%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 20 05:08:07 EDT 2022

% Result   : Theorem 0.20s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Sep  3 07:27:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34  Usage: tptp [options] [-file:]file
% 0.20/0.34    -h, -?       prints this message.
% 0.20/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.20/0.34    -m, -model   generate model.
% 0.20/0.34    -p, -proof   generate proof.
% 0.20/0.34    -c, -core    generate unsat core of named formulas.
% 0.20/0.34    -st, -statistics display statistics.
% 0.20/0.34    -t:timeout   set timeout (in second).
% 0.20/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.20/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34    -<param>:<value> configuration parameter and value.
% 0.20/0.34    -o:<output-file> file to place output in.
% 0.20/0.40  % SZS status Theorem
% 0.20/0.40  % SZS output start Proof
% 0.20/0.40  tff(member_type, type, (
% 0.20/0.40     member: ( $i * $i ) > $o)).
% 0.20/0.40  tff(tptp_fun_B_13_type, type, (
% 0.20/0.40     tptp_fun_B_13: $i)).
% 0.20/0.40  tff(tptp_fun_A_14_type, type, (
% 0.20/0.40     tptp_fun_A_14: $i)).
% 0.20/0.40  tff(subset_type, type, (
% 0.20/0.40     subset: ( $i * $i ) > $o)).
% 0.20/0.40  tff(tptp_fun_X_0_type, type, (
% 0.20/0.40     tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.40  tff(strict_well_order_type, type, (
% 0.20/0.40     strict_well_order: ( $i * $i ) > $o)).
% 0.20/0.40  tff(member_predicate_type, type, (
% 0.20/0.40     member_predicate: $i)).
% 0.20/0.40  tff(set_type, type, (
% 0.20/0.40     set: $i > $o)).
% 0.20/0.40  tff(on_type, type, (
% 0.20/0.40     on: $i)).
% 0.20/0.40  tff(tptp_fun_X_3_type, type, (
% 0.20/0.40     tptp_fun_X_3: $i > $i)).
% 0.20/0.40  tff(apply_type, type, (
% 0.20/0.40     apply: ( $i * $i * $i ) > $o)).
% 0.20/0.40  tff(strict_order_type, type, (
% 0.20/0.40     strict_order: ( $i * $i ) > $o)).
% 0.20/0.40  tff(tptp_fun_Z_10_type, type, (
% 0.20/0.40     tptp_fun_Z_10: ( $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_Y_11_type, type, (
% 0.20/0.40     tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_X_12_type, type, (
% 0.20/0.40     tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_X_9_type, type, (
% 0.20/0.40     tptp_fun_X_9: ( $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_Y_8_type, type, (
% 0.20/0.40     tptp_fun_Y_8: ( $i * $i ) > $i)).
% 0.20/0.40  tff(least_type, type, (
% 0.20/0.40     least: ( $i * $i * $i ) > $o)).
% 0.20/0.40  tff(tptp_fun_Y_4_type, type, (
% 0.20/0.40     tptp_fun_Y_4: ( $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_A_5_type, type, (
% 0.20/0.40     tptp_fun_A_5: ( $i * $i ) > $i)).
% 0.20/0.40  tff(tptp_fun_X_6_type, type, (
% 0.20/0.40     tptp_fun_X_6: ( $i * $i ) > $i)).
% 0.20/0.40  tff(1,plain,
% 0.20/0.40      (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(2,plain,
% 0.20/0.40      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40  tff(3,plain,
% 0.20/0.40      (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(4,plain,
% 0.20/0.40      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40  tff(5,plain,
% 0.20/0.40      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40      inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40  tff(6,plain,
% 0.20/0.40      (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(7,plain,
% 0.20/0.40      (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40  tff(8,plain,
% 0.20/0.40      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40      inference(rewrite,[status(thm)],[])).
% 0.20/0.40  tff(9,plain,
% 0.20/0.40      (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.40      inference(bind,[status(th)],[])).
% 0.20/0.40  tff(10,plain,
% 0.20/0.40      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40      inference(quant_intro,[status(thm)],[9])).
% 0.20/0.40  tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.40  tff(12,plain,
% 0.20/0.40      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.40  tff(13,plain,
% 0.20/0.40      (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.40  tff(14,plain,(
% 0.20/0.40      ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.20/0.40      inference(skolemize,[status(sab)],[13])).
% 0.20/0.40  tff(15,plain,
% 0.20/0.40      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.40  tff(16,plain,
% 0.20/0.40      (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40      inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.40  tff(17,plain,
% 0.20/0.40      ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(A!14, B!13)) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13)))) | (~(subset(A!14, B!13) | (~((~member(tptp_fun_X_0(B!13, A!14), A!14)) | member(tptp_fun_X_0(B!13, A!14), B!13)))))))),
% 0.20/0.40      inference(quant_inst,[status(thm)],[])).
