%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET775+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET775+4 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 05:41:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(apply_type, type, (
% 0.19/0.38 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_X_10_type, type, (
% 0.19/0.38 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_E_22_type, type, (
% 0.19/0.38 tptp_fun_E_22: $i)).
% 0.19/0.38 tff(tptp_fun_R_20_type, type, (
% 0.19/0.38 tptp_fun_R_20: $i)).
% 0.19/0.38 tff(tptp_fun_P_21_type, type, (
% 0.19/0.38 tptp_fun_P_21: $i)).
% 0.19/0.38 tff(member_type, type, (
% 0.19/0.38 member: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_X_12_type, type, (
% 0.19/0.38 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_Y_11_type, type, (
% 0.19/0.38 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.19/0.38 tff(equivalence_type, type, (
% 0.19/0.38 equivalence: ( $i * $i ) > $o)).
% 0.19/0.38 tff(pre_order_type, type, (
% 0.19/0.38 pre_order: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_Z_13_type, type, (
% 0.19/0.38 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X_15_type, type, (
% 0.19/0.38 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_Y_14_type, type, (
% 0.19/0.38 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_Z_17_type, type, (
% 0.19/0.38 tptp_fun_Z_17: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X_19_type, type, (
% 0.19/0.38 tptp_fun_X_19: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_Y_18_type, type, (
% 0.19/0.38 tptp_fun_Y_18: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X_16_type, type, (
% 0.19/0.38 tptp_fun_X_16: ( $i * $i ) > $i)).
% 0.19/0.38 tff(1,assumption,(~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | member(tptp_fun_X_12(R!20, E!22), E!22)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (member(tptp_fun_X_12(R!20, E!22), E!22)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | member(tptp_fun_Y_11(R!20, E!22), E!22)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (member(tptp_fun_Y_11(R!20, E!22), E!22)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl(((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22))) <=> ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22))) <=> ![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(A, E!22) & member(B, E!22)) <=> (~((~member(A, E!22)) | (~member(B, E!22))))), ((~(member(A, E!22) & member(B, E!22))) <=> (~(~((~member(A, E!22)) | (~member(B, E!22))))))), rewrite((~(~((~member(A, E!22)) | (~member(B, E!22))))) <=> ((~member(A, E!22)) | (~member(B, E!22)))), ((~(member(A, E!22) & member(B, E!22))) <=> ((~member(A, E!22)) | (~member(B, E!22))))), trans(trans(monotonicity(rewrite((apply(P!21, A, B) & apply(P!21, B, A)) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))), ((apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))) <=> (apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))))), rewrite((apply(R!20, A, B) <=> (~((~apply(P!21, A, B)) | (~apply(P!21, B, A))))) <=> (~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B)))), ((apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))) <=> (~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))))), rewrite((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) <=> (~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B)))), ((apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))) <=> (~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))))), (((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) <=> (((~member(A, E!22)) | (~member(B, E!22))) | (~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B)))))), rewrite((((~member(A, E!22)) | (~member(B, E!22))) | (~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B)))) <=> ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))), (((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) <=> ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) <=> ![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) & (~equivalence(R!20, E!22))) <=> (pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) & (~equivalence(R!20, E!22)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) <=> (pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) & (~equivalence(R!20, E!22))) <=> ((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) & (~equivalence(R!20, E!22)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[11])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (((pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))) & (~equivalence(R!20, E!22))) <=> (pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) & (~equivalence(R!20, E!22)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[12, 10])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 ((~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))) <=> (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ((~![E: $i, P: $i, R: $i] : ((pre_order(P, E) & ![A: $i, B: $i] : ((member(A, E) & member(B, E)) => (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A))))) => equivalence(R, E))) <=> (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(16,axiom,(~![E: $i, P: $i, R: $i] : ((pre_order(P, E) & ![A: $i, B: $i] : ((member(A, E) & member(B, E)) => (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A))))) => equivalence(R, E))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII11')).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~![E: $i, P: $i, R: $i] : ((~(pre_order(P, E) & ![A: $i, B: $i] : ((~(member(A, E) & member(B, E))) | (apply(R, A, B) <=> (apply(P, A, B) & apply(P, B, A)))))) | equivalence(R, E))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (pre_order(P!21, E!22) & ![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A)))) & (~equivalence(R!20, E!22))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~(member(A, E!22) & member(B, E!22))) | (apply(R!20, A, B) <=> (apply(P!21, A, B) & apply(P!21, B, A))))),
% 0.19/0.39 inference(and_elim,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 ((((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) <=> (((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22))) <=> ((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[31, 26])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[33, 25])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (~(((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[36, 24, 5, 3])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 1])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ((((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | ((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | ((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 37])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (((~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 ((~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) <=> (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (((~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22))) <=> ((~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (((~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[48, 43])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (~(((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[51, 24, 5, 3])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 1])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (~((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[56, 52])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (((~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ((~((~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))))) | (~apply(P!21, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))) | (~apply(P!21, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[62, 61, 59, 42])).
