%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET773+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:26:19 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET773+4 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:43:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(apply_type, type, (
% 0.21/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_X_12_type, type, (
% 0.21/0.39 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_E_23_type, type, (
% 0.21/0.39 tptp_fun_E_23: $i)).
% 0.21/0.39 tff(tptp_fun_R_20_type, type, (
% 0.21/0.39 tptp_fun_R_20: $i)).
% 0.21/0.39 tff(tptp_fun_Y_11_type, type, (
% 0.21/0.39 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_R2_21_type, type, (
% 0.21/0.39 tptp_fun_R2_21: $i)).
% 0.21/0.39 tff(tptp_fun_R1_22_type, type, (
% 0.21/0.39 tptp_fun_R1_22: $i)).
% 0.21/0.39 tff(member_type, type, (
% 0.21/0.39 member: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_X_10_type, type, (
% 0.21/0.39 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.21/0.39 tff(equivalence_type, type, (
% 0.21/0.39 equivalence: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_Z_13_type, type, (
% 0.21/0.39 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_X_15_type, type, (
% 0.21/0.39 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_Y_14_type, type, (
% 0.21/0.39 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.21/0.39 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)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (((~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)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (member(tptp_fun_X_10(R!20, E!23), E!23)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (^[A: $i, B: $i] : refl(((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23))) <=> ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23))) <=> ![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (^[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))))), trans(trans(monotonicity(rewrite((apply(R1!22, A, B) & apply(R2!21, 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))) <=> (apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))))), rewrite((apply(R!20, A, B) <=> (~((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))))) <=> (~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B)))), ((apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))) <=> (~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))))), rewrite((~(((~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))) <=> apply(R!20, A, B)))), ((apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B))) <=> (~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, 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(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B)))))), rewrite((((~member(A, E!23)) | (~member(B, E!23))) | (~(((~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))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))), (((~(member(A, E!23) & member(B, E!23))) | (apply(R!20, A, B) <=> (apply(R1!22, A, B) & apply(R2!21, A, B)))) <=> ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![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] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (((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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((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)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (((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)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[9])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (((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)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[10, 8])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 ((~![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 ((~![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 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')).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (~![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))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (~![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))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (~![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))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (~![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))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (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))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (![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))))),
% 0.21/0.39 inference(and_elim,[status(thm)],[19])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 5])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~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))) | (~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)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~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))) | (~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)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (((~(((~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)))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23))) <=> ((~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))) | (~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)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 ((~(((~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)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (((~(((~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)))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~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))) | (~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)))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (((~(((~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)))) <=> 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)) | (~member(tptp_fun_X_10(R!20, E!23), E!23))) <=> ((~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))) | (~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)))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[26, 24])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~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))) | (~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))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~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))) | (~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)))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[28, 23])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | (~member(tptp_fun_X_10(R!20, E!23), E!23)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~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))) | (~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))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (~(((~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)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[31, 22, 3])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (((~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)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (~apply(R!20, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[33, 1])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((((~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)))) <=> 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))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 ((((~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)))) <=> 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))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 ((~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)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[36, 32])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (^[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)))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (![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))))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (^[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)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (![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))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (^[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)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (![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))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (![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))))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[43, 41])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (^[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))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![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))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (^[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))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (^[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)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.41 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')).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.21/0.41 tff(55,plain,(