% 0.20/0.40  tff(18,plain,
% 0.20/0.40      (~((~((~subset(A!14, B!13)) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13)))) | (~(subset(A!14, B!13) | (~((~member(tptp_fun_X_0(B!13, A!14), A!14)) | member(tptp_fun_X_0(B!13, A!14), B!13))))))),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.40  tff(19,plain,
% 0.20/0.40      (((~((~subset(A!14, B!13)) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13)))) | (~(subset(A!14, B!13) | (~((~member(tptp_fun_X_0(B!13, A!14), A!14)) | member(tptp_fun_X_0(B!13, A!14), B!13)))))) | ((~subset(A!14, B!13)) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13)))),
% 0.20/0.41      inference(tautology,[status(thm)],[])).
% 0.20/0.41  tff(20,plain,
% 0.20/0.41      ((~subset(A!14, B!13)) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13))),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.41  tff(21,plain,
% 0.20/0.41      (^[A: $i] : rewrite((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(22,plain,
% 0.20/0.41      (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[21])).
% 0.20/0.41  tff(23,plain,
% 0.20/0.41      (^[A: $i] : refl((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(24,plain,
% 0.20/0.41      (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[23])).
% 0.20/0.41  tff(25,plain,
% 0.20/0.41      (^[A: $i] : rewrite((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(26,plain,
% 0.20/0.41      (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[25])).
% 0.20/0.41  tff(27,plain,
% 0.20/0.41      (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.41      inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.41  tff(28,plain,
% 0.20/0.41      (^[A: $i] : trans(monotonicity(rewrite(((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) <=> ((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))), rewrite((member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))) <=> (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))), ((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))), rewrite((((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))), ((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(29,plain,
% 0.20/0.41      (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[28])).
% 0.20/0.41  tff(30,plain,
% 0.20/0.41      (^[A: $i] : rewrite((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))) <=> (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(31,plain,
% 0.20/0.41      (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))) <=> ![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41  tff(32,plain,
% 0.20/0.41      (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) <=> ![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(33,plain,
% 0.20/0.41      (^[A: $i] : rewrite((member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A)))) <=> (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(34,plain,
% 0.20/0.41      (![A: $i] : (member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A)))) <=> ![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[33])).
% 0.20/0.41  tff(35,axiom,(![A: $i] : (member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax','ordinal_number')).
% 0.20/0.41  tff(36,plain,
% 0.20/0.41      (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.41  tff(37,plain,
% 0.20/0.41      (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.41  tff(38,plain,(
% 0.20/0.41      ![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))),
% 0.20/0.41      inference(skolemize,[status(sab)],[37])).
% 0.20/0.41  tff(39,plain,
% 0.20/0.41      (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.41  tff(40,plain,
% 0.20/0.41      (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.41  tff(41,plain,
% 0.20/0.41      (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[40, 27])).
% 0.20/0.41  tff(42,plain,
% 0.20/0.41      (![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[41, 22])).
% 0.20/0.41  tff(43,plain,
% 0.20/0.41      ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(B!13, on) | (~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~((~member(tptp_fun_X_3(B!13), B!13)) | subset(tptp_fun_X_3(B!13), B!13))))) | (~((~member(B!13, on)) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13)))))))))),
% 0.20/0.41      inference(quant_inst,[status(thm)],[])).
% 0.20/0.41  tff(44,plain,
% 0.20/0.41      (~((~(member(B!13, on) | (~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~((~member(tptp_fun_X_3(B!13), B!13)) | subset(tptp_fun_X_3(B!13), B!13))))) | (~((~member(B!13, on)) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))))))))),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.41  tff(45,plain,
% 0.20/0.41      (((~(member(B!13, on) | (~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~((~member(tptp_fun_X_3(B!13), B!13)) | subset(tptp_fun_X_3(B!13), B!13))))) | (~((~member(B!13, on)) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13)))))))) | ((~member(B!13, on)) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))))))),
% 0.20/0.41      inference(tautology,[status(thm)],[])).
% 0.20/0.41  tff(46,plain,
% 0.20/0.41      ((~member(B!13, on)) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13)))))),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.41  tff(47,plain,
% 0.20/0.41      ((~((~(member(A!14, on) & member(B!13, on))) | (~(member(A!14, B!13) & member(B!13, A!14))))) <=> (~((~(member(A!14, on) & member(B!13, on))) | (~(member(A!14, B!13) & member(B!13, A!14)))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(48,plain,
% 0.20/0.41      ((~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A))))) <=> (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A)))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(49,plain,
% 0.20/0.41      ((~![A: $i, B: $i] : ((member(A, on) & member(B, on)) => (~(member(A, B) & member(B, A))))) <=> (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A)))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(50,axiom,(~![A: $i, B: $i] : ((member(A, on) & member(B, on)) => (~(member(A, B) & member(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thV3')).