% 0.19/0.41 tff(64,plain,((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(65,assumption,(~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))), introduced(assumption)).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | member(tptp_fun_Y_14(R!20, E!22), E!22)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (member(tptp_fun_Y_14(R!20, E!22), E!22)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | member(tptp_fun_Z_13(R!20, E!22), E!22)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (member(tptp_fun_Z_13(R!20, E!22), E!22)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (((~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) <=> (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (((~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) <=> ((~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (((~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[75, 70])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (~(((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 24, 69, 67])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[80, 65])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ((((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ((((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (~((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[83, 79])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | member(tptp_fun_X_15(R!20, E!22), E!22)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (member(tptp_fun_X_15(R!20, E!22), E!22)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 65])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22))) <=> ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[92, 90])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[94, 89])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[97, 24, 67, 88])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 65])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 ((((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 ((((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[102, 98])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) <=> (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) <=> ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22))) <=> ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[111, 106])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (~(((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[114, 24, 69, 88])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[116, 65])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 ((((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | ((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 ((((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | ((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 ((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[121, 84])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 (((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22)))) | apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[123, 103])).
% 0.19/0.44 tff(125,assumption,(apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))), introduced(assumption)).
% 0.19/0.44 tff(126,assumption,(apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))), introduced(assumption)).
% 0.19/0.44 tff(127,assumption,(~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))), introduced(assumption)).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (^[R: $i, E: $i] : refl((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 (^[R: $i, E: $i] : rewrite((~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[133, 131])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (^[R: $i, E: $i] : trans(monotonicity(rewrite(((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))) <=> (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), rewrite((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))), ((pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))) <=> (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))))), rewrite((((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))), ((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))) <=> ![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[135])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (^[R: $i, E: $i] : rewrite((((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))) <=> ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[137])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) <=> ![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (^[R: $i, E: $i] : rewrite((pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.45 tff(142,axiom,(![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : (member(X, E) => apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (((member(X, E) & member(Y, E)) & member(Z, E)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','pre_order')).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (![R: $i, E: $i] : (pre_order(R, E) <=> (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.19/0.45 tff(145,plain,(
% 0.19/0.45 ![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | ((~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[144])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (![R: $i, E: $i] : (((~pre_order(R, E)) | (![X: $i] : ((~member(X, E)) | apply(R, X, X)) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, E) & member(Y, E) & member(Z, E)))))) & (pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R)) & apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R)))) | (~(member(tptp_fun_X_19(E, R), E) & member(tptp_fun_Y_18(E, R), E) & member(tptp_fun_Z_17(E, R), E)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[146, 136])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 (![R: $i, E: $i] : (~((~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z)))))))) | (~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[147, 134])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 (![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[148, 129])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~((~member(tptp_fun_Z_17(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~((~member(tptp_fun_Z_17(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 ((~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(P!21, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(P!21, X, Y)) | (~apply(P!21, Y, Z)))))))))) <=> (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~((~member(tptp_fun_Z_17(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(P!21, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(P!21, X, Y)) | (~apply(P!21, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~((~member(tptp_fun_Z_17(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(P!21, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(P!21, X, Y)) | (~apply(P!21, Y, Z))))))))))) <=> ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~((~member(tptp_fun_Z_17(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[152, 150])).