%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV569+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:29:25 AM UTC 2025
% Result : Theorem 22.38s 22.57s
% Output : Proof 22.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV569+1 : TPTP v9.1.0. Released v9.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:41:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 22.38/22.57 % SZS status Theorem
% 22.38/22.57 % SZS output start Proof
% 22.38/22.57 tff(mem_type, type, (
% 22.38/22.57 mem: ( $i * $i ) > $o)).
% 22.38/22.57 tff(e_type, type, (
% 22.38/22.57 e: $i)).
% 22.38/22.57 tff(a_type, type, (
% 22.38/22.57 a: ( $i * $i ) > $i)).
% 22.38/22.57 tff(n_type, type, (
% 22.38/22.57 n: $i > $i)).
% 22.38/22.57 tff(s_type, type, (
% 22.38/22.57 s: $i > $i)).
% 22.38/22.57 tff(u_type, type, (
% 22.38/22.57 u: ( $i * $i ) > $i)).
% 22.38/22.57 tff(tptp_fun_Z_0_type, type, (
% 22.38/22.57 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 22.38/22.57 tff(subq_type, type, (
% 22.38/22.57 subq: ( $i * $i ) > $o)).
% 22.38/22.57 tff(1,assumption,(~(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))), introduced(assumption)).
% 22.38/22.57 tff(2,plain,
% 22.38/22.57 (^[X: $i, Y: $i] : refl((mem(X, s(Y)) <=> (X = Y)) <=> (mem(X, s(Y)) <=> (X = Y)))),
% 22.38/22.57 inference(bind,[status(th)],[])).
% 22.38/22.57 tff(3,plain,
% 22.38/22.57 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 22.38/22.57 inference(quant_intro,[status(thm)],[2])).
% 22.38/22.57 tff(4,plain,
% 22.38/22.57 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 22.38/22.57 inference(rewrite,[status(thm)],[])).
% 22.38/22.57 tff(5,axiom,(![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','s_ax')).
% 22.38/22.57 tff(6,plain,
% 22.38/22.57 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 22.38/22.57 inference(modus_ponens,[status(thm)],[5, 4])).
% 22.38/22.57 tff(7,plain,(
% 22.38/22.57 ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 22.38/22.57 inference(skolemize,[status(sab)],[6])).
% 22.38/22.57 tff(8,plain,
% 22.38/22.57 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 22.38/22.57 inference(modus_ponens,[status(thm)],[7, 3])).
% 22.38/22.57 tff(9,plain,
% 22.38/22.57 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))),
% 22.38/22.57 inference(quant_inst,[status(thm)],[])).
% 22.38/22.57 tff(10,plain,
% 22.38/22.57 ($false),
% 22.38/22.57 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 22.38/22.57 tff(11,plain,(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e)), inference(lemma,lemma(discharge,[]))).
% 22.38/22.57 tff(12,assumption,(mem(a(n(e), n(e)), e)), introduced(assumption)).
% 22.38/22.57 tff(13,plain,
% 22.38/22.57 (^[X: $i] : refl((~mem(X, e)) <=> (~mem(X, e)))),
% 22.38/22.57 inference(bind,[status(th)],[])).
% 22.38/22.57 tff(14,plain,
% 22.38/22.57 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 22.38/22.57 inference(quant_intro,[status(thm)],[13])).
% 22.38/22.57 tff(15,plain,
% 22.38/22.57 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 22.38/22.57 inference(rewrite,[status(thm)],[])).
% 22.38/22.57 tff(16,axiom,(![X: $i] : (~mem(X, e))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','e_ax')).
% 22.38/22.57 tff(17,plain,
% 22.38/22.57 (![X: $i] : (~mem(X, e))),
% 22.38/22.57 inference(modus_ponens,[status(thm)],[16, 15])).
% 22.38/22.57 tff(18,plain,(
% 22.38/22.57 ![X: $i] : (~mem(X, e))),
% 22.38/22.57 inference(skolemize,[status(sab)],[17])).
% 22.38/22.57 tff(19,plain,
% 22.38/22.57 (![X: $i] : (~mem(X, e))),
% 22.38/22.57 inference(modus_ponens,[status(thm)],[18, 14])).
% 22.38/22.57 tff(20,plain,
% 22.38/22.57 ((~![X: $i] : (~mem(X, e))) | (~mem(a(n(e), n(e)), e))),
% 22.38/22.57 inference(quant_inst,[status(thm)],[])).
% 22.38/22.57 tff(21,plain,
% 22.38/22.57 ($false),
% 22.38/22.57 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 22.38/22.57 tff(22,plain,(~mem(a(n(e), n(e)), e)), inference(lemma,lemma(discharge,[]))).
% 22.38/22.57 tff(23,plain,
% 22.38/22.57 (^[X: $i, Y: $i, Z: $i] : refl((mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y))) <=> (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y))))),
% 22.38/22.57 inference(bind,[status(th)],[])).
% 22.38/22.57 tff(24,plain,
% 22.38/22.57 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 22.38/22.57 inference(quant_intro,[status(thm)],[23])).
% 22.38/22.57 tff(25,plain,
% 22.38/22.57 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 22.38/22.57 inference(rewrite,[status(thm)],[])).
