%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET806+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:26:23 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET806+4 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:43:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(subset_type, type, (
% 0.20/0.39 subset: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_X_10_type, type, (
% 0.20/0.39 tptp_fun_X_10: ( $i * $i ) > $i)).
% 0.20/0.39 tff(power_set_type, type, (
% 0.20/0.39 power_set: $i > $i)).
% 0.20/0.39 tff(tptp_fun_E_20_type, type, (
% 0.20/0.39 tptp_fun_E_20: $i)).
% 0.20/0.39 tff(equal_set_predicate_type, type, (
% 0.20/0.39 equal_set_predicate: $i)).
% 0.20/0.39 tff(equal_set_type, type, (
% 0.20/0.39 equal_set: ( $i * $i ) > $o)).
% 0.20/0.39 tff(apply_type, type, (
% 0.20/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(member_type, type, (
% 0.20/0.39 member: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_Z_13_type, type, (
% 0.20/0.39 tptp_fun_Z_13: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X_15_type, type, (
% 0.20/0.39 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_Y_14_type, type, (
% 0.20/0.39 tptp_fun_Y_14: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X_0_type, type, (
% 0.20/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X_12_type, type, (
% 0.20/0.39 tptp_fun_X_12: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_Y_11_type, type, (
% 0.20/0.39 tptp_fun_Y_11: ( $i * $i ) > $i)).
% 0.20/0.39 tff(equivalence_type, type, (
% 0.20/0.39 equivalence: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.40 tff(8,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[7])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((~(~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) <=> (subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ((~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 ((((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> ((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 ((((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 ((((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[17, 13])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 ((~(((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> (~(~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~(((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> (subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[19, 12])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[21, 11])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[24, 10])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl((apply(equal_set_predicate, X, Y) <=> equal_set(X, Y)) <=> (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y)) <=> ![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y)) <=> ![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(29,axiom,(![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rel_equal_set')).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.20/0.40 inference(skolemize,[status(sab)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.40 tff(45,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.40 tff(48,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[47])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (~((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))))) | (subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (~(((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 10])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[57, 32])).
% 0.20/0.41 tff(59,assumption,(~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))), introduced(assumption)).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 ((~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | (~equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (~equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[63, 58])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 ((((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[66, 56])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (~((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[68, 50])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 ((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (~(((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[72, 10])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[74, 32])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[76, 59])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~(apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~(apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[79, 75])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[82, 73])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 ((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[87, 71])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (~((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[89, 50])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 ((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (~(((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[93, 10])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[95, 32])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[97, 59])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 ((~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 ((~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[100, 96])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[103, 94])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 ((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[108, 92])).
% 0.20/0.42 tff(110,assumption,(~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))), introduced(assumption)).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.43 tff(113,assumption,(![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))), introduced(assumption)).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[116, 113, 112])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[118, 110])).
% 0.20/0.43 tff(120,assumption,(![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))), introduced(assumption)).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (((~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[123, 120, 119, 117])).
% 0.20/0.43 tff(125,plain,(((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | (~![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 ((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[125, 109, 88])).
% 0.20/0.43 tff(127,assumption,((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))), introduced(assumption)).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[128, 50, 127])).
% 0.20/0.43 tff(130,plain,(~((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (((~((~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))))) | (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 ((~(subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))))) | subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[134, 126])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 ((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[136, 135, 67])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 ((~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ((~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[139, 54])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (~((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[143, 50])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 ((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[147, 83])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 ((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 ((~((~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))) | ![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[150, 146])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[154, 151, 142])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[156, 140])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (~((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[158, 50])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))))) | ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 ((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[162, 104])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 ((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 ((~((~subset(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))))) | ![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[165, 161])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (((~![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 ((~![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | ((~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 ((~![X: $i] : ((~member(X, tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_Y_14(equal_set_predicate, power_set(E!20))))) | (~member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_X_15(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), tptp_fun_X_15(equal_set_predicate, power_set(E!20))), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[169, 166, 157, 155])).
% 0.20/0.45 tff(171,plain,((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (~(((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[172, 10])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 (apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[174, 32])).
% 0.20/0.45 tff(176,assumption,(~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))), introduced(assumption)).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 (((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 (~apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.20/0.45 tff(179,plain,
% 0.20/0.45 ((~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 ((~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 (~equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[180, 175])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 ((((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | ((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 ((((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | ((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.20/0.45 tff(184,plain,
% 0.20/0.45 ((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[183, 173])).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(186,plain,
% 0.20/0.45 (~(((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[185, 10])).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : (apply(equal_set_predicate, X, Y) <=> equal_set(X, Y))) | (apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 (apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[187, 32])).