% 0.20/0.41  tff(51,plain,
% 0.20/0.41      (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.41  tff(52,plain,
% 0.20/0.41      (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[51, 48])).
% 0.20/0.41  tff(53,plain,
% 0.20/0.41      (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.41  tff(54,plain,
% 0.20/0.41      (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[53, 48])).
% 0.20/0.41  tff(55,plain,
% 0.20/0.41      (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[54, 48])).
% 0.20/0.41  tff(56,plain,
% 0.20/0.41      (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.41  tff(57,plain,
% 0.20/0.41      (~![A: $i, B: $i] : ((~(member(A, on) & member(B, on))) | (~(member(A, B) & member(B, A))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[56, 48])).
% 0.20/0.41  tff(58,plain,(
% 0.20/0.41      ~((~(member(A!14, on) & member(B!13, on))) | (~(member(A!14, B!13) & member(B!13, A!14))))),
% 0.20/0.41      inference(skolemize,[status(sab)],[57])).
% 0.20/0.41  tff(59,plain,
% 0.20/0.41      (~((~(member(A!14, on) & member(B!13, on))) | (~(member(A!14, B!13) & member(B!13, A!14))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[58, 47])).
% 0.20/0.42  tff(60,plain,
% 0.20/0.42      (member(A!14, on) & member(B!13, on)),
% 0.20/0.42      inference(or_elim,[status(thm)],[59])).
% 0.20/0.42  tff(61,plain,
% 0.20/0.42      (member(B!13, on)),
% 0.20/0.42      inference(and_elim,[status(thm)],[60])).
% 0.20/0.42  tff(62,plain,
% 0.20/0.42      ((~((~member(B!13, on)) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))))))) | (~member(B!13, on)) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13)))))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(63,plain,
% 0.20/0.42      ((~((~member(B!13, on)) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))))))) | (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13)))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.42  tff(64,plain,
% 0.20/0.42      (~((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[63, 46])).
% 0.20/0.42  tff(65,plain,
% 0.20/0.42      (((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13)))) | ![X: $i] : ((~member(X, B!13)) | subset(X, B!13))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(66,plain,
% 0.20/0.42      (![X: $i] : ((~member(X, B!13)) | subset(X, B!13))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.42  tff(67,plain,
% 0.20/0.42      (member(A!14, B!13) & member(B!13, A!14)),
% 0.20/0.42      inference(or_elim,[status(thm)],[59])).
% 0.20/0.42  tff(68,plain,
% 0.20/0.42      (member(A!14, B!13)),
% 0.20/0.42      inference(and_elim,[status(thm)],[67])).
% 0.20/0.42  tff(69,plain,
% 0.20/0.42      (((~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))) | ((~member(A!14, B!13)) | subset(A!14, B!13))) <=> ((~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))) | (~member(A!14, B!13)) | subset(A!14, B!13))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(70,plain,
% 0.20/0.42      ((~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))) | ((~member(A!14, B!13)) | subset(A!14, B!13))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(71,plain,
% 0.20/0.42      ((~![X: $i] : ((~member(X, B!13)) | subset(X, B!13))) | (~member(A!14, B!13)) | subset(A!14, B!13)),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.42  tff(72,plain,
% 0.20/0.42      (subset(A!14, B!13)),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[71, 68, 66])).
% 0.20/0.42  tff(73,plain,
% 0.20/0.42      ((~((~subset(A!14, B!13)) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13)))) | (~subset(A!14, B!13)) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(74,plain,
% 0.20/0.42      ((~((~subset(A!14, B!13)) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13)))) | ![X: $i] : ((~member(X, A!14)) | member(X, B!13))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.42  tff(75,plain,
% 0.20/0.42      (![X: $i] : ((~member(X, A!14)) | member(X, B!13))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[74, 20])).
% 0.20/0.42  tff(76,plain,
% 0.20/0.42      (member(B!13, A!14)),
% 0.20/0.42      inference(and_elim,[status(thm)],[67])).
% 0.20/0.42  tff(77,plain,
% 0.20/0.42      (((~![X: $i] : ((~member(X, A!14)) | member(X, B!13))) | ((~member(B!13, A!14)) | member(B!13, B!13))) <=> ((~![X: $i] : ((~member(X, A!14)) | member(X, B!13))) | (~member(B!13, A!14)) | member(B!13, B!13))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(78,plain,
% 0.20/0.42      ((~![X: $i] : ((~member(X, A!14)) | member(X, B!13))) | ((~member(B!13, A!14)) | member(B!13, B!13))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(79,plain,
% 0.20/0.42      ((~![X: $i] : ((~member(X, A!14)) | member(X, B!13))) | (~member(B!13, A!14)) | member(B!13, B!13)),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42  tff(80,plain,
% 0.20/0.42      (member(B!13, B!13)),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[79, 76, 75])).
