TSTP Solution File: SET773+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET773+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 05:07:57 EDT 2022
% Result : Theorem 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET773+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat Sep 3 08:06:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.17/0.39 % SZS status Theorem
% 0.17/0.39 % SZS output start Proof
% 0.17/0.39 tff(apply_type, type, (
% 0.17/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.17/0.39 tff(tptp_fun_X_12_type, type, (
% 0.17/0.39 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_E_23_type, type, (
% 0.17/0.39 tptp_fun_E_23: $i)).
% 0.17/0.39 tff(tptp_fun_R_20_type, type, (
% 0.17/0.39 tptp_fun_R_20: $i)).
% 0.17/0.39 tff(tptp_fun_Y_11_type, type, (
% 0.17/0.39 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_R2_21_type, type, (
% 0.17/0.39 tptp_fun_R2_21: $i)).
% 0.17/0.39 tff(tptp_fun_R1_22_type, type, (
% 0.17/0.39 tptp_fun_R1_22: $i)).
% 0.17/0.39 tff(member_type, type, (
% 0.17/0.39 member: ( $i * $i ) > $o)).
% 0.17/0.39 tff(tptp_fun_X_10_type, type, (
% 0.17/0.39 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.17/0.39 tff(equivalence_type, type, (
% 0.17/0.39 equivalence: ( $i * $i ) > $o)).
% 0.17/0.39 tff(tptp_fun_Z_13_type, type, (
% 0.17/0.39 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_Y_14_type, type, (
% 0.17/0.39 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_X_15_type, type, (
% 0.17/0.39 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.17/0.39 tff(1,assumption,(~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))), introduced(assumption)).
% 0.17/0.39 tff(2,plain,
% 0.17/0.39 (((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | member(tptp_fun_X_10(R!20, E!23), E!23)),
% 0.17/0.39 inference(tautology,[status(thm)],[])).
% 0.17/0.39 tff(3,plain,
% 0.17/0.39 (member(tptp_fun_X_10(R!20, E!23), E!23)),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.17/0.39 tff(4,plain,
% 0.17/0.39 (^[A: $i, B: $i] : refl(((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B)))))) <=> ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B)))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(5,plain,
% 0.17/0.39 (![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B)))))) <=> ![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.17/0.39 tff(6,plain,
% 0.17/0.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(A, E!23) & member(B, E!23)) <=> (~((~member(A, E!23)) | (~member(B, E!23))))), ((~(member(A, E!23) & member(B, E!23))) <=> (~(~((~member(A, E!23)) | (~member(B, E!23))))))), rewrite((~(~((~member(A, E!23)) | (~member(B, E!23))))) <=> ((~member(A, E!23)) | (~member(B, E!23)))), ((~(member(A, E!23) & member(B, E!23))) <=> ((~member(A, E!23)) | (~member(B, E!23))))), rewrite((apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))) <=> (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B)))))), (((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B)))) <=> (((~member(A, E!23)) | (~member(B, E!23))) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B)))))))), rewrite((((~member(A, E!23)) | (~member(B, E!23))) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B)))))) <=> ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))), (((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B)))) <=> ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(7,plain,
% 0.17/0.39 (![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B)))) <=> ![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.39 tff(8,plain,
% 0.17/0.39 (((equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))))) & (~equivalence(R!20, E!23))) <=> (equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B)))) & (~equivalence(R!20, E!23)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(9,plain,
% 0.17/0.39 ((equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))))) <=> (equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B)))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(10,plain,
% 0.17/0.39 (((equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))))) & (~equivalence(R!20, E!23))) <=> ((equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))))) & (~equivalence(R!20, E!23)))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[9])).
% 0.17/0.39 tff(11,plain,
% 0.17/0.39 (((equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))))) & (~equivalence(R!20, E!23))) <=> (equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B)))) & (~equivalence(R!20, E!23)))),
% 0.17/0.39 inference(transitivity,[status(thm)],[10, 8])).