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~(apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_Z_17(E!22, P!21), E!22)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(P!21, X, Z) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | (~apply(P!21, X, Y)) | (~apply(P!21, Y, Z))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 ((~![R: $i, E: $i] : (~((~(pre_order(R, E) | (~((~member(tptp_fun_X_16(E, R), E)) | apply(R, tptp_fun_X_16(E, R), tptp_fun_X_16(E, R)))) | (~(apply(R, tptp_fun_X_19(E, R), tptp_fun_Z_17(E, R)) | (~apply(R, tptp_fun_X_19(E, R), tptp_fun_Y_18(E, R))) | (~apply(R, tptp_fun_Y_18(E, R), tptp_fun_Z_17(E, R))) | (~member(tptp_fun_X_19(E, R), E)) | (~member(tptp_fun_Y_18(E, R), E)) | (~member(tptp_fun_Z_17(E, R), E)))))) | (~((~pre_order(R, E)) | (~((~![X: $i] : ((~member(X, E)) | apply(R, X, X))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~member(Y, E)) | (~member(Z, E)) | (~member(X, E)) | (~apply(R, X, Y)) | (~apply(R, Y, Z))))))))))) | (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~((~member(tptp_fun_Z_17(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (~((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~((~member(tptp_fun_Z_17(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[155, 149])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (((~(pre_order(P!21, E!22) | (~((~member(tptp_fun_X_16(E!22, P!21), E!22)) | apply(P!21, tptp_fun_X_16(E!22, P!21), tptp_fun_X_16(E!22, P!21)))) | (~((~member(tptp_fun_Z_17(E!22, P!21), E!22)) | (~member(tptp_fun_Y_18(E!22, P!21), E!22)) | (~member(tptp_fun_X_19(E!22, P!21), E!22)) | (~apply(P!21, tptp_fun_Y_18(E!22, P!21), tptp_fun_Z_17(E!22, P!21))) | (~apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Y_18(E!22, P!21))) | apply(P!21, tptp_fun_X_19(E!22, P!21), tptp_fun_Z_17(E!22, P!21)))))) | (~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))))) | ((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 ((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.19/0.46 tff(159,plain,
% 0.19/0.46 (pre_order(P!21, E!22)),
% 0.19/0.46 inference(and_elim,[status(thm)],[21])).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 ((~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))) | (~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(161,plain,
% 0.19/0.46 ((~((~pre_order(P!21, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))))) | (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 (~((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))) | ![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.19/0.46 tff(165,assumption,(member(tptp_fun_X_15(R!20, E!22), E!22)), introduced(assumption)).
% 0.19/0.46 tff(166,assumption,(member(tptp_fun_Y_14(R!20, E!22), E!22)), introduced(assumption)).
% 0.19/0.46 tff(167,assumption,(member(tptp_fun_Z_13(R!20, E!22), E!22)), introduced(assumption)).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 (((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[170, 168])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[173, 167, 166, 165, 164, 127, 126, 125])).
% 0.19/0.47 tff(175,plain,(apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_X_15(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 (apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[175, 69, 67, 88, 124, 122])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 ((~((~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22))))) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(P!21, tptp_fun_Z_13(R!20, E!22), tptp_fun_X_15(R!20, E!22)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[177, 176, 120])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 (((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22)))) <=> ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[180])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[181, 179])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | ((~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y)))) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(P!21, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(P!21, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[184, 69, 67, 88, 164, 178, 105, 86])).
% 0.19/0.47 tff(186,plain,((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 (^[A: $i, R: $i] : refl((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[189])).
% 0.19/0.48 tff(191,plain,
% 0.19/0.48 (^[A: $i, R: $i] : rewrite((~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(192,plain,
% 0.19/0.48 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[191])).
% 0.19/0.48 tff(193,plain,
% 0.19/0.48 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[192, 190])).
% 0.19/0.48 tff(194,plain,
% 0.19/0.48 (^[A: $i, R: $i] : trans(monotonicity(rewrite(((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))), trans(monotonicity(rewrite((~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) <=> (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A))))), rewrite((~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))) <=> (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), rewrite((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))), ((equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))) <=> (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))))), rewrite((((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))), ((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(195,plain,
% 0.19/0.48 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))) <=> ![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[194])).
% 0.19/0.48 tff(196,plain,
% 0.19/0.48 (^[A: $i, R: $i] : rewrite((((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(197,plain,
% 0.19/0.48 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))) <=> ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[196])).