% 0.20/0.42  tff(81,plain,
% 0.20/0.42      (^[R: $i, E: $i] : rewrite((~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))) <=> (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(82,plain,
% 0.20/0.42      (![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[81])).
% 0.20/0.42  tff(83,plain,
% 0.20/0.42      (^[R: $i, E: $i] : refl((~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))) <=> (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(84,plain,
% 0.21/0.42      (![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[83])).
% 0.21/0.42  tff(85,plain,
% 0.21/0.42      (^[R: $i, E: $i] : rewrite((~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))) <=> (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(86,plain,
% 0.21/0.42      (![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[85])).
% 0.21/0.42  tff(87,plain,
% 0.21/0.42      (![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))))),
% 0.21/0.42      inference(transitivity,[status(thm)],[86, 84])).
% 0.21/0.42  tff(88,plain,
% 0.21/0.42      (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) <=> (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))), rewrite((~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E))))) <=> (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))), ((strict_order(R, E) | (~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E)))))) <=> (strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))), rewrite((strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))) <=> (strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))), ((strict_order(R, E) | (~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E)))))) <=> (strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))), ((((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | (~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E))))))) <=> (((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))) & (strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))))), rewrite((((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))) & (strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) <=> (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))))), ((((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | (~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E))))))) <=> (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(89,plain,
% 0.21/0.42      (![R: $i, E: $i] : (((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | (~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))))),
% 0.21/0.43      inference(quant_intro,[status(thm)],[88])).
% 0.21/0.43  tff(90,plain,
% 0.21/0.43      (^[R: $i, E: $i] : rewrite((((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | ((~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E)))))))) <=> (((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | (~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E))))))))),
% 0.21/0.43      inference(bind,[status(th)],[])).
% 0.21/0.43  tff(91,plain,
% 0.21/0.43      (![R: $i, E: $i] : (((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | ((~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | (~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E)))))))),
% 0.21/0.43      inference(quant_intro,[status(thm)],[90])).
% 0.21/0.43  tff(92,plain,
% 0.21/0.43      (![R: $i, E: $i] : (strict_order(R, E) <=> (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ![R: $i, E: $i] : (strict_order(R, E) <=> (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(93,plain,
% 0.21/0.43      (^[R: $i, E: $i] : rewrite((strict_order(R, E) <=> (![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (strict_order(R, E) <=> (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))))),
% 0.21/0.43      inference(bind,[status(th)],[])).
% 0.21/0.43  tff(94,plain,
% 0.21/0.43      (![R: $i, E: $i] : (strict_order(R, E) <=> (![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![R: $i, E: $i] : (strict_order(R, E) <=> (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.43      inference(quant_intro,[status(thm)],[93])).
% 0.21/0.43  tff(95,axiom,(![R: $i, E: $i] : (strict_order(R, E) <=> (![X: $i, Y: $i] : ((member(X, E) & member(Y, E)) => (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax','strict_order')).
% 0.21/0.43  tff(96,plain,
% 0.21/0.43      (![R: $i, E: $i] : (strict_order(R, E) <=> (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.43  tff(97,plain,
% 0.21/0.43      (![R: $i, E: $i] : (strict_order(R, E) <=> (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.43  tff(98,plain,(
% 0.21/0.43      ![R: $i, E: $i] : (((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | ((~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E))))))))),
% 0.21/0.43      inference(skolemize,[status(sab)],[97])).
% 0.21/0.43  tff(99,plain,
% 0.21/0.43      (![R: $i, E: $i] : (((~strict_order(R, E)) | (![X: $i, Y: $i] : ((~(member(X, E) & member(Y, E))) | (~(apply(R, X, Y) & apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (strict_order(R, E) | (~((~(member(tptp_fun_X_9(E, R), E) & member(tptp_fun_Y_8(E, R), E))) | (~(apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R)) & apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R)))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R)) & apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R)))) | (~(member(tptp_fun_X_12(E, R), E) & member(tptp_fun_Y_11(E, R), E) & member(tptp_fun_Z_10(E, R), E)))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[98, 91])).
% 0.21/0.43  tff(100,plain,
% 0.21/0.43      (![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[99, 89])).
% 0.21/0.43  tff(101,plain,
% 0.21/0.43      (![R: $i, E: $i] : (~((~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E)))))))) | (~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E))))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[100, 87])).
% 0.21/0.43  tff(102,plain,
% 0.21/0.43      (![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[101, 82])).