% 0.21/0.41 ![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))))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[54])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![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))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (![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))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[57, 44])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![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))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 39])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (((~![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)))) | (~((~member(tptp_fun_Y_11(R1!22, E!23), E!23)) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)))) | (~((~member(tptp_fun_Z_13(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(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_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | 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)))) | (~((~member(tptp_fun_Y_11(R1!22, E!23), E!23)) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)))) | (~((~member(tptp_fun_Z_13(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(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_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 ((~((~(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] : (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)))) | (~((~member(tptp_fun_Y_11(R1!22, E!23), E!23)) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)))) | (~((~member(tptp_fun_Z_13(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(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_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (((~![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))))))))))) <=> ((~![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)))) | (~((~member(tptp_fun_Y_11(R1!22, E!23), E!23)) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)))) | (~((~member(tptp_fun_Z_13(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(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_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (((~![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))))))))))) <=> ((~![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)))) | (~((~member(tptp_fun_Y_11(R1!22, E!23), E!23)) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)))) | (~((~member(tptp_fun_Z_13(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(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_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[62, 60])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 ((~![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(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))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 ((~![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(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)))) | (~((~member(tptp_fun_Y_11(R1!22, E!23), E!23)) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)))) | (~((~member(tptp_fun_Z_13(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(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_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (~((~(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)))) | (~((~member(tptp_fun_Y_11(R1!22, E!23), E!23)) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)))) | (~((~member(tptp_fun_Z_13(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(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_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[65, 59])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (((~(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)))) | (~((~member(tptp_fun_Y_11(R1!22, E!23), E!23)) | (~member(tptp_fun_X_12(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_12(R1!22, E!23), tptp_fun_Y_11(R1!22, E!23))) | apply(R1!22, tptp_fun_Y_11(R1!22, E!23), tptp_fun_X_12(R1!22, E!23)))) | (~((~member(tptp_fun_Z_13(R1!22, E!23), E!23)) | (~member(tptp_fun_Y_14(R1!22, E!23), E!23)) | (~member(tptp_fun_X_15(R1!22, E!23), E!23)) | (~apply(R1!22, tptp_fun_Y_14(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_X_15(R1!22, E!23), tptp_fun_Z_13(R1!22, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | 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] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 ((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (equivalence(R1!22, E!23)),
% 0.21/0.44 inference(and_elim,[status(thm)],[19])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 ((~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | 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] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 ((~((~equivalence(R1!22, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | 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] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (~((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 (((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | 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))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 (![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (((~![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 ((~![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)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 ((~![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))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 (apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[77, 74, 3])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (((~![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)))) | (~((~member(tptp_fun_Y_11(R2!21, E!23), E!23)) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)))) | (~((~member(tptp_fun_Z_13(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(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_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~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)))) | (~((~member(tptp_fun_Y_11(R2!21, E!23), E!23)) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)))) | (~((~member(tptp_fun_Z_13(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(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_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 ((~((~(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)))) | (~((~member(tptp_fun_Y_11(R2!21, E!23), E!23)) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)))) | (~((~member(tptp_fun_Z_13(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(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_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (((~![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)))) | (~((~member(tptp_fun_Y_11(R2!21, E!23), E!23)) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)))) | (~((~member(tptp_fun_Z_13(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(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_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[80])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (((~![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)))) | (~((~member(tptp_fun_Y_11(R2!21, E!23), E!23)) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)))) | (~((~member(tptp_fun_Z_13(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(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_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[81, 79])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 ((~![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))))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 ((~![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)))) | (~((~member(tptp_fun_Y_11(R2!21, E!23), E!23)) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)))) | (~((~member(tptp_fun_Z_13(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(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_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (~((~(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)))) | (~((~member(tptp_fun_Y_11(R2!21, E!23), E!23)) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)))) | (~((~member(tptp_fun_Z_13(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(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_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[84, 59])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (((~(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)))) | (~((~member(tptp_fun_Y_11(R2!21, E!23), E!23)) | (~member(tptp_fun_X_12(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_X_12(R2!21, E!23), tptp_fun_Y_11(R2!21, E!23))) | apply(R2!21, tptp_fun_Y_11(R2!21, E!23), tptp_fun_X_12(R2!21, E!23)))) | (~((~member(tptp_fun_Z_13(R2!21, E!23), E!23)) | (~member(tptp_fun_Y_14(R2!21, E!23), E!23)) | (~member(tptp_fun_X_15(R2!21, E!23), E!23)) | (~apply(R2!21, tptp_fun_Y_14(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_X_15(R2!21, E!23), tptp_fun_Z_13(R2!21, 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, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~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] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 ((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 (equivalence(R2!21, E!23)),
% 0.21/0.46 inference(and_elim,[status(thm)],[19])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 ((~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~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] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 ((~((~equivalence(R2!21, E!23)) | (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~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] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (~((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~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))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (((~![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 ((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~member(tptp_fun_X_10(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[96, 93, 3])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 ((~((~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))))) | (~apply(R1!22, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23))) | (~apply(R2!21, tptp_fun_X_10(R!20, E!23), tptp_fun_X_10(R!20, E!23)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[98, 97, 78, 37])).
% 0.21/0.46 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,[]))).