% 22.38/22.57 tff(26,plain,
% 22.38/22.57 (^[X: $i, Y: $i, Z: $i] : rewrite((mem(X, u(Y, Z)) <=> (mem(X, Y) | mem(X, Z))) <=> (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y))))),
% 22.38/22.57 inference(bind,[status(th)],[])).
% 22.38/22.57 tff(27,plain,
% 22.38/22.57 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Y) | mem(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 22.38/22.57 inference(quant_intro,[status(thm)],[26])).
% 22.38/22.57 tff(28,axiom,(![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Y) | mem(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','u_ax')).
% 22.38/22.57 tff(29,plain,
% 22.38/22.57 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[28, 27])).
% 22.38/22.58 tff(30,plain,
% 22.38/22.58 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[29, 25])).
% 22.38/22.58 tff(31,plain,(
% 22.38/22.58 ![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 22.38/22.58 inference(skolemize,[status(sab)],[30])).
% 22.38/22.58 tff(32,plain,
% 22.38/22.58 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[31, 24])).
% 22.38/22.58 tff(33,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(34,plain,
% 22.38/22.58 ((mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e))) <=> (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(35,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[34])).
% 22.38/22.58 tff(36,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))))),
% 22.38/22.58 inference(transitivity,[status(thm)],[35, 33])).
% 22.38/22.58 tff(37,plain,
% 22.38/22.58 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e)))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(38,plain,
% 22.38/22.58 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[37, 36])).
% 22.38/22.58 tff(39,plain,
% 22.38/22.58 (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[38, 32])).
% 22.38/22.58 tff(40,plain,
% 22.38/22.58 (^[X: $i, Y: $i] : refl((a(X, Y) = u(X, s(Y))) <=> (a(X, Y) = u(X, s(Y))))),
% 22.38/22.58 inference(bind,[status(th)],[])).
% 22.38/22.58 tff(41,plain,
% 22.38/22.58 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 22.38/22.58 inference(quant_intro,[status(thm)],[40])).
% 22.38/22.58 tff(42,plain,
% 22.38/22.58 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(43,axiom,(![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','a_def')).
% 22.38/22.58 tff(44,plain,
% 22.38/22.58 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[43, 42])).
% 22.38/22.58 tff(45,plain,(
% 22.38/22.58 ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 22.38/22.58 inference(skolemize,[status(sab)],[44])).
% 22.38/22.58 tff(46,plain,
% 22.38/22.58 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[45, 41])).
% 22.38/22.58 tff(47,plain,
% 22.38/22.58 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(e, e) = u(e, s(e)))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(48,plain,
% 22.38/22.58 (a(e, e) = u(e, s(e))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[47, 46])).
% 22.38/22.58 tff(49,plain,
% 22.38/22.58 (u(e, s(e)) = a(e, e)),
% 22.38/22.58 inference(symmetry,[status(thm)],[48])).
% 22.38/22.58 tff(50,plain,
% 22.38/22.58 (mem(a(n(e), n(e)), u(e, s(e))) <=> mem(a(n(e), n(e)), a(e, e))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[49])).
% 22.38/22.58 tff(51,plain,
% 22.38/22.58 (mem(a(n(e), n(e)), a(e, e)) <=> mem(a(n(e), n(e)), u(e, s(e)))),
% 22.38/22.58 inference(symmetry,[status(thm)],[50])).
% 22.38/22.58 tff(52,plain,
% 22.38/22.58 (^[X: $i] : refl((n(X) = a(X, X)) <=> (n(X) = a(X, X)))),
% 22.38/22.58 inference(bind,[status(th)],[])).
% 22.38/22.58 tff(53,plain,
% 22.38/22.58 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 22.38/22.58 inference(quant_intro,[status(thm)],[52])).
% 22.38/22.58 tff(54,plain,
% 22.38/22.58 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(55,axiom,(![X: $i] : (n(X) = a(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','n_def')).
% 22.38/22.58 tff(56,plain,
% 22.38/22.58 (![X: $i] : (n(X) = a(X, X))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[55, 54])).
% 22.38/22.58 tff(57,plain,(
% 22.38/22.58 ![X: $i] : (n(X) = a(X, X))),
% 22.38/22.58 inference(skolemize,[status(sab)],[56])).
% 22.38/22.58 tff(58,plain,
% 22.38/22.58 (![X: $i] : (n(X) = a(X, X))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[57, 53])).
% 22.38/22.58 tff(59,plain,
% 22.38/22.58 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(e)) = a(n(e), n(e)))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(60,plain,
% 22.38/22.58 (n(n(e)) = a(n(e), n(e))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[59, 58])).
% 22.38/22.58 tff(61,plain,
% 22.38/22.58 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(e)) <=> (a(e, e) = e))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(62,plain,
% 22.38/22.58 (mem(a(e, e), s(e)) <=> (a(e, e) = e)),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[61, 8])).
% 22.38/22.58 tff(63,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), e) | mem(a(e, e), s(e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), e) | mem(a(e, e), s(e)))))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(64,plain,
% 22.38/22.58 ((mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), s(e)) | mem(a(e, e), e))) <=> (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), e) | mem(a(e, e), s(e))))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(65,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), s(e)) | mem(a(e, e), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), e) | mem(a(e, e), s(e)))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[64])).