% 0.21/0.43  tff(103,plain,
% 0.21/0.43      (((~![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13))))))))))) <=> ((~![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13)))))))))))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(104,plain,
% 0.21/0.43      ((~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~member(X, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, Z)) | (~member(X, B!13)) | (~member(Y, B!13)) | (~member(Z, B!13)))))))))) <=> (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13))))))))))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(105,plain,
% 0.21/0.43      (((~![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~member(X, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, Z)) | (~member(X, B!13)) | (~member(Y, B!13)) | (~member(Z, B!13))))))))))) <=> ((~![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13)))))))))))),
% 0.21/0.44      inference(monotonicity,[status(thm)],[104])).
% 0.21/0.44  tff(106,plain,
% 0.21/0.44      (((~![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~member(X, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, Z)) | (~member(X, B!13)) | (~member(Y, B!13)) | (~member(Z, B!13))))))))))) <=> ((~![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13)))))))))))),
% 0.21/0.44      inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.44  tff(107,plain,
% 0.21/0.44      ((~![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~member(X, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, Z)) | (~member(X, B!13)) | (~member(Y, B!13)) | (~member(Z, B!13))))))))))),
% 0.21/0.44      inference(quant_inst,[status(thm)],[])).
% 0.21/0.44  tff(108,plain,
% 0.21/0.44      ((~![R: $i, E: $i] : (~((~(strict_order(R, E) | (~((~member(tptp_fun_X_9(E, R), E)) | (~member(tptp_fun_Y_8(E, R), E)) | (~apply(R, tptp_fun_X_9(E, R), tptp_fun_Y_8(E, R))) | (~apply(R, tptp_fun_Y_8(E, R), tptp_fun_X_9(E, R))))) | (~(apply(R, tptp_fun_X_12(E, R), tptp_fun_Z_10(E, R)) | (~apply(R, tptp_fun_X_12(E, R), tptp_fun_Y_11(E, R))) | (~apply(R, tptp_fun_Y_11(E, R), tptp_fun_Z_10(E, R))) | (~member(tptp_fun_X_12(E, R), E)) | (~member(tptp_fun_Y_11(E, R), E)) | (~member(tptp_fun_Z_10(E, R), E)))))) | (~((~strict_order(R, E)) | (~((~![X: $i, Y: $i] : ((~member(Y, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, X)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)) | (~member(Y, E)) | (~member(Z, E))))))))))) | (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13))))))))))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.44  tff(109,plain,
% 0.21/0.44      (~((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13)))))))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[108, 102])).
% 0.21/0.44  tff(110,plain,
% 0.21/0.44      (((~(strict_order(member_predicate, B!13) | (~((~member(tptp_fun_X_9(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_8(B!13, member_predicate), B!13)) | (~apply(member_predicate, tptp_fun_X_9(B!13, member_predicate), tptp_fun_Y_8(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_8(B!13, member_predicate), tptp_fun_X_9(B!13, member_predicate))))) | (~(apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate)) | (~apply(member_predicate, tptp_fun_X_12(B!13, member_predicate), tptp_fun_Y_11(B!13, member_predicate))) | (~apply(member_predicate, tptp_fun_Y_11(B!13, member_predicate), tptp_fun_Z_10(B!13, member_predicate))) | (~member(tptp_fun_X_12(B!13, member_predicate), B!13)) | (~member(tptp_fun_Y_11(B!13, member_predicate), B!13)) | (~member(tptp_fun_Z_10(B!13, member_predicate), B!13)))))) | (~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13))))))))) | ((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13)))))))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(111,plain,
% 0.21/0.44      ((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13))))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[110, 109])).
% 0.21/0.44  tff(112,plain,
% 0.21/0.44      (^[R: $i, E: $i] : rewrite((~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))) <=> (~((~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))) | (~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | least(tptp_fun_Y_4(A, R), R, A) | ![X: $i] : (~member(X, A)))))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(113,plain,
% 0.21/0.44      (![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))) <=> ![R: $i, E: $i] : (~((~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))) | (~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | least(tptp_fun_Y_4(A, R), R, A) | ![X: $i] : (~member(X, A))))))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[112])).
% 0.21/0.44  tff(114,plain,
% 0.21/0.44      (^[R: $i, E: $i] : refl((~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))) <=> (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(115,plain,
% 0.21/0.44      (![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))) <=> ![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[114])).
% 0.21/0.44  tff(116,plain,
% 0.21/0.44      (^[R: $i, E: $i] : rewrite((~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))) <=> (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(117,plain,
% 0.21/0.44      (![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))) <=> ![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[116])).
% 0.21/0.44  tff(118,plain,
% 0.21/0.44      (![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))) <=> ![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))))),
% 0.21/0.44      inference(transitivity,[status(thm)],[117, 115])).