% 0.21/0.46 tff(101,assumption,(~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23)))), introduced(assumption)).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23))) | member(tptp_fun_Y_14(R!20, E!23), E!23)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (member(tptp_fun_Y_14(R!20, E!23), E!23)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23))) | member(tptp_fun_Z_13(R!20, E!23), E!23)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (member(tptp_fun_Z_13(R!20, E!23), E!23)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(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(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)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(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(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)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (((~(((~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)))) | (~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)) | (~member(tptp_fun_Y_14(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(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)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 ((~(((~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)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (((~(((~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)))) | (~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(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)))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (((~(((~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)))) | (~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)) | (~member(tptp_fun_Y_14(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(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)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(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(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))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[110])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(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(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)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[111, 106])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(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(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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (~(((~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)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[114, 22, 105, 103])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 (((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_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))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 (apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[116, 101])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 ((((~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))))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 ((((~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)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (~((~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))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 (((~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))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 (apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23))) | member(tptp_fun_X_15(R!20, E!23), E!23)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 (member(tptp_fun_X_15(R!20, E!23), E!23)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[123, 101])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), 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)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), 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)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 (((~(((~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)))) | (~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_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), 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)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 ((~(((~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)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (((~(((~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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), 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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (((~(((~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)))) | (~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_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), 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)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), 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))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[129])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), 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)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[130, 125])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), 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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (~(((~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)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[133, 22, 103, 124])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_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))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[135, 101])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 ((((~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))))) | (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 ((((~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)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (~((~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))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[138, 134])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (((~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))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(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)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(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)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (((~(((~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)))) | (~member(tptp_fun_X_15(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)) | (~member(tptp_fun_X_15(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(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)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 ((~(((~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)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 (((~(((~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)))) | (~member(tptp_fun_X_15(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(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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[144])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (((~(((~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)))) | (~member(tptp_fun_X_15(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)) | (~member(tptp_fun_X_15(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(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)))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[145, 143])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(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))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[146])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(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)))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[147, 142])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (~(((~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)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[150, 22, 105, 124])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 (((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_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)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (~apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[152, 101])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 ((((~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)))) | apply(R!20, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 ((((~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))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 ((~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)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[155, 151])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 (((~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))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[157, 120])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (((~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))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[159, 139])).
% 0.21/0.48 tff(161,assumption,(apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))), introduced(assumption)).
% 0.21/0.48 tff(162,assumption,(apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))), introduced(assumption)).
% 0.21/0.48 tff(163,assumption,(~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))), introduced(assumption)).
% 0.21/0.48 tff(164,assumption,(member(tptp_fun_X_15(R!20, E!23), E!23)), introduced(assumption)).
% 0.21/0.48 tff(165,assumption,(member(tptp_fun_Y_14(R!20, E!23), E!23)), introduced(assumption)).
% 0.21/0.48 tff(166,assumption,(member(tptp_fun_Z_13(R!20, E!23), E!23)), introduced(assumption)).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))) | ![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[167, 72])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 (((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, 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_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_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, 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_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] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[170])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, 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_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] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[171, 169])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | ((~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, 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_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)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.48 tff(175,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[174, 168, 166, 165, 164, 163, 162, 161])).
% 0.21/0.48 tff(176,plain,(apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | (~apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R1!22, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(177,plain,
% 0.21/0.48 (apply(R1!22, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[176, 105, 103, 124, 160, 158])).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 ((~((~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)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(179,plain,
% 0.21/0.48 (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[178, 177, 156])).
% 0.21/0.48 tff(180,plain,
% 0.21/0.48 (((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))) | ![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[180, 91])).
% 0.21/0.48 tff(182,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), 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))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), 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))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(183,plain,
% 0.21/0.49 (((~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, 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)) | 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_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), 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))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(184,plain,
% 0.21/0.49 (((~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, 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)) | 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] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), 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))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[183])).
% 0.21/0.49 tff(185,plain,
% 0.21/0.49 (((~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, 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)) | 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] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), 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))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[184, 182])).
% 0.21/0.49 tff(186,plain,
% 0.21/0.49 ((~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | ((~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, 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)) | 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))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(187,plain,
% 0.21/0.49 ((~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Z_13(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_15(R!20, E!23), tptp_fun_Y_14(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_14(R!20, E!23), tptp_fun_Z_13(R!20, E!23)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[187, 181, 105, 103, 124, 179, 141, 122])).