% 0.17/0.39 tff(12,plain,
% 0.17/0.39 ((~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E))) <=> (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(13,plain,
% 0.17/0.39 ((~![E: $i, R1: $i, R2: $i, R: $i] : (((equivalence(R1, E) & equivalence(R2, E)) & ![A: $i, B: $i] : ((member(A, E) & member(B, E)) => (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B))))) => equivalence(R, E))) <=> (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(14,axiom,(~![E: $i, R1: $i, R2: $i, R: $i] : (((equivalence(R1, E) & equivalence(R2, E)) & ![A: $i, B: $i] : ((member(A, E) & member(B, E)) => (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B))))) => equivalence(R, E))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII09')).
% 0.17/0.39 tff(15,plain,
% 0.17/0.39 (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.17/0.39 tff(16,plain,
% 0.17/0.39 (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.17/0.39 tff(17,plain,
% 0.17/0.39 (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.17/0.39 tff(18,plain,
% 0.17/0.39 (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.17/0.39 tff(19,plain,
% 0.17/0.39 (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.17/0.40 tff(20,plain,
% 0.17/0.40 (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.17/0.40 tff(21,plain,
% 0.17/0.40 (~![E: $i, R1: $i, R2: $i, R: $i] : ((~(equivalence(R1, E) & equivalence(R2, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(R1, A, B) & apply(R2, A, B)))))) | equivalence(R, E))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.17/0.40 tff(22,plain,
% 0.17/0.40 (equivalence(R1!22, E!23) & equivalence(R2!21, E!23) & ![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B)))) & (~equivalence(R!20, E!23))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.17/0.40 tff(23,plain,
% 0.17/0.40 (![A: $i, B: $i] : ((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))))),
% 0.17/0.40 inference(and_elim,[status(thm)],[22])).
% 0.17/0.40 tff(24,plain,
% 0.17/0.40 (![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.17/0.40 tff(25,plain,
% 0.17/0.40 (![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.17/0.40 tff(26,plain,
% 0.17/0.40 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(27,plain,
% 0.17/0.40 (((~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))))) <=> ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(28,plain,
% 0.17/0.40 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))))))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.17/0.40 tff(29,plain,
% 0.17/0.40 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))))))),
% 0.17/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.17/0.40 tff(30,plain,
% 0.17/0.40 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(31,plain,
% 0.17/0.40 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.17/0.40 tff(32,plain,
% 0.17/0.40 (apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[31, 25, 3])).
% 0.17/0.40 tff(33,plain,
% 0.17/0.40 (((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(34,plain,
% 0.17/0.40 (~apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[33, 1])).
% 0.17/0.40 tff(35,plain,
% 0.17/0.40 ((~(apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))))) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) | ((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(36,plain,
% 0.17/0.40 ((~(apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))))) | ((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.17/0.40 tff(37,plain,
% 0.17/0.40 ((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[36, 32])).
% 0.17/0.40 tff(38,plain,
% 0.17/0.40 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(39,plain,
% 0.17/0.40 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.17/0.40 tff(40,plain,
% 0.17/0.40 (^[A: $i, R: $i] : refl((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(41,plain,
% 0.17/0.40 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.17/0.40 tff(42,plain,
% 0.17/0.40 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(43,plain,
% 0.17/0.40 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.17/0.40 tff(44,plain,
% 0.17/0.40 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.17/0.40 inference(transitivity,[status(thm)],[43, 41])).
% 0.17/0.40 tff(45,plain,
% 0.17/0.40 (^[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))))))))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(46,plain,
% 0.17/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.17/0.41 tff(47,plain,
% 0.17/0.41 (^[A: $i, R: $i] : rewrite((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(48,plain,
% 0.17/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.17/0.41 tff(49,plain,
% 0.17/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(50,plain,
% 0.17/0.41 (^[A: $i, R: $i] : rewrite((equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(51,plain,
% 0.17/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.17/0.41 tff(52,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')).
% 0.17/0.41 tff(53,plain,
% 0.17/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.17/0.41 tff(54,plain,
% 0.17/0.41 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.17/0.41 tff(55,plain,(
% 0.17/0.41 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.17/0.41 inference(skolemize,[status(sab)],[54])).