% 0.20/0.45 tff(189,plain,
% 0.20/0.45 (((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 (apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[189, 176])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 ((~(apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 ((~(apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))) | equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.20/0.45 tff(193,plain,
% 0.20/0.45 (equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[192, 188])).
% 0.20/0.45 tff(194,plain,
% 0.20/0.45 ((((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))))) | (~equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(195,plain,
% 0.20/0.45 ((((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) <=> equal_set(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.20/0.45 tff(196,plain,
% 0.20/0.45 (~((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[195, 186])).
% 0.20/0.45 tff(197,plain,
% 0.20/0.45 (((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(198,plain,
% 0.20/0.45 (subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (((~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(200,plain,
% 0.20/0.45 (subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[199, 196])).
% 0.20/0.45 tff(201,plain,
% 0.20/0.45 ((~((~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))))) | (~subset(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))) | (~subset(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(202,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[201, 200, 198, 184])).
% 0.20/0.45 tff(203,plain,((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(204,plain,
% 0.20/0.45 (^[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)))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 (![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))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[204])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 (^[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)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(207,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[206])).
% 0.20/0.46 tff(208,plain,
% 0.20/0.46 (^[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)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(209,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[208])).
% 0.20/0.46 tff(210,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[209, 207])).
% 0.20/0.46 tff(211,plain,
% 0.20/0.46 (^[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))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(212,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[211])).
% 0.20/0.46 tff(213,plain,
% 0.20/0.46 (^[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))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(214,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[213])).
% 0.20/0.46 tff(215,plain,
% 0.20/0.46 (![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))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(216,plain,
% 0.20/0.46 (^[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)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(217,plain,
% 0.20/0.46 (![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))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[216])).
% 0.20/0.46 tff(218,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')).
% 0.20/0.46 tff(219,plain,
% 0.20/0.46 (![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))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.46 tff(220,plain,
% 0.20/0.46 (![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))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.20/0.47 tff(221,plain,(
% 0.20/0.47 ![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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))))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[220])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (![A: $i, R: $i] : (((~equivalence(R, A)) | (![X: $i] : ((~member(X, A)) | apply(R, X, X)) & ![X: $i, Y: $i] : (apply(R, Y, X) | (~(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)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[222, 212])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[223, 210])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 (![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[224, 205])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))) <=> ((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 ((~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))))))))))) <=> (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(228,plain,
% 0.20/0.47 (((~![A: $i, R: $i] : (~((~(equivalence(R, A) | (~((~member(tptp_fun_X_10(R, A), A)) | apply(R, tptp_fun_X_10(R, A), tptp_fun_X_10(R, A)))) | (~(apply(R, tptp_fun_Y_11(R, A), tptp_fun_X_12(R, A)) | (~apply(R, tptp_fun_X_12(R, A), tptp_fun_Y_11(R, A))) | (~member(tptp_fun_X_12(R, A), A)) | (~member(tptp_fun_Y_11(R, A), A)))) | (~(apply(R, tptp_fun_X_15(R, A), tptp_fun_Z_13(R, A)) | (~apply(R, tptp_fun_X_15(R, A), tptp_fun_Y_14(R, A))) | (~apply(R, tptp_fun_Y_14(R, A), tptp_fun_Z_13(R, A))) | (~member(tptp_fun_X_15(R, A), A)) | (~member(tptp_fun_Y_14(R, A), A)) | (~member(tptp_fun_Z_13(R, A), A)))))) | (~((~equivalence(R, A)) | (~((~![X: $i] : ((~member(X, A)) | apply(R, X, X))) | (~![X: $i, Y: $i] : (apply(R, Y, X) | (~apply(R, X, Y)) | (~member(X, A)) | (~member(Y, A)))) | (~![X: $i, Y: $i, Z: $i] : (apply(R, X, Z) | (~apply(R, X, Y)) | (~apply(R, Y, Z)) | (~member(X, A)) | (~member(Y, A)) | (~member(Z, A))))))))))) | (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))) <=> ((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[227])).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 (((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))) <=> ((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[228, 226])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 ((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))))) | (~(apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 ((~![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(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 (~((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20))))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[231, 225])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 (((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~equivalence(equal_set_predicate, power_set(E!20))) | (~((~![X: $i] : ((~member(X, power_set(E!20))) | apply(equal_set_predicate, X, X))) | (~![X: $i, Y: $i] : (apply(equal_set_predicate, Y, X) | (~apply(equal_set_predicate, X, Y)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))))) | (~![X: $i, Y: $i, Z: $i] : (apply(equal_set_predicate, X, Z) | (~apply(equal_set_predicate, X, Y)) | (~apply(equal_set_predicate, Y, Z)) | (~member(X, power_set(E!20))) | (~member(Y, power_set(E!20))) | (~member(Z, power_set(E!20)))))))))) | (equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 (equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 ((~![E: $i] : equivalence(equal_set_predicate, power_set(E))) <=> (~![E: $i] : equivalence(equal_set_predicate, power_set(E)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(236,axiom,(~![E: $i] : equivalence(equal_set_predicate, power_set(E))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIII13')).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[237, 235])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[238, 235])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 (~![E: $i] : equivalence(equal_set_predicate, power_set(E))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[239, 235])).