% 22.38/22.58 tff(66,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), s(e)) | mem(a(e, e), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), e) | mem(a(e, e), s(e)))))),
% 22.38/22.58 inference(transitivity,[status(thm)],[65, 63])).
% 22.38/22.58 tff(67,plain,
% 22.38/22.58 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), s(e)) | mem(a(e, e), e)))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(68,plain,
% 22.38/22.58 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), e) | mem(a(e, e), s(e))))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[67, 66])).
% 22.38/22.58 tff(69,plain,
% 22.38/22.58 (mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), e) | mem(a(e, e), s(e)))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[68, 32])).
% 22.38/22.58 tff(70,plain,
% 22.38/22.58 (mem(a(e, e), u(e, s(e))) <=> mem(a(e, e), a(e, e))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[49])).
% 22.38/22.58 tff(71,plain,
% 22.38/22.58 (mem(a(e, e), a(e, e)) <=> mem(a(e, e), u(e, s(e)))),
% 22.38/22.58 inference(symmetry,[status(thm)],[70])).
% 22.38/22.58 tff(72,assumption,(~(a(e, e) = u(n(e), s(n(n(e)))))), introduced(assumption)).
% 22.38/22.58 tff(73,plain,
% 22.38/22.58 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(a(e, e))) <=> (e = a(e, e)))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(74,plain,
% 22.38/22.58 (mem(e, s(a(e, e))) <=> (e = a(e, e))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[73, 8])).
% 22.38/22.58 tff(75,plain,
% 22.38/22.58 ((~![X: $i] : (n(X) = a(X, X))) | (n(e) = a(e, e))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(76,plain,
% 22.38/22.58 (n(e) = a(e, e)),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[75, 58])).
% 22.38/22.58 tff(77,plain,
% 22.38/22.58 (a(e, e) = n(e)),
% 22.38/22.58 inference(symmetry,[status(thm)],[76])).
% 22.38/22.58 tff(78,plain,
% 22.38/22.58 (s(a(e, e)) = s(n(e))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[77])).
% 22.38/22.58 tff(79,assumption,(~mem(a(e, e), s(n(n(n(e)))))), introduced(assumption)).
% 22.38/22.58 tff(80,plain,
% 22.38/22.58 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(n(e), n(n(e))) = u(n(e), s(n(n(e)))))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(81,plain,
% 22.38/22.58 (a(n(e), n(n(e))) = u(n(e), s(n(n(e))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[80, 46])).
% 22.38/22.58 tff(82,plain,
% 22.38/22.58 (a(n(e), n(e)) = n(n(e))),
% 22.38/22.58 inference(symmetry,[status(thm)],[60])).
% 22.38/22.58 tff(83,assumption,(a(e, e) = a(n(e), n(e))), introduced(assumption)).
% 22.38/22.58 tff(84,plain,
% 22.38/22.58 (n(e) = n(n(e))),
% 22.38/22.58 inference(transitivity,[status(thm)],[76, 83, 82])).
% 22.38/22.58 tff(85,plain,
% 22.38/22.58 (a(n(e), n(n(e))) = a(n(n(e)), n(n(e)))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[84])).
% 22.38/22.58 tff(86,plain,
% 22.38/22.58 (a(n(n(e)), n(n(e))) = a(n(e), n(n(e)))),
% 22.38/22.58 inference(symmetry,[status(thm)],[85])).
% 22.38/22.58 tff(87,plain,
% 22.38/22.58 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(n(e))) = a(n(n(e)), n(n(e))))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(88,plain,
% 22.38/22.58 (n(n(n(e))) = a(n(n(e)), n(n(e)))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[87, 58])).
% 22.38/22.58 tff(89,plain,
% 22.38/22.58 (a(n(e), n(e)) = a(e, e)),
% 22.38/22.58 inference(symmetry,[status(thm)],[83])).
% 22.38/22.58 tff(90,plain,
% 22.38/22.58 (n(n(e)) = n(e)),
% 22.38/22.58 inference(transitivity,[status(thm)],[60, 89, 77])).
% 22.38/22.58 tff(91,plain,
% 22.38/22.58 (n(n(n(e))) = n(n(e))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[90])).
% 22.38/22.58 tff(92,plain,
% 22.38/22.58 (n(n(e)) = n(n(n(e)))),
% 22.38/22.58 inference(symmetry,[status(thm)],[91])).
% 22.38/22.58 tff(93,plain,
% 22.38/22.58 (a(e, e) = u(n(e), s(n(n(e))))),
% 22.38/22.58 inference(transitivity,[status(thm)],[83, 82, 92, 88, 86, 81])).
% 22.38/22.58 tff(94,plain,
% 22.38/22.58 ($false),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[72, 93])).
% 22.38/22.58 tff(95,plain,((~(a(e, e) = a(n(e), n(e)))) | (a(e, e) = u(n(e), s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.58 tff(96,plain,
% 22.38/22.58 (~(a(e, e) = a(n(e), n(e)))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[95, 72])).
% 22.38/22.58 tff(97,plain,
% 22.38/22.58 (s(a(n(e), n(e))) = s(n(n(e)))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[82])).
% 22.38/22.58 tff(98,plain,
% 22.38/22.58 (mem(a(e, e), s(a(n(e), n(e)))) <=> mem(a(e, e), s(n(n(e))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[97])).