% 0.21/0.44  tff(119,plain,
% 0.21/0.44      (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))) <=> ((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))), trans(monotonicity(rewrite((subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))) <=> (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))), ((strict_well_order(R, E) | (~strict_order(R, E)) | (subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))) <=> (strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))), rewrite((strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))) <=> (strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))), ((strict_well_order(R, E) | (~strict_order(R, E)) | (subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))) <=> (strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))), ((((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | (~strict_order(R, E)) | (subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))) <=> (((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))))) & (strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))))), rewrite((((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))))) & (strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))) <=> (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))))), ((((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | (~strict_order(R, E)) | (subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))) <=> (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(120,plain,
% 0.21/0.44      (![R: $i, E: $i] : (((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | (~strict_order(R, E)) | (subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))) <=> ![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[119])).
% 0.21/0.44  tff(121,plain,
% 0.21/0.44      (^[R: $i, E: $i] : rewrite((((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : (((~subset(A, E)) | ![X: $i] : (~member(X, A))) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | ((~strict_order(R, E)) | ((subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))) <=> (((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | (~strict_order(R, E)) | (subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(122,plain,
% 0.21/0.44      (![R: $i, E: $i] : (((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : (((~subset(A, E)) | ![X: $i] : (~member(X, A))) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | ((~strict_order(R, E)) | ((subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))) <=> ![R: $i, E: $i] : (((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | (~strict_order(R, E)) | (subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[121])).
% 0.21/0.44  tff(123,plain,
% 0.21/0.44      (![R: $i, E: $i] : (strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((~(subset(A, E) & ?[X: $i] : member(X, A))) | ?[Y: $i] : least(Y, R, A)))) <=> ![R: $i, E: $i] : (strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((~(subset(A, E) & ?[X: $i] : member(X, A))) | ?[Y: $i] : least(Y, R, A))))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(124,plain,
% 0.21/0.44      (^[R: $i, E: $i] : rewrite((strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((subset(A, E) & ?[X: $i] : member(X, A)) => ?[Y: $i] : least(Y, R, A)))) <=> (strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((~(subset(A, E) & ?[X: $i] : member(X, A))) | ?[Y: $i] : least(Y, R, A)))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(125,plain,
% 0.21/0.44      (![R: $i, E: $i] : (strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((subset(A, E) & ?[X: $i] : member(X, A)) => ?[Y: $i] : least(Y, R, A)))) <=> ![R: $i, E: $i] : (strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((~(subset(A, E) & ?[X: $i] : member(X, A))) | ?[Y: $i] : least(Y, R, A))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[124])).
% 0.21/0.44  tff(126,axiom,(![R: $i, E: $i] : (strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((subset(A, E) & ?[X: $i] : member(X, A)) => ?[Y: $i] : least(Y, R, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax','strict_well_order')).
% 0.21/0.44  tff(127,plain,
% 0.21/0.44      (![R: $i, E: $i] : (strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((~(subset(A, E) & ?[X: $i] : member(X, A))) | ?[Y: $i] : least(Y, R, A))))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.44  tff(128,plain,
% 0.21/0.44      (![R: $i, E: $i] : (strict_well_order(R, E) <=> (strict_order(R, E) & ![A: $i] : ((~(subset(A, E) & ?[X: $i] : member(X, A))) | ?[Y: $i] : least(Y, R, A))))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[127, 123])).
% 0.21/0.44  tff(129,plain,(
% 0.21/0.44      ![R: $i, E: $i] : (((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : (((~subset(A, E)) | ![X: $i] : (~member(X, A))) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | ((~strict_order(R, E)) | ((subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))),
% 0.21/0.44      inference(skolemize,[status(sab)],[128])).
% 0.21/0.44  tff(130,plain,
% 0.21/0.44      (![R: $i, E: $i] : (((~strict_well_order(R, E)) | (strict_order(R, E) & ![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A)))) & (strict_well_order(R, E) | (~strict_order(R, E)) | (subset(tptp_fun_A_5(E, R), E) & member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R)) & ![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[129, 122])).
% 0.21/0.44  tff(131,plain,
% 0.21/0.44      (![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[130, 120])).
% 0.21/0.45  tff(132,plain,
% 0.21/0.45      (![R: $i, E: $i] : (~((~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | ![X: $i] : (~member(X, A)) | least(tptp_fun_Y_4(A, R), R, A))))))) | (~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R))))))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[131, 118])).
% 0.21/0.45  tff(133,plain,
% 0.21/0.45      (![R: $i, E: $i] : (~((~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))) | (~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | least(tptp_fun_Y_4(A, R), R, A) | ![X: $i] : (~member(X, A))))))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[132, 113])).
