TSTP Solution File: SET775+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET775+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:58 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET775+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 08:03:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(apply_type, type, (
% 0.19/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_X_10_type, type, (
% 0.19/0.40 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_E_22_type, type, (
% 0.19/0.40 tptp_fun_E_22: $i)).
% 0.19/0.40 tff(tptp_fun_R_20_type, type, (
% 0.19/0.40 tptp_fun_R_20: $i)).
% 0.19/0.40 tff(tptp_fun_P_21_type, type, (
% 0.19/0.40 tptp_fun_P_21: $i)).
% 0.19/0.40 tff(member_type, type, (
% 0.19/0.40 member: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_Y_11_type, type, (
% 0.19/0.40 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_12_type, type, (
% 0.19/0.40 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.19/0.40 tff(equivalence_type, type, (
% 0.19/0.40 equivalence: ( $i * $i ) > $o)).
% 0.19/0.40 tff(pre_order_type, type, (
% 0.19/0.40 pre_order: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_Z_13_type, type, (
% 0.19/0.40 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Y_14_type, type, (
% 0.19/0.40 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_15_type, type, (
% 0.19/0.40 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Z_17_type, type, (
% 0.19/0.40 tptp_fun_Z_17: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Y_18_type, type, (
% 0.19/0.40 tptp_fun_Y_18: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_19_type, type, (
% 0.19/0.40 tptp_fun_X_19: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_16_type, type, (
% 0.19/0.40 tptp_fun_X_16: ( $i * $i ) > $i)).
% 0.19/0.40 tff(1,assumption,(~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22))) | member(tptp_fun_Y_11(R!20, E!22), E!22)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (member(tptp_fun_Y_11(R!20, E!22), E!22)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 ((apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22))) | member(tptp_fun_X_12(R!20, E!22), E!22)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (member(tptp_fun_X_12(R!20, E!22), E!22)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl(((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A)))))) <=> ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A)))))) <=> ![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(A, E!22) & member(B, E!22)) <=> (~((~member(A, E!22)) | (~member(B, E!22))))), ((~(member(A, E!22) & member(B, E!22))) <=> (~(~((~member(A, E!22)) | (~member(B, E!22))))))), rewrite((~(~((~member(A, E!22)) | (~member(B, E!22))))) <=> ((~member(A, E!22)) | (~member(B, E!22)))), ((~(member(A, E!22) & member(B, E!22))) <=> ((~member(A, E!22)) | (~member(B, E!22))))), rewrite((apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))) <=> (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A)))))), (((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) <=> (((~member(A, E!22)) | (~member(B, E!22))) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A)))))))), rewrite((((~member(A, E!22)) | (~member(B, E!22))) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A)))))) <=> ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))), (((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) <=> ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) <=> ![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) & (~equivalence(R!20, E!22))) <=> (pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) & (~equivalence(R!20, E!22)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 ((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) <=> (pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) & (~equivalence(R!20, E!22))) <=> ((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) & (~equivalence(R!20, E!22)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) & (~equivalence(R!20, E!22))) <=> (pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) & (~equivalence(R!20, E!22)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[12, 10])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))) <=> (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 ((~![E: $i, P: $i, R: $i] : ((pre_order(P, E) & ![A: $i, B: $i] : ((member(A, E) & member(B, E)) => (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A))))) => equivalence(R, E))) <=> (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(16,axiom,(~![E: $i, P: $i, R: $i] : ((pre_order(P, E) & ![A: $i, B: $i] : ((member(A, E) & member(B, E)) => (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A))))) => equivalence(R, E))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII11')).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) & (~equivalence(R!20, E!22))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))),
% 0.19/0.41 inference(and_elim,[status(thm)],[24])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 9])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 7])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))) <=> ((~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 ((~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))) <=> (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))) <=> ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))) <=> ((~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[32, 29])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[34, 28])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[37, 27, 5, 3])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 ((apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22))) | (~apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (~apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[39, 1])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 ((~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | ((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 ((~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))) | ((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 ((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[42, 38])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[46, 27, 5, 3])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 ((apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22))) | apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[48, 1])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((~(apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))))) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 ((~(apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))))) | (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[51, 47])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 ((~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[57, 56, 54, 43])).