% 0.19/0.48 tff(198,plain,
% 0.19/0.48 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(199,plain,
% 0.19/0.48 (^[A: $i, R: $i] : rewrite((equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(200,plain,
% 0.19/0.48 (![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z))))) <=> ![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[199])).
% 0.19/0.48 tff(201,axiom,(![A: $i, R: $i] : (equivalence(R, A) <=> ((![X: $i] : (member(X, A) => apply(R, X, X)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, A)) => (apply(R, X, Y) => apply(R, Y, X)))) & ![X: $i, Y: $i, Z: $i] : (((member(X, A) & member(Y, A)) & member(Z, A)) => ((apply(R, X, Y) & apply(R, Y, Z)) => apply(R, X, Z)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax','equivalence')).
% 0.19/0.48 tff(202,plain,
% 0.19/0.48 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.48 tff(203,plain,
% 0.19/0.48 (![A: $i, R: $i] : (equivalence(R, A) <=> (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.19/0.48 tff(204,plain,(
% 0.19/0.48 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | ((~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[203])).
% 0.19/0.48 tff(205,plain,
% 0.19/0.48 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(member(X, A) & member(Y, A))) | (~apply(R, X, Y))) & ![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~(apply(R, X, Y) & apply(R, Y, Z))) | (~(member(X, A) & member(Y, A) & member(Z, A)))))) & (equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~(member(tptp_fun_X_12(R, A), A) & member(tptp_fun_Y_11(R, A), A))) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A)) & apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A)))) | (~(member(tptp_fun_X_15(R, A), A) & member(tptp_fun_Y_14(R, A), A) & member(tptp_fun_Z_13(R, A), A)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.19/0.48 tff(206,plain,
% 0.19/0.48 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[205, 195])).
% 0.19/0.48 tff(207,plain,
% 0.19/0.48 (![A: $i, R: $i] : (~((~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A)))))))) | (~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[206, 193])).
% 0.19/0.48 tff(208,plain,
% 0.19/0.48 (![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[207, 188])).
% 0.19/0.48 tff(209,plain,
% 0.19/0.48 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(210,plain,
% 0.19/0.49 ((~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22)))))))))) <=> (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(211,plain,
% 0.19/0.49 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[210])).
% 0.19/0.49 tff(212,plain,
% 0.19/0.49 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))) <=> ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[211, 209])).
% 0.19/0.49 tff(213,plain,
% 0.19/0.49 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~(apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~member(tptp_fun_Y_11(R!20, E!22), E!22)))) | (~(apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_Z_13(R!20, E!22), E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : (apply(R!20, Y, X) | (~apply(R!20, X, Y)) | (~member(X, E!22)) | (~member(Y, E!22)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)) | (~member(Y, E!22)) | (~member(Z, E!22))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(214,plain,
% 0.19/0.49 ((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.49 tff(215,plain,
% 0.19/0.49 (~((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[214, 208])).
% 0.19/0.49 tff(216,plain,
% 0.19/0.49 (((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~equivalence(R!20, E!22)) | (~((~![X: $i] : ((~member(X, E!22)) | apply(R!20, X, X))) | (~![X: $i, Y: $i] : ((~member(X, E!22)) | (~member(Y, E!22)) | (~apply(R!20, X, Y)) | apply(R!20, Y, X))) | (~![X: $i, Y: $i, Z: $i] : ((~member(Y, E!22)) | (~member(Z, E!22)) | apply(R!20, X, Z) | (~apply(R!20, X, Y)) | (~apply(R!20, Y, Z)) | (~member(X, E!22))))))))) | (equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(217,plain,
% 0.19/0.49 (equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.19/0.50 tff(218,plain,
% 0.19/0.50 (~equivalence(R!20, E!22)),
% 0.19/0.50 inference(and_elim,[status(thm)],[21])).