% 22.38/22.58 tff(99,plain,
% 22.38/22.58 (mem(a(e, e), s(n(n(e)))) <=> mem(a(e, e), s(a(n(e), n(e))))),
% 22.38/22.58 inference(symmetry,[status(thm)],[98])).
% 22.38/22.58 tff(100,assumption,(mem(a(e, e), s(n(n(e))))), introduced(assumption)).
% 22.38/22.58 tff(101,plain,
% 22.38/22.58 (mem(a(e, e), s(a(n(e), n(e))))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[100, 99])).
% 22.38/22.58 tff(102,plain,
% 22.38/22.58 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(n(e), n(e)))) <=> (a(e, e) = a(n(e), n(e))))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(103,plain,
% 22.38/22.58 (mem(a(e, e), s(a(n(e), n(e)))) <=> (a(e, e) = a(n(e), n(e)))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[102, 8])).
% 22.38/22.58 tff(104,assumption,(~(a(e, e) = a(n(e), n(e)))), introduced(assumption)).
% 22.38/22.58 tff(105,plain,
% 22.38/22.58 ((~(mem(a(e, e), s(a(n(e), n(e)))) <=> (a(e, e) = a(n(e), n(e))))) | (~mem(a(e, e), s(a(n(e), n(e))))) | (a(e, e) = a(n(e), n(e)))),
% 22.38/22.58 inference(tautology,[status(thm)],[])).
% 22.38/22.58 tff(106,plain,
% 22.38/22.58 ((~(mem(a(e, e), s(a(n(e), n(e)))) <=> (a(e, e) = a(n(e), n(e))))) | (~mem(a(e, e), s(a(n(e), n(e)))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[105, 104])).
% 22.38/22.58 tff(107,plain,
% 22.38/22.58 (~mem(a(e, e), s(a(n(e), n(e))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[106, 103])).
% 22.38/22.58 tff(108,plain,
% 22.38/22.58 ($false),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[107, 101])).
% 22.38/22.58 tff(109,plain,((~mem(a(e, e), s(n(n(e))))) | (a(e, e) = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.58 tff(110,plain,
% 22.38/22.58 (~mem(a(e, e), s(n(n(e))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[109, 96])).
% 22.38/22.58 tff(111,plain,
% 22.38/22.58 (u(n(e), s(n(n(e)))) = a(n(e), n(n(e)))),
% 22.38/22.58 inference(symmetry,[status(thm)],[81])).
% 22.38/22.58 tff(112,plain,
% 22.38/22.58 (s(u(n(e), s(n(n(e))))) = s(a(n(e), n(n(e))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[111])).
% 22.38/22.58 tff(113,plain,
% 22.38/22.58 (mem(a(e, e), s(u(n(e), s(n(n(e)))))) <=> mem(a(e, e), s(a(n(e), n(n(e)))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[112])).
% 22.38/22.58 tff(114,plain,
% 22.38/22.58 (mem(a(e, e), s(a(n(e), n(n(e))))) <=> mem(a(e, e), s(u(n(e), s(n(n(e))))))),
% 22.38/22.58 inference(symmetry,[status(thm)],[113])).
% 22.38/22.58 tff(115,assumption,(mem(a(e, e), s(a(n(e), n(n(e)))))), introduced(assumption)).
% 22.38/22.58 tff(116,plain,
% 22.38/22.58 (mem(a(e, e), s(u(n(e), s(n(n(e))))))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[115, 114])).
% 22.38/22.58 tff(117,plain,
% 22.38/22.58 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(u(n(e), s(n(n(e)))))) <=> (a(e, e) = u(n(e), s(n(n(e))))))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(118,plain,
% 22.38/22.58 (mem(a(e, e), s(u(n(e), s(n(n(e)))))) <=> (a(e, e) = u(n(e), s(n(n(e)))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[117, 8])).
% 22.38/22.58 tff(119,plain,
% 22.38/22.58 ((~(mem(a(e, e), s(u(n(e), s(n(n(e)))))) <=> (a(e, e) = u(n(e), s(n(n(e))))))) | (~mem(a(e, e), s(u(n(e), s(n(n(e))))))) | (a(e, e) = u(n(e), s(n(n(e)))))),
% 22.38/22.58 inference(tautology,[status(thm)],[])).
% 22.38/22.58 tff(120,plain,
% 22.38/22.58 ((~(mem(a(e, e), s(u(n(e), s(n(n(e)))))) <=> (a(e, e) = u(n(e), s(n(n(e))))))) | (~mem(a(e, e), s(u(n(e), s(n(n(e)))))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[119, 72])).
% 22.38/22.58 tff(121,plain,
% 22.38/22.58 (~mem(a(e, e), s(u(n(e), s(n(n(e))))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[120, 118])).
% 22.38/22.58 tff(122,plain,
% 22.38/22.58 ($false),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[121, 116])).
% 22.38/22.58 tff(123,plain,((~mem(a(e, e), s(a(n(e), n(n(e)))))) | (a(e, e) = u(n(e), s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.58 tff(124,plain,
% 22.38/22.58 (~mem(a(e, e), s(a(n(e), n(n(e)))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[123, 72])).
% 22.38/22.58 tff(125,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e)))))))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(126,plain,
% 22.38/22.58 ((mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(s(n(e)), s(n(e)))) | mem(a(e, e), a(e, e)))) <=> (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(127,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(s(n(e)), s(n(e)))) | mem(a(e, e), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e)))))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[126])).