% 0.19/0.42 tff(59,plain,(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(60,assumption,(~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))), introduced(assumption)).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 ((apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) | member(tptp_fun_Y_14(R!20, E!22), E!22)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (member(tptp_fun_Y_14(R!20, E!22), E!22)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 ((apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) | member(tptp_fun_X_15(R!20, E!22), E!22)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (member(tptp_fun_X_15(R!20, E!22), E!22)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[67, 27, 64, 62])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 ((apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[69, 60])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 ((~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 ((~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))))) | (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[72, 68])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 ((apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) | member(tptp_fun_Z_13(R!20, E!22), E!22)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (member(tptp_fun_Z_13(R!20, E!22), E!22)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[76, 60])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[80, 27, 62, 77])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 ((apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) | apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[82, 60])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 ((~(apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 ((~(apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))))) | (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[85, 81])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[91, 27, 64, 77])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 ((apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[93, 60])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 ((~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))))))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | ((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 ((~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))))))) | ((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 ((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[96, 92])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) | apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[98, 73])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[100, 86])).
% 0.19/0.44 tff(102,assumption,(apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))), introduced(assumption)).
% 0.19/0.44 tff(103,assumption,(apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))), introduced(assumption)).
% 0.19/0.44 tff(104,assumption,(~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))), introduced(assumption)).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (^[R: $i, E: $i] : refl((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[110, 108])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))) <=> (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), rewrite((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))), rewrite((((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 (^[R: $i, E: $i] : rewrite((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 (^[R: $i, E: $i] : rewrite((pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.45 tff(119,axiom,(![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','pre_order')).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.45 tff(122,plain,(
% 0.19/0.45 ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[121])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[123, 113])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[124, 111])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 (![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[125, 106])).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 ((~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(P!21, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, X, Y)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)))))))))) <=> (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(129,plain,
% 0.19/0.45 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(P!21, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, X, Y)) | (~apply(P!21, Y, Z)) | (~member(X, E!22))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(P!21, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, X, Y)) | (~apply(P!21, Y, Z)) | (~member(X, E!22))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(P!21, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, X, Y)) | (~apply(P!21, Y, Z)) | (~member(X, E!22))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, E))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[132, 126])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))))) | ((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 ((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 (pre_order(P!21, E!22)),
% 0.19/0.46 inference(and_elim,[status(thm)],[24])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 ((~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))) | (~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 ((~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))) | ![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.46 tff(142,assumption,(member(tptp_fun_Z_13(R!20, E!22), E!22)), introduced(assumption)).
% 0.19/0.46 tff(143,assumption,(member(tptp_fun_Y_14(R!20, E!22), E!22)), introduced(assumption)).
% 0.19/0.46 tff(144,assumption,(member(tptp_fun_X_15(R!20, E!22), E!22)), introduced(assumption)).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[147, 145])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[150, 144, 143, 142, 141, 104, 103, 102])).
% 0.19/0.47 tff(152,plain,(apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 (apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[152, 64, 62, 77, 101, 99])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 ((~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))))) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[154, 153, 97])).
% 0.19/0.47 tff(156,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(157,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[157])).
% 0.19/0.47 tff(159,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[158, 156])).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.47 tff(162,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[161, 64, 62, 77, 141, 155, 88, 75])).
% 0.19/0.47 tff(163,plain,(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(165,plain,
% 0.19/0.47 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[164])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 (^[A: $i, R: $i] : refl((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[166])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[168])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[169, 167])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 (^[A: $i, R: $i] : trans(monotonicity(rewrite(((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) <=> (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A))))), rewrite((~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))) <=> (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), rewrite((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))), rewrite((((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[171])).
% 0.19/0.48 tff(173,plain,
% 0.19/0.48 (^[A: $i, R: $i] : rewrite((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(174,plain,
% 0.19/0.48 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[173])).