% 0.17/0.41 tff(56,plain,
% 0.17/0.41 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.17/0.41 tff(57,plain,
% 0.17/0.41 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.17/0.41 tff(58,plain,
% 0.17/0.41 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[57, 44])).
% 0.17/0.41 tff(59,plain,
% 0.17/0.41 (![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))))))))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[58, 39])).
% 0.17/0.41 tff(60,plain,
% 0.17/0.41 (((~![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(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))))))) <=> ((~![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(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(61,plain,
% 0.17/0.41 ((~((~(equivalence(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : (apply(R1!22, Y, X) | (~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~apply(R1!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))) <=> (~((~(equivalence(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(62,plain,
% 0.17/0.41 (((~![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(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : (apply(R1!22, Y, X) | (~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~apply(R1!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![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(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.17/0.41 tff(63,plain,
% 0.17/0.41 (((~![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(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : (apply(R1!22, Y, X) | (~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~apply(R1!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![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(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.17/0.42 inference(transitivity,[status(thm)],[62, 60])).
% 0.17/0.42 tff(64,plain,
% 0.17/0.42 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : (apply(R1!22, Y, X) | (~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~apply(R1!22, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(65,plain,
% 0.17/0.42 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.17/0.42 tff(66,plain,
% 0.17/0.42 (~((~(equivalence(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[65, 59])).
% 0.17/0.42 tff(67,plain,
% 0.17/0.42 (((~(equivalence(R1!22, E!23) | (~((~member(tptp_fun_X_10(R1!22, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R1!22, E!23), tptp_fun_X_10(R1!22, E!23)))) | (~(apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_11(R1!22, E!23), E!23)))) | (~(apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23)) | (~apply(R1!22, tptp_fun_X_15(R1!22, E!23), tptp_fun_Y_14(R1!22, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R1!22, E!23), tptp_fun_Z_13(R1!22, E!23))) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_Z_13(R1!22, E!23), E!23)))))) | (~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))))) | ((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(68,plain,
% 0.17/0.42 ((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.17/0.42 tff(69,plain,
% 0.17/0.42 (equivalence(R1!22, E!23)),
% 0.17/0.42 inference(and_elim,[status(thm)],[22])).
% 0.17/0.42 tff(70,plain,
% 0.17/0.42 ((~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))) | (~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(71,plain,
% 0.17/0.42 ((~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.17/0.42 tff(72,plain,
% 0.17/0.42 (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.17/0.42 tff(73,plain,
% 0.17/0.42 (((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))) | ![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(74,plain,
% 0.17/0.42 (![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.17/0.42 tff(75,plain,
% 0.17/0.42 (((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) <=> ((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(76,plain,
% 0.17/0.42 ((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(77,plain,
% 0.17/0.42 ((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.17/0.42 tff(78,plain,
% 0.17/0.42 (apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[77, 74, 3])).
% 0.17/0.42 tff(79,plain,
% 0.17/0.42 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))))))) <=> ((~![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(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))))))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(80,plain,
% 0.17/0.43 ((~((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : (apply(R2!21, Y, X) | (~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R2!21, X, Z) | (~apply(R2!21, X, Y)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))) <=> (~((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))))))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(81,plain,
% 0.17/0.43 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : (apply(R2!21, Y, X) | (~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R2!21, X, Z) | (~apply(R2!21, X, Y)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![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(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))))))),
% 0.17/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.17/0.43 tff(82,plain,
% 0.17/0.43 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : (apply(R2!21, Y, X) | (~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R2!21, X, Z) | (~apply(R2!21, X, Y)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![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(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))))))),
% 0.17/0.43 inference(transitivity,[status(thm)],[81, 79])).
% 0.17/0.43 tff(83,plain,
% 0.17/0.43 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : (apply(R2!21, Y, X) | (~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R2!21, X, Z) | (~apply(R2!21, X, Y)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(84,plain,
% 0.17/0.43 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))))))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.17/0.43 tff(85,plain,
% 0.17/0.43 (~((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[84, 59])).