% 0.21/0.45  tff(134,plain,
% 0.21/0.45      ((~![R: $i, E: $i] : (~((~(strict_well_order(R, E) | (~strict_order(R, E)) | (~((~subset(tptp_fun_A_5(E, R), E)) | (~member(tptp_fun_X_6(E, R), tptp_fun_A_5(E, R))) | (~![Y: $i] : (~least(Y, R, tptp_fun_A_5(E, R)))))))) | (~((~strict_well_order(R, E)) | (~((~strict_order(R, E)) | (~![A: $i] : ((~subset(A, E)) | least(tptp_fun_Y_4(A, R), R, A) | ![X: $i] : (~member(X, A))))))))))) | (~((~(strict_well_order(member_predicate, B!13) | (~strict_order(member_predicate, B!13)) | (~((~subset(tptp_fun_A_5(B!13, member_predicate), B!13)) | (~member(tptp_fun_X_6(B!13, member_predicate), tptp_fun_A_5(B!13, member_predicate))) | (~![Y: $i] : (~least(Y, member_predicate, tptp_fun_A_5(B!13, member_predicate)))))))) | (~((~strict_well_order(member_predicate, B!13)) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A))))))))))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(135,plain,
% 0.21/0.45      (~((~(strict_well_order(member_predicate, B!13) | (~strict_order(member_predicate, B!13)) | (~((~subset(tptp_fun_A_5(B!13, member_predicate), B!13)) | (~member(tptp_fun_X_6(B!13, member_predicate), tptp_fun_A_5(B!13, member_predicate))) | (~![Y: $i] : (~least(Y, member_predicate, tptp_fun_A_5(B!13, member_predicate)))))))) | (~((~strict_well_order(member_predicate, B!13)) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A)))))))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[134, 133])).
% 0.21/0.45  tff(136,plain,
% 0.21/0.45      (((~(strict_well_order(member_predicate, B!13) | (~strict_order(member_predicate, B!13)) | (~((~subset(tptp_fun_A_5(B!13, member_predicate), B!13)) | (~member(tptp_fun_X_6(B!13, member_predicate), tptp_fun_A_5(B!13, member_predicate))) | (~![Y: $i] : (~least(Y, member_predicate, tptp_fun_A_5(B!13, member_predicate)))))))) | (~((~strict_well_order(member_predicate, B!13)) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A))))))))) | ((~strict_well_order(member_predicate, B!13)) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A)))))))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(137,plain,
% 0.21/0.45      ((~strict_well_order(member_predicate, B!13)) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A))))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[136, 135])).
% 0.21/0.45  tff(138,plain,
% 0.21/0.45      (((~set(B!13)) | (~strict_well_order(member_predicate, B!13)) | (~![X: $i] : ((~member(X, B!13)) | subset(X, B!13)))) | strict_well_order(member_predicate, B!13)),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(139,plain,
% 0.21/0.45      (strict_well_order(member_predicate, B!13)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[138, 64])).
% 0.21/0.45  tff(140,plain,
% 0.21/0.45      ((~((~strict_well_order(member_predicate, B!13)) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A)))))))) | (~strict_well_order(member_predicate, B!13)) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A))))))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(141,plain,
% 0.21/0.45      ((~((~strict_well_order(member_predicate, B!13)) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A)))))))) | (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A))))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.45  tff(142,plain,
% 0.21/0.45      (~((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A)))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[141, 137])).
% 0.21/0.45  tff(143,plain,
% 0.21/0.45      (((~strict_order(member_predicate, B!13)) | (~![A: $i] : ((~subset(A, B!13)) | least(tptp_fun_Y_4(A, member_predicate), member_predicate, A) | ![X: $i] : (~member(X, A))))) | strict_order(member_predicate, B!13)),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(144,plain,
% 0.21/0.45      (strict_order(member_predicate, B!13)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[143, 142])).
% 0.21/0.45  tff(145,plain,
% 0.21/0.45      ((~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13)))))))) | (~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13))))))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(146,plain,
% 0.21/0.45      ((~((~strict_order(member_predicate, B!13)) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13)))))))) | (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13))))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[145, 144])).
% 0.21/0.45  tff(147,plain,
% 0.21/0.45      (~((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13)))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[146, 111])).
% 0.21/0.45  tff(148,plain,
% 0.21/0.45      (((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Z, B!13)) | (~apply(member_predicate, Y, Z)) | apply(member_predicate, X, Z) | (~apply(member_predicate, X, Y)) | (~member(Y, B!13)) | (~member(X, B!13))))) | ![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(149,plain,
% 0.21/0.45      (![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[148, 147])).