% 0.20/0.48 tff(241,plain,(
% 0.20/0.48 ~equivalence(equal_set_predicate, power_set(E!20))),
% 0.20/0.48 inference(skolemize,[status(sab)],[240])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 ((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 ((~(equivalence(equal_set_predicate, power_set(E!20)) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20))))))) | (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 ((~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_12(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_X_12(equal_set_predicate, power_set(E!20)), tptp_fun_Y_11(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_Y_11(equal_set_predicate, power_set(E!20)), tptp_fun_X_12(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[243, 234])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 ((~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~((~member(tptp_fun_Z_13(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~member(tptp_fun_X_15(equal_set_predicate, power_set(E!20)), power_set(E!20))) | (~apply(equal_set_predicate, tptp_fun_Y_14(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Y_14(equal_set_predicate, power_set(E!20)))) | apply(equal_set_predicate, tptp_fun_X_15(equal_set_predicate, power_set(E!20)), tptp_fun_Z_13(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[244, 203])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (~((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[245, 171])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (((~member(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), power_set(E!20))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | (~apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (~apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[247, 246])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 ((~(apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(250,plain,
% 0.20/0.49 ((~(apply(equal_set_predicate, tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.20/0.49 tff(251,plain,
% 0.20/0.49 (~equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[250, 34])).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 ((~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 ((~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) <=> equal_set(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[253, 25])).
% 0.20/0.49 tff(255,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(256,plain,
% 0.20/0.49 ((~(~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 (($false | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(258,plain,
% 0.20/0.49 ((~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))))) <=> (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(259,plain,
% 0.20/0.49 ((~$true) <=> $false),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(260,plain,
% 0.20/0.49 (((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | $true) <=> $true),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(261,plain,
% 0.20/0.49 (![X: $i] : $true <=> $true),
% 0.20/0.49 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.49 tff(262,plain,
% 0.20/0.49 (![X: $i] : $true <=> ![X: $i] : $true),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(263,plain,
% 0.20/0.49 (![X: $i] : $true <=> $true),
% 0.20/0.49 inference(transitivity,[status(thm)],[262, 261])).
% 0.20/0.49 tff(264,plain,
% 0.20/0.49 (^[X: $i] : rewrite(((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> $true)),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(265,plain,
% 0.20/0.49 (![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> ![X: $i] : $true),
% 0.20/0.49 inference(quant_intro,[status(thm)],[264])).
% 0.20/0.49 tff(266,plain,
% 0.20/0.49 (![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) <=> $true),
% 0.20/0.49 inference(transitivity,[status(thm)],[265, 263])).
% 0.20/0.49 tff(267,plain,
% 0.20/0.49 (((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> ((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | $true)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[266])).
% 0.20/0.49 tff(268,plain,
% 0.20/0.49 (((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20))))) <=> $true),
% 0.20/0.49 inference(transitivity,[status(thm)],[267, 260])).
% 0.20/0.49 tff(269,plain,
% 0.20/0.49 ((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) <=> (~$true)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[268])).
% 0.20/0.49 tff(270,plain,
% 0.20/0.49 ((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) <=> $false),
% 0.20/0.49 inference(transitivity,[status(thm)],[269, 259])).
% 0.20/0.49 tff(271,plain,
% 0.20/0.49 (((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))) <=> ($false | (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[270, 258])).
% 0.20/0.49 tff(272,plain,
% 0.20/0.49 (((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))) <=> (~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[271, 257])).
% 0.20/0.49 tff(273,plain,
% 0.20/0.49 ((~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))))))) <=> (~(~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[272])).
% 0.20/0.49 tff(274,plain,
% 0.20/0.49 ((~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))))))) <=> subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[273, 256])).
% 0.20/0.49 tff(275,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[274])).
% 0.20/0.49 tff(276,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[275, 255])).
% 0.20/0.49 tff(277,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | ![X: $i] : ((~member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(X, tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))) | (~(subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))) | (~((~member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))) | member(tptp_fun_X_0(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20))), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(278,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(tptp_fun_X_10(equal_set_predicate, power_set(E!20)), tptp_fun_X_10(equal_set_predicate, power_set(E!20)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.20/0.49 tff(279,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[278, 50, 254])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------