% 0.19/0.48 tff(175,plain,
% 0.19/0.48 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(176,plain,
% 0.19/0.48 (^[A: $i, R: $i] : rewrite((equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(177,plain,
% 0.19/0.48 (![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[176])).
% 0.19/0.48 tff(178,axiom,(![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.19/0.48 tff(179,plain,
% 0.19/0.48 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.48 tff(180,plain,
% 0.19/0.48 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.19/0.48 tff(181,plain,(
% 0.19/0.48 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[180])).
% 0.19/0.48 tff(182,plain,
% 0.19/0.48 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.19/0.48 tff(183,plain,
% 0.19/0.48 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.19/0.48 tff(184,plain,
% 0.19/0.48 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[183, 170])).
% 0.19/0.48 tff(185,plain,
% 0.19/0.48 (![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[184, 165])).
% 0.19/0.48 tff(186,plain,
% 0.19/0.48 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~member(X, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~member(X, E!22)))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(187,plain,
% 0.19/0.48 ((~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))))) <=> (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~member(X, E!22))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(188,plain,
% 0.19/0.48 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~member(X, E!22)))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[187])).
% 0.19/0.49 tff(189,plain,
% 0.19/0.49 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~member(X, E!22)))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[188, 186])).
% 0.19/0.49 tff(190,plain,
% 0.19/0.49 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(191,plain,
% 0.19/0.49 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~member(X, E!22))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.49 tff(192,plain,
% 0.19/0.49 (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~member(X, E!22)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[191, 185])).
% 0.19/0.49 tff(193,plain,
% 0.19/0.49 (((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~member(X, E!22))))))))) | (equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(194,plain,
% 0.19/0.49 (equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.49 tff(195,plain,
% 0.19/0.49 (~equivalence(R!20, E!22)),
% 0.19/0.49 inference(and_elim,[status(thm)],[24])).
% 0.19/0.49 tff(196,plain,
% 0.19/0.49 ((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(197,plain,
% 0.19/0.49 ((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.19/0.49 tff(198,plain,
% 0.19/0.49 ((~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[197, 194])).
% 0.19/0.49 tff(199,plain,
% 0.19/0.49 (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[198, 163, 59])).
% 0.19/0.49 tff(200,plain,
% 0.19/0.49 (((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | member(tptp_fun_X_10(R!20, E!22), E!22)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(201,plain,
% 0.19/0.49 (member(tptp_fun_X_10(R!20, E!22), E!22)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.19/0.49 tff(202,plain,
% 0.19/0.49 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(203,plain,
% 0.19/0.49 (((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(204,plain,
% 0.19/0.49 ((apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))))) <=> (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(205,plain,
% 0.19/0.49 (((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))))) <=> ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[204])).
% 0.19/0.50 tff(206,plain,
% 0.19/0.50 (((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))))) <=> ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[205, 203])).
% 0.19/0.50 tff(207,plain,
% 0.19/0.50 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[206])).
% 0.19/0.50 tff(208,plain,
% 0.19/0.50 (((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[207, 202])).
% 0.19/0.50 tff(209,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> (~((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(210,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~member(A, E!22)) | (~member(B, E!22)) | (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.19/0.50 tff(211,plain,
% 0.19/0.50 (apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[210, 27, 201])).
% 0.19/0.50 tff(212,plain,
% 0.19/0.50 (((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | (~apply(P!21, Y, Z)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))) | ![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(213,plain,
% 0.19/0.50 (![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[212, 139])).
% 0.19/0.50 tff(214,plain,
% 0.19/0.50 (((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> ((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(215,plain,
% 0.19/0.50 ((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(216,plain,
% 0.19/0.50 ((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.19/0.50 tff(217,plain,
% 0.19/0.50 (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[216, 201, 213])).
% 0.19/0.50 tff(218,plain,
% 0.19/0.50 (((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(219,plain,
% 0.19/0.50 (~apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[218, 199])).
% 0.19/0.50 tff(220,plain,
% 0.19/0.50 ((~(apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(221,plain,
% 0.19/0.50 ((~(apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.19/0.50 tff(222,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[221, 217, 211])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------