% 0.17/0.43 tff(86,plain,
% 0.17/0.43 (((~(equivalence(R2!21, E!23) | (~((~member(tptp_fun_X_10(R2!21, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R2!21, E!23), tptp_fun_X_10(R2!21, E!23)))) | (~(apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_11(R2!21, E!23), E!23)))) | (~(apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23)) | (~apply(R2!21, tptp_fun_X_15(R2!21, E!23), tptp_fun_Y_14(R2!21, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R2!21, E!23), tptp_fun_Z_13(R2!21, E!23))) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_Z_13(R2!21, E!23), E!23)))))) | (~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))))) | ((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))),
% 0.17/0.43 inference(tautology,[status(thm)],[])).
% 0.17/0.43 tff(87,plain,
% 0.17/0.43 ((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.17/0.44 tff(88,plain,
% 0.17/0.44 (equivalence(R2!21, E!23)),
% 0.17/0.44 inference(and_elim,[status(thm)],[22])).
% 0.17/0.44 tff(89,plain,
% 0.17/0.44 ((~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))) | (~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(90,plain,
% 0.17/0.44 ((~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.17/0.44 tff(91,plain,
% 0.17/0.44 (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.17/0.44 tff(92,plain,
% 0.17/0.44 (((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))) | ![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(93,plain,
% 0.17/0.44 (![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.17/0.44 tff(94,plain,
% 0.17/0.44 (((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) <=> ((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(95,plain,
% 0.17/0.44 ((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | ((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(96,plain,
% 0.17/0.44 ((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.17/0.44 tff(97,plain,
% 0.17/0.44 (apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[96, 93, 3])).
% 0.17/0.44 tff(98,plain,
% 0.17/0.44 ((~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))) | (~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(99,plain,
% 0.17/0.44 ($false),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[98, 97, 78, 37])).
% 0.17/0.44 tff(100,plain,((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.44 tff(101,assumption,(~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))), introduced(assumption)).
% 0.17/0.44 tff(102,plain,
% 0.17/0.44 ((apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))) | member(tptp_fun_Y_14(R!20, E!23), E!23)),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(103,plain,
% 0.17/0.44 (member(tptp_fun_Y_14(R!20, E!23), E!23)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.17/0.44 tff(104,plain,
% 0.17/0.44 ((apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))) | member(tptp_fun_X_15(R!20, E!23), E!23)),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(105,plain,
% 0.17/0.44 (member(tptp_fun_X_15(R!20, E!23), E!23)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.17/0.44 tff(106,plain,
% 0.17/0.44 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))))))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(107,plain,
% 0.17/0.44 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))))))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(108,plain,
% 0.17/0.44 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.17/0.44 tff(109,plain,
% 0.17/0.44 (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[108, 25, 105, 103])).
% 0.17/0.44 tff(110,plain,
% 0.17/0.44 ((apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))) | apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(111,plain,
% 0.17/0.44 (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[110, 101])).
% 0.17/0.44 tff(112,plain,
% 0.17/0.44 ((~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))))) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(113,plain,
% 0.17/0.44 ((~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))))) | (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.17/0.44 tff(114,plain,
% 0.17/0.44 (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[113, 109])).
% 0.17/0.44 tff(115,plain,
% 0.17/0.44 (((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(116,plain,
% 0.17/0.44 (apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.17/0.44 tff(117,plain,
% 0.17/0.44 ((apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))) | member(tptp_fun_Z_13(R!20, E!23), E!23)),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(118,plain,
% 0.17/0.44 (member(tptp_fun_Z_13(R!20, E!23), E!23)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[117, 101])).
% 0.17/0.44 tff(119,plain,
% 0.17/0.44 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(120,plain,
% 0.17/0.44 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(121,plain,
% 0.17/0.44 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.17/0.44 tff(122,plain,
% 0.17/0.44 (apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[121, 25, 103, 118])).
% 0.17/0.44 tff(123,plain,
% 0.17/0.44 ((apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))) | apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(124,plain,
% 0.17/0.44 (apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[123, 101])).
