52  tff(91,plain,
% 0.20/0.52      (![R: $i, E: $i] : (~((~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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)))))))) | (~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E))))))))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[90, 77])).
% 0.20/0.52  tff(92,plain,
% 0.20/0.52      (![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[91, 72])).
% 0.20/0.52  tff(93,plain,
% 0.20/0.52      (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15)))))))))))),
% 0.20/0.53      inference(rewrite,[status(thm)],[])).
% 0.20/0.53  tff(94,plain,
% 0.20/0.53      ((~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15)))))))))) <=> (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15))))))))))),
% 0.20/0.53      inference(rewrite,[status(thm)],[])).
% 0.20/0.53  tff(95,plain,
% 0.20/0.53      (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15)))))))))))),
% 0.20/0.53      inference(monotonicity,[status(thm)],[94])).
% 0.20/0.53  tff(96,plain,
% 0.20/0.53      (((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))) <=> ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15)))))))))))),
% 0.20/0.53      inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.53  tff(97,plain,
% 0.20/0.53      ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, Z)) | (~member(X, E!15)) | (~member(Y, E!15)) | (~member(Z, E!15))))))))))),
% 0.30/0.54      inference(quant_inst,[status(thm)],[])).
% 0.30/0.54  tff(98,plain,
% 0.30/0.54      ((~![R: $i, E: $i] : (~((~(order(R, E) | (~((~member(tptp_fun_X_0(E, R), E)) | apply(R, tptp_fun_X_0(E, R), tptp_fun_X_0(E, R)))) | (~((tptp_fun_X_2(E, R) = tptp_fun_Y_1(E, R)) | (~apply(R, tptp_fun_X_2(E, R), tptp_fun_Y_1(E, R))) | (~apply(R, tptp_fun_Y_1(E, R), tptp_fun_X_2(E, R))) | (~member(tptp_fun_X_2(E, R), E)) | (~member(tptp_fun_Y_1(E, R), E)))) | (~(apply(R, tptp_fun_X_5(E, R), tptp_fun_Z_3(E, R)) | (~apply(R, tptp_fun_X_5(E, R), tptp_fun_Y_4(E, R))) | (~apply(R, tptp_fun_Y_4(E, R), tptp_fun_Z_3(E, R))) | (~member(tptp_fun_X_5(E, R), E)) | (~member(tptp_fun_Y_4(E, R), E)) | (~member(tptp_fun_Z_3(E, R), E)))))) | (~((~order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)) | (~member(X, E)))) | (~![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))))))))))) | (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15))))))))))),
% 0.30/0.54      inference(modus_ponens,[status(thm)],[97, 96])).
% 0.30/0.54  tff(99,plain,
% 0.30/0.54      (~((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15)))))))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[98, 92])).
% 0.30/0.54  tff(100,plain,
% 0.30/0.54      (((~(order(R!16, E!15) | (~((~member(tptp_fun_X_0(E!15, R!16), E!15)) | apply(R!16, tptp_fun_X_0(E!15, R!16), tptp_fun_X_0(E!15, R!16)))) | (~((tptp_fun_X_2(E!15, R!16) = tptp_fun_Y_1(E!15, R!16)) | (~apply(R!16, tptp_fun_X_2(E!15, R!16), tptp_fun_Y_1(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_1(E!15, R!16), tptp_fun_X_2(E!15, R!16))) | (~member(tptp_fun_X_2(E!15, R!16), E!15)) | (~member(tptp_fun_Y_1(E!15, R!16), E!15)))) | (~(apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Z_3(E!15, R!16)) | (~apply(R!16, tptp_fun_X_5(E!15, R!16), tptp_fun_Y_4(E!15, R!16))) | (~apply(R!16, tptp_fun_Y_4(E!15, R!16), tptp_fun_Z_3(E!15, R!16))) | (~member(tptp_fun_X_5(E!15, R!16), E!15)) | (~member(tptp_fun_Y_4(E!15, R!16), E!15)) | (~member(tptp_fun_Z_3(E!15, R!16), E!15)))))) | (~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15))))))))) | ((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15)))))))),
% 0.30/0.54      inference(tautology,[status(thm)],[])).