% 22.38/22.58 tff(128,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(s(n(e)), s(n(e)))) | mem(a(e, e), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e)))))))),
% 22.38/22.58 inference(transitivity,[status(thm)],[127, 125])).
% 22.38/22.58 tff(129,plain,
% 22.38/22.58 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(s(n(e)), s(n(e)))) | mem(a(e, e), a(e, e))))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(130,plain,
% 22.38/22.58 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[129, 128])).
% 22.38/22.58 tff(131,plain,
% 22.38/22.58 (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e)))))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[130, 32])).
% 22.38/22.58 tff(132,assumption,(a(e, e) = u(n(e), n(s(n(e))))), introduced(assumption)).
% 22.38/22.58 tff(133,plain,
% 22.38/22.58 (u(n(e), n(s(n(e)))) = a(e, e)),
% 22.38/22.58 inference(symmetry,[status(thm)],[132])).
% 22.38/22.58 tff(134,plain,
% 22.38/22.58 ((~![X: $i] : (n(X) = a(X, X))) | (n(s(n(e))) = a(s(n(e)), s(n(e))))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(135,plain,
% 22.38/22.58 (n(s(n(e))) = a(s(n(e)), s(n(e)))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[134, 58])).
% 22.38/22.58 tff(136,plain,
% 22.38/22.58 (a(s(n(e)), s(n(e))) = n(s(n(e)))),
% 22.38/22.58 inference(symmetry,[status(thm)],[135])).
% 22.38/22.58 tff(137,plain,
% 22.38/22.58 (u(a(e, e), a(s(n(e)), s(n(e)))) = u(n(e), n(s(n(e))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[77, 136])).
% 22.38/22.58 tff(138,plain,
% 22.38/22.58 (u(a(e, e), a(s(n(e)), s(n(e)))) = a(e, e)),
% 22.38/22.58 inference(transitivity,[status(thm)],[137, 133])).
% 22.38/22.58 tff(139,plain,
% 22.38/22.58 (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> mem(a(e, e), a(e, e))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[138])).
% 22.38/22.58 tff(140,plain,
% 22.38/22.58 (mem(a(e, e), a(e, e)) <=> mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 22.38/22.58 inference(symmetry,[status(thm)],[139])).
% 22.38/22.58 tff(141,plain,
% 22.38/22.58 ((~mem(a(e, e), a(e, e))) <=> (~mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[140])).
% 22.38/22.58 tff(142,plain,
% 22.38/22.58 (mem(a(e, e), a(e, e)) <=> mem(u(n(e), n(s(n(e)))), a(e, e))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[132])).
% 22.38/22.58 tff(143,plain,
% 22.38/22.58 (mem(u(n(e), n(s(n(e)))), a(e, e)) <=> mem(a(e, e), a(e, e))),
% 22.38/22.58 inference(symmetry,[status(thm)],[142])).
% 22.38/22.58 tff(144,plain,
% 22.38/22.58 ((~mem(u(n(e), n(s(n(e)))), a(e, e))) <=> (~mem(a(e, e), a(e, e)))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[143])).
% 22.38/22.58 tff(145,plain,
% 22.38/22.58 (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> mem(u(n(e), n(s(n(e)))), a(e, e))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[49])).
% 22.38/22.58 tff(146,plain,
% 22.38/22.58 (mem(u(n(e), n(s(n(e)))), a(e, e)) <=> mem(u(n(e), n(s(n(e)))), u(e, s(e)))),
% 22.38/22.58 inference(symmetry,[status(thm)],[145])).
% 22.38/22.58 tff(147,assumption,(mem(u(n(e), n(s(n(e)))), a(e, e))), introduced(assumption)).
% 22.38/22.58 tff(148,plain,
% 22.38/22.58 (mem(u(n(e), n(s(n(e)))), u(e, s(e)))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[147, 146])).
% 22.38/22.58 tff(149,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e)))))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(150,plain,
% 22.38/22.58 ((mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), s(e)) | mem(u(n(e), n(s(n(e)))), e))) <=> (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e))))),
% 22.38/22.58 inference(rewrite,[status(thm)],[])).
% 22.38/22.58 tff(151,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), s(e)) | mem(u(n(e), n(s(n(e)))), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e)))))),
% 22.38/22.58 inference(monotonicity,[status(thm)],[150])).
% 22.38/22.58 tff(152,plain,
% 22.38/22.58 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), s(e)) | mem(u(n(e), n(s(n(e)))), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e)))))),
% 22.38/22.58 inference(transitivity,[status(thm)],[151, 149])).
% 22.38/22.58 tff(153,plain,
% 22.38/22.58 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), s(e)) | mem(u(n(e), n(s(n(e)))), e)))),
% 22.38/22.58 inference(quant_inst,[status(thm)],[])).
% 22.38/22.58 tff(154,plain,
% 22.38/22.58 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e))))),
% 22.38/22.58 inference(modus_ponens,[status(thm)],[153, 152])).
% 22.38/22.58 tff(155,plain,
% 22.38/22.58 (mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e)))),
% 22.38/22.58 inference(unit_resolution,[status(thm)],[154, 32])).