% 0.17/0.44 tff(125,plain,
% 0.17/0.44 ((~(apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(126,plain,
% 0.17/0.44 ((~(apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))))) | (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.17/0.44 tff(127,plain,
% 0.17/0.44 (~((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.17/0.44 tff(128,plain,
% 0.17/0.44 (((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))) | apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(129,plain,
% 0.17/0.44 (apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.17/0.44 tff(130,plain,
% 0.17/0.44 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(131,plain,
% 0.17/0.45 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))))),
% 0.17/0.45 inference(quant_inst,[status(thm)],[])).
% 0.17/0.45 tff(132,plain,
% 0.17/0.45 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.17/0.45 tff(133,plain,
% 0.17/0.45 (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[132, 25, 105, 118])).
% 0.17/0.45 tff(134,plain,
% 0.17/0.45 ((apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))),
% 0.17/0.45 inference(tautology,[status(thm)],[])).
% 0.17/0.45 tff(135,plain,
% 0.17/0.45 (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[134, 101])).
% 0.17/0.45 tff(136,plain,
% 0.17/0.45 ((~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))))) | apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | ((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.17/0.45 inference(tautology,[status(thm)],[])).
% 0.17/0.45 tff(137,plain,
% 0.17/0.45 ((~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))))) | ((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.17/0.45 tff(138,plain,
% 0.17/0.45 ((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[137, 133])).
% 0.17/0.45 tff(139,plain,
% 0.17/0.45 (((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.17/0.45 inference(tautology,[status(thm)],[])).
% 0.17/0.45 tff(140,plain,
% 0.17/0.45 (apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[139, 114])).
% 0.17/0.45 tff(141,plain,
% 0.17/0.45 (((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))) | apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.45 inference(tautology,[status(thm)],[])).
% 0.17/0.45 tff(142,plain,
% 0.17/0.45 (apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[141, 127])).
% 0.17/0.45 tff(143,assumption,(apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))), introduced(assumption)).
% 0.17/0.45 tff(144,assumption,(apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))), introduced(assumption)).
% 0.17/0.45 tff(145,assumption,(~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))), introduced(assumption)).
% 0.17/0.45 tff(146,assumption,(member(tptp_fun_Z_13(R!20, E!23), E!23)), introduced(assumption)).
% 0.17/0.45 tff(147,assumption,(member(tptp_fun_Y_14(R!20, E!23), E!23)), introduced(assumption)).
% 0.17/0.45 tff(148,assumption,(member(tptp_fun_X_15(R!20, E!23), E!23)), introduced(assumption)).
% 0.17/0.45 tff(149,plain,
% 0.17/0.45 (((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))) | ![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))),
% 0.17/0.45 inference(tautology,[status(thm)],[])).
% 0.17/0.45 tff(150,plain,
% 0.17/0.45 (![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[149, 91])).
% 0.17/0.45 tff(151,plain,
% 0.17/0.45 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(152,plain,
% 0.17/0.45 (((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))) <=> ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(153,plain,
% 0.17/0.45 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))))),
% 0.17/0.45 inference(monotonicity,[status(thm)],[152])).
% 0.17/0.45 tff(154,plain,
% 0.17/0.45 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.17/0.45 inference(transitivity,[status(thm)],[153, 151])).
% 0.17/0.45 tff(155,plain,
% 0.17/0.45 ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.17/0.45 inference(quant_inst,[status(thm)],[])).
% 0.17/0.45 tff(156,plain,
% 0.17/0.45 ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.17/0.45 tff(157,plain,
% 0.17/0.45 ($false),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[156, 150, 148, 147, 146, 145, 144, 143])).
% 0.17/0.45 tff(158,plain,(apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.45 tff(159,plain,
% 0.17/0.45 (apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[158, 105, 103, 118, 142, 140])).
% 0.17/0.45 tff(160,plain,
% 0.17/0.45 ((~((~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))),
% 0.17/0.45 inference(tautology,[status(thm)],[])).
% 0.17/0.45 tff(161,plain,
% 0.17/0.45 (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[160, 159, 138])).