% 0.30/0.54  tff(101,plain,
% 0.30/0.54      ((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15))))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[100, 99])).
% 0.30/0.54  tff(102,plain,
% 0.30/0.54      (order(R!16, E!15)),
% 0.30/0.54      inference(and_elim,[status(thm)],[41])).
% 0.30/0.54  tff(103,plain,
% 0.30/0.54      ((~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15)))))))) | (~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15))))))),
% 0.30/0.54      inference(tautology,[status(thm)],[])).
% 0.30/0.54  tff(104,plain,
% 0.30/0.54      ((~((~order(R!16, E!15)) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15)))))))) | (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15))))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[103, 102])).
% 0.30/0.54  tff(105,plain,
% 0.30/0.54      (~((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15)))))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[104, 101])).
% 0.30/0.55  tff(106,plain,
% 0.30/0.55      (((~![X: $i] : ((~member(X, E!15)) | apply(R!16, X, X))) | (~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, E!15)) | (~apply(R!16, Y, Z)) | (~member(Y, E!15)) | apply(R!16, X, Z) | (~apply(R!16, X, Y)) | (~member(X, E!15))))) | ![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))),
% 0.30/0.55      inference(tautology,[status(thm)],[])).
% 0.30/0.55  tff(107,plain,
% 0.30/0.55      (![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[106, 105])).
% 0.30/0.55  tff(108,plain,
% 0.30/0.55      (~(M!14 = X!17)),
% 0.30/0.55      inference(or_elim,[status(thm)],[42])).
% 0.30/0.55  tff(109,plain,
% 0.30/0.55      (((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | ((M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)) | (~apply(R!16, M!14, X!17)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)) | (~apply(R!16, M!14, X!17)))),
% 0.30/0.55      inference(rewrite,[status(thm)],[])).
% 0.30/0.55  tff(110,plain,
% 0.30/0.55      (((M!14 = X!17) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14)) | (~member(M!14, E!15))) <=> ((M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)) | (~apply(R!16, M!14, X!17)))),
% 0.30/0.55      inference(rewrite,[status(thm)],[])).
% 0.30/0.55  tff(111,plain,
% 0.30/0.55      (((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | ((M!14 = X!17) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14)) | (~member(M!14, E!15)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | ((M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)) | (~apply(R!16, M!14, X!17))))),
% 0.30/0.55      inference(monotonicity,[status(thm)],[110])).
% 0.30/0.55  tff(112,plain,
% 0.30/0.55      (((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | ((M!14 = X!17) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14)) | (~member(M!14, E!15)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)) | (~apply(R!16, M!14, X!17)))),
% 0.30/0.55      inference(transitivity,[status(thm)],[111, 109])).
% 0.30/0.55  tff(113,plain,
% 0.30/0.55      ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | ((M!14 = X!17) | (~member(X!17, E!15)) | (~apply(R!16, M!14, X!17)) | (~apply(R!16, X!17, M!14)) | (~member(M!14, E!15)))),
% 0.30/0.55      inference(quant_inst,[status(thm)],[])).
% 0.30/0.55  tff(114,plain,
% 0.30/0.55      ((~![X: $i, Y: $i] : ((X = Y) | (~member(Y, E!15)) | (~apply(R!16, X, Y)) | (~apply(R!16, Y, X)) | (~member(X, E!15)))) | (M!14 = X!17) | (~member(M!14, E!15)) | (~member(X!17, E!15)) | (~apply(R!16, X!17, M!14)) | (~apply(R!16, M!14, X!17))),
% 0.30/0.55      inference(modus_ponens,[status(thm)],[113, 112])).
% 0.30/0.55  tff(115,plain,
% 0.30/0.55      ($false),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[114, 108, 107, 66, 48, 70, 62])).
% 0.30/0.55  % SZS output end Proof
%------------------------------------------------------------------------------