% 22.38/22.59 tff(156,assumption,(~(mem(u(n(e), n(s(n(e)))), s(e)) <=> (u(n(e), n(s(n(e)))) = e))), introduced(assumption)).
% 22.38/22.59 tff(157,plain,
% 22.38/22.59 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(u(n(e), n(s(n(e)))), s(e)) <=> (u(n(e), n(s(n(e)))) = e))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(158,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[157, 8, 156])).
% 22.38/22.59 tff(159,plain,(mem(u(n(e), n(s(n(e)))), s(e)) <=> (u(n(e), n(s(n(e)))) = e)), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(160,assumption,(u(n(e), n(s(n(e)))) = e), introduced(assumption)).
% 22.38/22.59 tff(161,plain,
% 22.38/22.59 (u(a(e, e), a(s(n(e)), s(n(e)))) = e),
% 22.38/22.59 inference(transitivity,[status(thm)],[137, 160])).
% 22.38/22.59 tff(162,plain,
% 22.38/22.59 (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> mem(a(e, e), e)),
% 22.38/22.59 inference(monotonicity,[status(thm)],[161])).
% 22.38/22.59 tff(163,plain,
% 22.38/22.59 (mem(a(e, e), e) <=> mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 22.38/22.59 inference(symmetry,[status(thm)],[162])).
% 22.38/22.59 tff(164,plain,
% 22.38/22.59 ((~mem(a(e, e), e)) <=> (~mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[163])).
% 22.38/22.59 tff(165,plain,
% 22.38/22.59 ((~![X: $i] : (~mem(X, e))) | (~mem(a(e, e), e))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(166,plain,
% 22.38/22.59 (~mem(a(e, e), e)),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[165, 19])).
% 22.38/22.59 tff(167,plain,
% 22.38/22.59 (~mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 22.38/22.59 inference(modus_ponens,[status(thm)],[166, 164])).
% 22.38/22.59 tff(168,plain,
% 22.38/22.59 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(n(e)), s(n(e))) = u(s(n(e)), s(s(n(e)))))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(169,plain,
% 22.38/22.59 (a(s(n(e)), s(n(e))) = u(s(n(e)), s(s(n(e))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[168, 46])).
% 22.38/22.59 tff(170,plain,
% 22.38/22.59 (mem(a(e, e), a(s(n(e)), s(n(e)))) <=> mem(a(e, e), u(s(n(e)), s(s(n(e)))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[169])).
% 22.38/22.59 tff(171,plain,
% 22.38/22.59 (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> mem(a(e, e), a(s(n(e)), s(n(e))))),
% 22.38/22.59 inference(symmetry,[status(thm)],[170])).
% 22.38/22.59 tff(172,assumption,(~(mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))))), introduced(assumption)).
% 22.38/22.59 tff(173,plain,
% 22.38/22.59 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e)))))))),
% 22.38/22.59 inference(rewrite,[status(thm)],[])).
% 22.38/22.59 tff(174,plain,
% 22.38/22.59 ((mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(s(n(e)))) | mem(a(e, e), s(n(e))))) <=> (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))))),
% 22.38/22.59 inference(rewrite,[status(thm)],[])).
% 22.38/22.59 tff(175,plain,
% 22.38/22.59 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(s(n(e)))) | mem(a(e, e), s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e)))))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[174])).
% 22.38/22.59 tff(176,plain,
% 22.38/22.59 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(s(n(e)))) | mem(a(e, e), s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e)))))))),
% 22.38/22.59 inference(transitivity,[status(thm)],[175, 173])).
% 22.38/22.59 tff(177,plain,
% 22.38/22.59 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(s(n(e)))) | mem(a(e, e), s(n(e)))))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(178,plain,
% 22.38/22.59 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))))),
% 22.38/22.59 inference(modus_ponens,[status(thm)],[177, 176])).
% 22.38/22.59 tff(179,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[178, 32, 172])).
% 22.38/22.59 tff(180,plain,(mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(181,plain,
% 22.38/22.59 (mem(a(e, e), s(a(e, e))) <=> mem(a(e, e), s(n(e)))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[78])).
% 22.38/22.59 tff(182,plain,
% 22.38/22.59 (mem(a(e, e), s(n(e))) <=> mem(a(e, e), s(a(e, e)))),
% 22.38/22.59 inference(symmetry,[status(thm)],[181])).
% 22.38/22.59 tff(183,plain,
% 22.38/22.59 ((~mem(a(e, e), s(n(e)))) <=> (~mem(a(e, e), s(a(e, e))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[182])).
% 22.38/22.59 tff(184,assumption,(~mem(a(e, e), s(n(e)))), introduced(assumption)).
% 22.38/22.59 tff(185,plain,
% 22.38/22.59 (~mem(a(e, e), s(a(e, e)))),
% 22.38/22.59 inference(modus_ponens,[status(thm)],[184, 183])).
% 22.38/22.59 tff(186,plain,
% 22.38/22.59 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e)))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e))))),
% 22.38/22.59 inference(rewrite,[status(thm)],[])).
% 22.38/22.59 tff(187,plain,
% 22.38/22.59 ((mem(a(e, e), s(a(e, e))) <=> $true) <=> mem(a(e, e), s(a(e, e)))),
% 22.38/22.59 inference(rewrite,[status(thm)],[])).