% 0.21/0.45  tff(150,plain,
% 0.21/0.45      (^[X: $i, Y: $i] : refl((apply(member_predicate, X, Y) <=> member(X, Y)) <=> (apply(member_predicate, X, Y) <=> member(X, Y)))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(151,plain,
% 0.21/0.45      (![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y)) <=> ![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[150])).
% 0.21/0.45  tff(152,plain,
% 0.21/0.45      (![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y)) <=> ![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(153,axiom,(![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax','rel_member')).
% 0.21/0.45  tff(154,plain,
% 0.21/0.45      (![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.45  tff(155,plain,(
% 0.21/0.45      ![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y))),
% 0.21/0.45      inference(skolemize,[status(sab)],[154])).
% 0.21/0.45  tff(156,plain,
% 0.21/0.45      (![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[155, 151])).
% 0.21/0.45  tff(157,plain,
% 0.21/0.45      ((~![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y))) | (apply(member_predicate, B!13, A!14) <=> member(B!13, A!14))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(158,plain,
% 0.21/0.45      (apply(member_predicate, B!13, A!14) <=> member(B!13, A!14)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[157, 156])).
% 0.21/0.45  tff(159,plain,
% 0.21/0.45      ((~(apply(member_predicate, B!13, A!14) <=> member(B!13, A!14))) | apply(member_predicate, B!13, A!14) | (~member(B!13, A!14))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(160,plain,
% 0.21/0.45      ((~(apply(member_predicate, B!13, A!14) <=> member(B!13, A!14))) | apply(member_predicate, B!13, A!14)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[159, 76])).
% 0.21/0.45  tff(161,plain,
% 0.21/0.45      (apply(member_predicate, B!13, A!14)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[160, 158])).
% 0.21/0.45  tff(162,plain,
% 0.21/0.45      ((~![X: $i, Y: $i] : (apply(member_predicate, X, Y) <=> member(X, Y))) | (apply(member_predicate, A!14, B!13) <=> member(A!14, B!13))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(163,plain,
% 0.21/0.45      (apply(member_predicate, A!14, B!13) <=> member(A!14, B!13)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[162, 156])).
% 0.21/0.45  tff(164,plain,
% 0.21/0.45      ((~(apply(member_predicate, A!14, B!13) <=> member(A!14, B!13))) | apply(member_predicate, A!14, B!13) | (~member(A!14, B!13))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(165,plain,
% 0.21/0.45      ((~(apply(member_predicate, A!14, B!13) <=> member(A!14, B!13))) | apply(member_predicate, A!14, B!13)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[164, 68])).
% 0.21/0.45  tff(166,plain,
% 0.21/0.45      (apply(member_predicate, A!14, B!13)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[165, 163])).
% 0.21/0.45  tff(167,plain,
% 0.21/0.45      (((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | ((~member(A!14, B!13)) | (~apply(member_predicate, A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~member(B!13, B!13)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~member(A!14, B!13)) | (~apply(member_predicate, A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~member(B!13, B!13)))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(168,plain,
% 0.21/0.45      (((~member(A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~apply(member_predicate, A!14, B!13)) | (~member(B!13, B!13))) <=> ((~member(A!14, B!13)) | (~apply(member_predicate, A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~member(B!13, B!13)))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(169,plain,
% 0.21/0.45      (((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | ((~member(A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~apply(member_predicate, A!14, B!13)) | (~member(B!13, B!13)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | ((~member(A!14, B!13)) | (~apply(member_predicate, A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~member(B!13, B!13))))),
% 0.21/0.45      inference(monotonicity,[status(thm)],[168])).
% 0.21/0.45  tff(170,plain,
% 0.21/0.45      (((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | ((~member(A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~apply(member_predicate, A!14, B!13)) | (~member(B!13, B!13)))) <=> ((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~member(A!14, B!13)) | (~apply(member_predicate, A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~member(B!13, B!13)))),
% 0.21/0.45      inference(transitivity,[status(thm)],[169, 167])).
% 0.21/0.45  tff(171,plain,
% 0.21/0.45      ((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | ((~member(A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~apply(member_predicate, A!14, B!13)) | (~member(B!13, B!13)))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(172,plain,
% 0.21/0.45      ((~![X: $i, Y: $i] : ((~member(Y, B!13)) | (~apply(member_predicate, X, Y)) | (~apply(member_predicate, Y, X)) | (~member(X, B!13)))) | (~member(A!14, B!13)) | (~apply(member_predicate, A!14, B!13)) | (~apply(member_predicate, B!13, A!14)) | (~member(B!13, B!13))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[171, 170])).
% 0.21/0.45  tff(173,plain,
% 0.21/0.45      ($false),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[172, 68, 166, 161, 149, 80])).
% 0.21/0.45  % SZS output end Proof
%------------------------------------------------------------------------------