% 0.17/0.45 tff(162,plain,
% 0.17/0.45 (((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))) | ![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))),
% 0.17/0.46 inference(tautology,[status(thm)],[])).
% 0.17/0.46 tff(163,plain,
% 0.17/0.46 (![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[162, 72])).
% 0.17/0.46 tff(164,plain,
% 0.17/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(165,plain,
% 0.17/0.46 (((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23))) <=> ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(166,plain,
% 0.17/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[165])).
% 0.17/0.46 tff(167,plain,
% 0.17/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.17/0.46 inference(transitivity,[status(thm)],[166, 164])).
% 0.17/0.46 tff(168,plain,
% 0.17/0.46 ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(169,plain,
% 0.17/0.46 ((~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.17/0.46 tff(170,plain,
% 0.17/0.46 ($false),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[169, 163, 105, 103, 118, 161, 129, 116])).
% 0.17/0.46 tff(171,plain,(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.46 tff(172,plain,
% 0.17/0.46 (((~![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!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y))))))))))) <=> ((~![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!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)))))))))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(173,plain,
% 0.17/0.46 ((~((~(equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23)))))))))) <=> (~((~(equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y))))))))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(174,plain,
% 0.17/0.46 (((~![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!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![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!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)))))))))))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[173])).
% 0.17/0.46 tff(175,plain,
% 0.17/0.46 (((~![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!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))) <=> ((~![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!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)))))))))))),
% 0.17/0.47 inference(transitivity,[status(thm)],[174, 172])).
% 0.17/0.47 tff(176,plain,
% 0.17/0.47 ((~![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!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!23)) | (~member(Y, E!23)) | (~member(Z, E!23))))))))))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(177,plain,
% 0.17/0.47 ((~![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!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y))))))))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.17/0.47 tff(178,plain,
% 0.17/0.47 (~((~(equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)))))))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[177, 59])).
% 0.17/0.47 tff(179,plain,
% 0.17/0.47 (((~(equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~equivalence(R!20, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | apply(R!20, Y, X) | (~apply(R!20, X, Y)))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | (~apply(R!20, Y, Z)) | apply(R!20, X, Z) | (~apply(R!20, X, Y))))))))) | (equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))),
% 0.17/0.47 inference(tautology,[status(thm)],[])).
% 0.17/0.47 tff(180,plain,
% 0.17/0.47 (equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.17/0.47 tff(181,plain,
% 0.17/0.47 (~equivalence(R!20, E!23)),
% 0.17/0.47 inference(and_elim,[status(thm)],[22])).
% 0.17/0.47 tff(182,plain,
% 0.17/0.47 ((~(equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))))),
% 0.17/0.47 inference(tautology,[status(thm)],[])).
% 0.17/0.47 tff(183,plain,
% 0.17/0.47 ((~(equivalence(R!20, E!23) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))))) | (~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.17/0.47 tff(184,plain,
% 0.17/0.47 ((~((~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[183, 180])).
% 0.17/0.47 tff(185,plain,
% 0.17/0.47 (~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[184, 171, 100])).
% 0.17/0.47 tff(186,plain,
% 0.17/0.47 ((apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23))) | member(tptp_fun_Y_11(R!20, E!23), E!23)),
% 0.17/0.47 inference(tautology,[status(thm)],[])).
% 0.17/0.47 tff(187,plain,
% 0.17/0.47 (member(tptp_fun_Y_11(R!20, E!23), E!23)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.17/0.47 tff(188,plain,
% 0.17/0.47 ((apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23))) | member(tptp_fun_X_12(R!20, E!23), E!23)),
% 0.17/0.47 inference(tautology,[status(thm)],[])).
% 0.17/0.47 tff(189,plain,
% 0.17/0.47 (member(tptp_fun_X_12(R!20, E!23), E!23)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[188, 185])).
% 0.17/0.47 tff(190,plain,
% 0.17/0.47 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(191,plain,
% 0.17/0.47 (((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))))) <=> ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(192,plain,
% 0.17/0.47 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))))))),
% 0.17/0.47 inference(monotonicity,[status(thm)],[191])).