% 22.38/22.59 tff(188,plain,
% 22.38/22.59 ((a(e, e) = a(e, e)) <=> $true),
% 22.38/22.59 inference(rewrite,[status(thm)],[])).
% 22.38/22.59 tff(189,plain,
% 22.38/22.59 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> (mem(a(e, e), s(a(e, e))) <=> $true)),
% 22.38/22.59 inference(monotonicity,[status(thm)],[188])).
% 22.38/22.59 tff(190,plain,
% 22.38/22.59 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> mem(a(e, e), s(a(e, e)))),
% 22.38/22.59 inference(transitivity,[status(thm)],[189, 187])).
% 22.38/22.59 tff(191,plain,
% 22.38/22.59 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e)))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[190])).
% 22.38/22.59 tff(192,plain,
% 22.38/22.59 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e)))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e))))),
% 22.38/22.59 inference(transitivity,[status(thm)],[191, 186])).
% 22.38/22.59 tff(193,plain,
% 22.38/22.59 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e)))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(194,plain,
% 22.38/22.59 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e)))),
% 22.38/22.59 inference(modus_ponens,[status(thm)],[193, 192])).
% 22.38/22.59 tff(195,plain,
% 22.38/22.59 (mem(a(e, e), s(a(e, e)))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[194, 8])).
% 22.38/22.59 tff(196,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[195, 185])).
% 22.38/22.59 tff(197,plain,(mem(a(e, e), s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(198,plain,
% 22.38/22.59 ((mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))) | (~mem(a(e, e), s(n(e))))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(199,plain,
% 22.38/22.59 (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[198, 197])).
% 22.38/22.59 tff(200,plain,
% 22.38/22.59 ((~(mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))))) | mem(a(e, e), u(s(n(e)), s(s(n(e))))) | (~(mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(201,plain,
% 22.38/22.59 ((~(mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(s(n(e))))))) | mem(a(e, e), u(s(n(e)), s(s(n(e)))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[200, 199])).
% 22.38/22.59 tff(202,plain,
% 22.38/22.59 (mem(a(e, e), u(s(n(e)), s(s(n(e)))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[201, 180])).
% 22.38/22.59 tff(203,plain,
% 22.38/22.59 (mem(a(e, e), a(s(n(e)), s(n(e))))),
% 22.38/22.59 inference(modus_ponens,[status(thm)],[202, 171])).
% 22.38/22.59 tff(204,plain,
% 22.38/22.59 ((mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))) | (~mem(a(e, e), a(s(n(e)), s(n(e)))))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(205,plain,
% 22.38/22.59 (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[204, 203])).
% 22.38/22.59 tff(206,plain,
% 22.38/22.59 ((~(mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))) | mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) | (~(mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(207,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[206, 205, 167, 131])).
% 22.38/22.59 tff(208,plain,(~(u(n(e), n(s(n(e)))) = e)), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(209,plain,
% 22.38/22.59 ((~(mem(u(n(e), n(s(n(e)))), s(e)) <=> (u(n(e), n(s(n(e)))) = e))) | (~mem(u(n(e), n(s(n(e)))), s(e))) | (u(n(e), n(s(n(e)))) = e)),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(210,plain,
% 22.38/22.59 ((~(mem(u(n(e), n(s(n(e)))), s(e)) <=> (u(n(e), n(s(n(e)))) = e))) | (~mem(u(n(e), n(s(n(e)))), s(e)))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[209, 208])).
% 22.38/22.59 tff(211,plain,
% 22.38/22.59 (~mem(u(n(e), n(s(n(e)))), s(e))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[210, 159])).
% 22.38/22.59 tff(212,assumption,(mem(u(n(e), n(s(n(e)))), e)), introduced(assumption)).
% 22.38/22.59 tff(213,plain,
% 22.38/22.59 ((~![X: $i] : (~mem(X, e))) | (~mem(u(n(e), n(s(n(e)))), e))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(214,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[213, 19, 212])).
% 22.38/22.59 tff(215,plain,(~mem(u(n(e), n(s(n(e)))), e)), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(216,plain,
% 22.38/22.59 ((~(mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e)))) | mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(217,plain,
% 22.38/22.59 (~(mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e)))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[216, 215, 211])).
% 22.38/22.59 tff(218,plain,
% 22.38/22.59 ((~(mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e))))) | (~mem(u(n(e), n(s(n(e)))), u(e, s(e)))) | (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e)))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(219,plain,
% 22.38/22.59 ((~(mem(u(n(e), n(s(n(e)))), u(e, s(e))) <=> (mem(u(n(e), n(s(n(e)))), e) | mem(u(n(e), n(s(n(e)))), s(e))))) | (~mem(u(n(e), n(s(n(e)))), u(e, s(e))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[218, 217])).
% 22.38/22.59 tff(220,plain,
% 22.38/22.59 (~mem(u(n(e), n(s(n(e)))), u(e, s(e)))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[219, 155])).
% 22.38/22.59 tff(221,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[220, 148])).
% 22.38/22.59 tff(222,plain,(~mem(u(n(e), n(s(n(e)))), a(e, e))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(223,plain,
% 22.38/22.59 (~mem(a(e, e), a(e, e))),
% 22.38/22.59 inference(modus_ponens,[status(thm)],[222, 144])).