% 0.19/0.50 tff(219,plain,
% 0.19/0.50 ((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(220,plain,
% 0.19/0.50 ((~(equivalence(R!20, E!22) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22)))))) | (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.19/0.50 tff(221,plain,
% 0.19/0.50 ((~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~((~member(tptp_fun_Y_11(R!20, E!22), E!22)) | (~member(tptp_fun_X_12(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_X_12(R!20, E!22), tptp_fun_Y_11(R!20, E!22))) | apply(R!20, tptp_fun_Y_11(R!20, E!22), tptp_fun_X_12(R!20, E!22)))) | (~((~member(tptp_fun_Z_13(R!20, E!22), E!22)) | (~member(tptp_fun_Y_14(R!20, E!22), E!22)) | (~member(tptp_fun_X_15(R!20, E!22), E!22)) | (~apply(R!20, tptp_fun_Y_14(R!20, E!22), tptp_fun_Z_13(R!20, E!22))) | (~apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Y_14(R!20, E!22))) | apply(R!20, tptp_fun_X_15(R!20, E!22), tptp_fun_Z_13(R!20, E!22))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[220, 217])).
% 0.19/0.50 tff(222,plain,
% 0.19/0.50 (~((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[221, 186, 64])).
% 0.19/0.50 tff(223,plain,
% 0.19/0.50 (((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | member(tptp_fun_X_10(R!20, E!22), E!22)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(224,plain,
% 0.19/0.50 (member(tptp_fun_X_10(R!20, E!22), E!22)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.19/0.50 tff(225,plain,
% 0.19/0.50 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(226,plain,
% 0.19/0.50 (((apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22))) <=> ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(227,plain,
% 0.19/0.50 ((~(~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))) <=> (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(228,plain,
% 0.19/0.50 ((~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> (~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(229,plain,
% 0.19/0.50 (((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) <=> (~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(230,plain,
% 0.19/0.50 (((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(231,plain,
% 0.19/0.50 ((((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) <=> ((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[230])).
% 0.19/0.50 tff(232,plain,
% 0.19/0.50 ((((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) <=> (~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[231, 229])).
% 0.19/0.50 tff(233,plain,
% 0.19/0.50 ((((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) <=> (~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[232, 228])).
% 0.19/0.50 tff(234,plain,
% 0.19/0.50 ((~(((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> (~(~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[233])).
% 0.19/0.50 tff(235,plain,
% 0.19/0.50 ((~(((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[234, 227])).
% 0.19/0.50 tff(236,plain,
% 0.19/0.50 (((~(((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22))) <=> ((apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[235])).
% 0.19/0.50 tff(237,plain,
% 0.19/0.50 (((~(((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22))) <=> ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[236, 226])).
% 0.19/0.50 tff(238,plain,
% 0.19/0.50 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[237])).
% 0.19/0.50 tff(239,plain,
% 0.19/0.50 (((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)))) <=> ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[238, 225])).
% 0.19/0.50 tff(240,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | ((~(((~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (~member(tptp_fun_X_10(R!20, E!22), E!22)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(241,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~(((~apply(P!21, A, B)) | (~apply(P!21, B, A))) <=> apply(R!20, A, B))) | (~member(A, E!22)) | (~member(B, E!22)))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.19/0.50 tff(242,plain,
% 0.19/0.50 (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[241, 24, 224])).
% 0.19/0.50 tff(243,plain,
% 0.19/0.50 (((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~![X: $i, Y: $i, Z: $i] : ((~apply(P!21, Y, Z)) | (~member(Y, E!22)) | (~member(Z, E!22)) | (~member(X, E!22)) | apply(P!21, X, Z) | (~apply(P!21, X, Y))))) | ![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(244,plain,
% 0.19/0.50 (![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[243, 162])).
% 0.19/0.50 tff(245,plain,
% 0.19/0.50 (((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) <=> ((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(246,plain,
% 0.19/0.50 ((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | ((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(247,plain,
% 0.19/0.50 ((~![X: $i] : ((~member(X, E!22)) | apply(P!21, X, X))) | (~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.19/0.50 tff(248,plain,
% 0.19/0.50 (apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[247, 224, 244])).
% 0.19/0.50 tff(249,plain,
% 0.19/0.50 (((~member(tptp_fun_X_10(R!20, E!22), E!22)) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | (~apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(250,plain,
% 0.19/0.50 (~apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[249, 222])).
% 0.19/0.50 tff(251,plain,
% 0.19/0.50 ((~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))) | apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(252,plain,
% 0.19/0.50 ((~(apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)) <=> apply(R!20, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))) | (~apply(P!21, tptp_fun_X_10(R!20, E!22), tptp_fun_X_10(R!20, E!22)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.19/0.50 tff(253,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[252, 248, 242])).
% 0.19/0.50 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------