% 0.21/0.49 tff(189,plain,((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))) <=> ((~![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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 ((~((~(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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(192,plain,
% 0.21/0.49 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[192, 190])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!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))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(195,plain,
% 0.21/0.49 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 (~((~(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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[195, 59])).
% 0.21/0.50 tff(197,plain,
% 0.21/0.50 (((~(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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z))))))))) | (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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23)))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(198,plain,
% 0.21/0.50 (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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.21/0.50 tff(199,plain,
% 0.21/0.50 (~equivalence(R!20, E!23)),
% 0.21/0.50 inference(and_elim,[status(thm)],[19])).
% 0.21/0.50 tff(200,plain,
% 0.21/0.50 ((~(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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, 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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(201,plain,
% 0.21/0.50 ((~(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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(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)))) | (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.21/0.50 tff(202,plain,
% 0.21/0.50 ((~((~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_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(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(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) | (~((~member(tptp_fun_Z_13(R!20, E!23), E!23)) | (~member(tptp_fun_Y_14(R!20, E!23), E!23)) | (~member(tptp_fun_X_15(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(R!20, 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_Z_13(R!20, E!23))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[201, 198])).
% 0.21/0.50 tff(203,plain,
% 0.21/0.50 (~((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[202, 189, 100])).
% 0.21/0.50 tff(204,plain,
% 0.21/0.50 (((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, 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)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(205,plain,
% 0.21/0.50 (member(tptp_fun_X_12(R!20, E!23), E!23)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.21/0.50 tff(206,plain,
% 0.21/0.50 (((~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_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | member(tptp_fun_Y_11(R!20, E!23), E!23)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(207,plain,
% 0.21/0.50 (member(tptp_fun_Y_11(R!20, E!23), E!23)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[206, 203])).
% 0.21/0.50 tff(208,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), 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)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), 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)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(209,plain,
% 0.21/0.50 (((~(((~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)))) | (~member(tptp_fun_Y_11(R!20, E!23), 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)) | (~(((~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)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(210,plain,
% 0.21/0.50 ((~(((~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)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(211,plain,
% 0.21/0.50 (((~(((~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)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), 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)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[210])).
% 0.21/0.50 tff(212,plain,
% 0.21/0.50 (((~(((~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)))) | (~member(tptp_fun_Y_11(R!20, E!23), 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)) | (~(((~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)))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[211, 209])).
% 0.21/0.50 tff(213,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), 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))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[212])).
% 0.21/0.50 tff(214,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), 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)))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[213, 208])).
% 0.21/0.50 tff(215,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(216,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), 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))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.21/0.50 tff(217,plain,
% 0.21/0.50 (~(((~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)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[216, 22, 207, 205])).
% 0.21/0.50 tff(218,plain,
% 0.21/0.50 (((~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_X_12(R!20, E!23), tptp_fun_Y_11(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_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(219,plain,
% 0.21/0.50 (~apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[218, 203])).
% 0.21/0.50 tff(220,plain,
% 0.21/0.50 ((((~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)))) | apply(R!20, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(221,plain,
% 0.21/0.51 ((((~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))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.21/0.51 tff(222,plain,
% 0.21/0.51 ((~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)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[221, 217])).
% 0.21/0.51 tff(223,plain,
% 0.21/0.51 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(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(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)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(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(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)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(224,plain,
% 0.21/0.51 (((~(((~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)))) | (~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)) | (~member(tptp_fun_X_12(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(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)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(225,plain,
% 0.21/0.51 ((~(((~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)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(226,plain,
% 0.21/0.51 (((~(((~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)))) | (~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(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)))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[225])).
% 0.21/0.51 tff(227,plain,
% 0.21/0.51 (((~(((~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)))) | (~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)) | (~member(tptp_fun_X_12(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(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)))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[226, 224])).
% 0.21/0.51 tff(228,plain,
% 0.21/0.51 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(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(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))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[227])).
% 0.21/0.51 tff(229,plain,
% 0.21/0.51 (((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(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(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)))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[228, 223])).
% 0.21/0.51 tff(230,plain,
% 0.21/0.51 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, 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)))) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(231,plain,
% 0.21/0.51 ((~![A: $i, B: $i] : ((~(((~apply(R1!22, A, B)) | (~apply(R2!21, A, B))) <=> apply(R!20, A, B))) | (~member(A, E!23)) | (~member(B, E!23)))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(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(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))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.21/0.51 tff(232,plain,
% 0.21/0.51 (~(((~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)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[231, 22, 207, 205])).