% 0.17/0.47 tff(193,plain,
% 0.17/0.47 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))))))),
% 0.17/0.48 inference(transitivity,[status(thm)],[192, 190])).
% 0.17/0.48 tff(194,plain,
% 0.17/0.48 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))))))),
% 0.17/0.48 inference(quant_inst,[status(thm)],[])).
% 0.17/0.48 tff(195,plain,
% 0.17/0.48 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.17/0.48 tff(196,plain,
% 0.17/0.48 (apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[195, 25, 189, 187])).
% 0.17/0.48 tff(197,plain,
% 0.17/0.48 ((apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23))) | (~apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(198,plain,
% 0.17/0.48 (~apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[197, 185])).
% 0.17/0.48 tff(199,plain,
% 0.17/0.48 ((~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | ((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(200,plain,
% 0.17/0.48 ((~(apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))))) | ((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.17/0.48 tff(201,plain,
% 0.17/0.48 ((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[200, 196])).
% 0.17/0.48 tff(202,plain,
% 0.17/0.48 (((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))))))) <=> ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))))))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(203,plain,
% 0.17/0.48 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))))))),
% 0.17/0.48 inference(quant_inst,[status(thm)],[])).
% 0.17/0.48 tff(204,plain,
% 0.17/0.48 ((~![A: $i, B: $i] : ((~member(A, E!23)) | (~member(B, E!23)) | (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.17/0.48 tff(205,plain,
% 0.17/0.48 (apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[204, 25, 189, 187])).
% 0.17/0.48 tff(206,plain,
% 0.17/0.48 ((apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23))) | apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(207,plain,
% 0.17/0.48 (apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[206, 185])).
% 0.17/0.48 tff(208,plain,
% 0.17/0.48 ((~(apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))))) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(209,plain,
% 0.17/0.48 ((~(apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)) <=> (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))))) | (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.17/0.48 tff(210,plain,
% 0.17/0.48 (~((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[209, 205])).
% 0.17/0.48 tff(211,plain,
% 0.17/0.48 (((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))) | apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(212,plain,
% 0.17/0.48 (apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.17/0.48 tff(213,plain,
% 0.17/0.48 (((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R2!21, Y, Z)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))) | ![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(214,plain,
% 0.17/0.48 (![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[213, 91])).
% 0.17/0.48 tff(215,plain,
% 0.17/0.48 (((~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(216,plain,
% 0.17/0.48 ((~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.17/0.48 inference(quant_inst,[status(thm)],[])).
% 0.17/0.48 tff(217,plain,
% 0.17/0.48 ((~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R2!21, X, Y)) | apply(R2!21, Y, X))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.17/0.48 tff(218,plain,
% 0.17/0.48 (apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[217, 214, 189, 187, 212])).
% 0.17/0.48 tff(219,plain,
% 0.17/0.48 (((~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))) | apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(220,plain,
% 0.17/0.48 (apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[219, 210])).
% 0.17/0.48 tff(221,plain,
% 0.17/0.48 (((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~apply(R1!22, Y, Z)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))) | ![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(222,plain,
% 0.17/0.48 (![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[221, 72])).
% 0.17/0.48 tff(223,plain,
% 0.17/0.48 (((~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) <=> ((~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(224,plain,
% 0.17/0.49 ((~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | ((~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.17/0.49 inference(quant_inst,[status(thm)],[])).
% 0.17/0.49 tff(225,plain,
% 0.17/0.49 ((~![X: $i, Y: $i] : ((~member(X, E!23)) | (~member(Y, E!23)) | (~apply(R1!22, X, Y)) | apply(R1!22, Y, X))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.17/0.49 tff(226,plain,
% 0.17/0.49 (apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[225, 222, 189, 187, 220])).
% 0.17/0.49 tff(227,plain,
% 0.17/0.49 ((~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))) | (~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.17/0.49 inference(tautology,[status(thm)],[])).
% 0.17/0.49 tff(228,plain,
% 0.17/0.49 ($false),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[227, 226, 218, 201])).
% 0.17/0.49 % SZS output end Proof
%------------------------------------------------------------------------------