% 0.21/0.51 tff(233,plain,
% 0.21/0.51 (((~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_X_12(R!20, E!23), tptp_fun_Y_11(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))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(234,plain,
% 0.21/0.51 (apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[233, 203])).
% 0.21/0.51 tff(235,plain,
% 0.21/0.51 ((((~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))))) | (~apply(R!20, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(236,plain,
% 0.21/0.51 ((((~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)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.21/0.51 tff(237,plain,
% 0.21/0.51 (~((~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))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[236, 232])).
% 0.21/0.51 tff(238,plain,
% 0.21/0.51 (((~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))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(239,plain,
% 0.21/0.51 (apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.21/0.51 tff(240,plain,
% 0.21/0.51 (((~![X: $i] : ((~member(X, E!23)) | apply(R2!21, X, X))) | (~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R2!21, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | (~member(X, E!23)) | apply(R2!21, X, Z) | (~apply(R2!21, X, Y))))) | ![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(241,plain,
% 0.21/0.51 (![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[240, 91])).
% 0.21/0.51 tff(242,plain,
% 0.21/0.51 (((~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))) <=> ((~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(243,plain,
% 0.21/0.51 (((~apply(R2!21, 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(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) <=> ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(244,plain,
% 0.21/0.51 (((~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | ((~apply(R2!21, 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(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) <=> ((~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[243])).
% 0.21/0.51 tff(245,plain,
% 0.21/0.51 (((~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | ((~apply(R2!21, 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(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) <=> ((~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[244, 242])).
% 0.21/0.51 tff(246,plain,
% 0.21/0.51 ((~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | ((~apply(R2!21, 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(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(247,plain,
% 0.21/0.51 ((~![X: $i, Y: $i] : ((~apply(R2!21, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R2!21, Y, X))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R2!21, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.21/0.51 tff(248,plain,
% 0.21/0.51 (apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[247, 241, 207, 205, 239])).
% 0.21/0.51 tff(249,plain,
% 0.21/0.51 (((~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))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(250,plain,
% 0.21/0.51 (apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[249, 237])).
% 0.21/0.51 tff(251,plain,
% 0.21/0.51 (((~![X: $i] : ((~member(X, E!23)) | apply(R1!22, X, X))) | (~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(R1!22, Y, Z)) | (~member(Y, E!23)) | (~member(Z, E!23)) | apply(R1!22, X, Z) | (~apply(R1!22, X, Y)) | (~member(X, E!23))))) | ![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(252,plain,
% 0.21/0.51 (![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[251, 72])).
% 0.21/0.51 tff(253,plain,
% 0.21/0.51 (((~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))) <=> ((~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(254,plain,
% 0.21/0.51 (((~apply(R1!22, 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(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) <=> ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(255,plain,
% 0.21/0.52 (((~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | ((~apply(R1!22, 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(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) <=> ((~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | ((~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[254])).
% 0.21/0.52 tff(256,plain,
% 0.21/0.52 (((~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | ((~apply(R1!22, 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(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))) <=> ((~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[255, 253])).
% 0.21/0.52 tff(257,plain,
% 0.21/0.52 ((~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | ((~apply(R1!22, 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(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(258,plain,
% 0.21/0.52 ((~![X: $i, Y: $i] : ((~apply(R1!22, X, Y)) | (~member(X, E!23)) | (~member(Y, E!23)) | apply(R1!22, Y, X))) | (~member(tptp_fun_Y_11(R!20, E!23), E!23)) | (~member(tptp_fun_X_12(R!20, E!23), E!23)) | apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)) | (~apply(R1!22, tptp_fun_X_12(R!20, E!23), tptp_fun_Y_11(R!20, E!23)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.21/0.52 tff(259,plain,
% 0.21/0.52 (apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[258, 252, 207, 205, 250])).
% 0.21/0.52 tff(260,plain,
% 0.21/0.52 ((~((~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))))) | (~apply(R1!22, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23))) | (~apply(R2!21, tptp_fun_Y_11(R!20, E!23), tptp_fun_X_12(R!20, E!23)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(261,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[260, 259, 248, 222])).
% 0.21/0.52 % SZS output end Proof
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------