% 22.38/22.59 tff(224,plain,
% 22.38/22.59 (~mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 22.38/22.59 inference(modus_ponens,[status(thm)],[223, 141])).
% 22.38/22.59 tff(225,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[206, 205, 224, 131])).
% 22.38/22.59 tff(226,plain,(~(a(e, e) = u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(227,assumption,(~(mem(a(e, e), s(u(n(e), n(s(n(e)))))) <=> (a(e, e) = u(n(e), n(s(n(e))))))), introduced(assumption)).
% 22.38/22.59 tff(228,plain,
% 22.38/22.59 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(u(n(e), n(s(n(e)))))) <=> (a(e, e) = u(n(e), n(s(n(e))))))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(229,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[228, 8, 227])).
% 22.38/22.59 tff(230,plain,(mem(a(e, e), s(u(n(e), n(s(n(e)))))) <=> (a(e, e) = u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(231,plain,
% 22.38/22.59 ((~(mem(a(e, e), s(u(n(e), n(s(n(e)))))) <=> (a(e, e) = u(n(e), n(s(n(e))))))) | (~mem(a(e, e), s(u(n(e), n(s(n(e))))))) | (a(e, e) = u(n(e), n(s(n(e)))))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(232,plain,
% 22.38/22.59 ((~mem(a(e, e), s(u(n(e), n(s(n(e))))))) | (a(e, e) = u(n(e), n(s(n(e)))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[231, 230])).
% 22.38/22.59 tff(233,plain,
% 22.38/22.59 (~mem(a(e, e), s(u(n(e), n(s(n(e))))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[232, 226])).
% 22.38/22.59 tff(234,plain,
% 22.38/22.59 ((~(mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))) | mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e))))))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(235,plain,
% 22.38/22.59 ((~(mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))) | mem(a(e, e), s(a(n(e), n(n(e)))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[234, 233])).
% 22.38/22.59 tff(236,plain,
% 22.38/22.59 (~(mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[235, 124])).
% 22.38/22.59 tff(237,assumption,(~(mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) <=> (mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e))))))))), introduced(assumption)).
% 22.38/22.59 tff(238,plain,
% 22.38/22.59 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) <=> (mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e))))))))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(239,plain,
% 22.38/22.59 ($false),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[238, 32, 237])).
% 22.38/22.59 tff(240,plain,(mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) <=> (mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.59 tff(241,plain,
% 22.38/22.59 ((~(mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) <=> (mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e))))))))) | (~mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))) | (mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))),
% 22.38/22.59 inference(tautology,[status(thm)],[])).
% 22.38/22.59 tff(242,plain,
% 22.38/22.59 ((~mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))) | (mem(a(e, e), s(a(n(e), n(n(e))))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[241, 240])).
% 22.38/22.59 tff(243,plain,
% 22.38/22.59 (~mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[242, 236])).
% 22.38/22.59 tff(244,plain,
% 22.38/22.59 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(245,plain,
% 22.38/22.59 (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[244, 32])).
% 22.38/22.59 tff(246,plain,
% 22.38/22.59 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))) = u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))),
% 22.38/22.59 inference(quant_inst,[status(thm)],[])).
% 22.38/22.59 tff(247,plain,
% 22.38/22.59 (a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))) = u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))),
% 22.38/22.59 inference(unit_resolution,[status(thm)],[246, 46])).
% 22.38/22.59 tff(248,plain,
% 22.38/22.59 (u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))) = a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e))))),
% 22.38/22.59 inference(symmetry,[status(thm)],[247])).
% 22.38/22.59 tff(249,plain,
% 22.38/22.59 (u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) = u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[248])).
% 22.38/22.59 tff(250,plain,
% 22.38/22.59 (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[249])).
% 22.38/22.59 tff(251,plain,
% 22.38/22.59 (mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.59 inference(symmetry,[status(thm)],[250])).
% 22.38/22.59 tff(252,plain,
% 22.38/22.59 (u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) = u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[248])).
% 22.38/22.59 tff(253,plain,
% 22.38/22.59 (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[252])).
% 22.38/22.59 tff(254,plain,
% 22.38/22.59 (mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.59 inference(symmetry,[status(thm)],[253])).
% 22.38/22.59 tff(255,plain,
% 22.38/22.59 ((~mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) <=> (~mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[254])).
% 22.38/22.59 tff(256,assumption,(~mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))), introduced(assumption)).
% 22.38/22.59 tff(257,plain,
% 22.38/22.59 (~mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.59 inference(modus_ponens,[status(thm)],[256, 255])).
% 22.38/22.59 tff(258,plain,
% 22.38/22.59 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))),
% 22.38/22.59 inference(rewrite,[status(thm)],[])).
% 22.38/22.59 tff(259,plain,
% 22.38/22.59 ((mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))))) <=> (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.59 inference(rewrite,[status(thm)],[])).
% 22.38/22.59 tff(260,plain,
% 22.38/22.59 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))),
% 22.38/22.59 inference(monotonicity,[status(thm)],[259])).
% 22.38/22.59 tff(261,plain,
% 22.38/22.59 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))),
% 22.38/22.59 inference(transitivity,[status(thm)],[260, 258])).
% 22.38/22.60 tff(262,plain,
% 22.38/22.60 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))))),
% 22.38/22.60 inference(quant_inst,[status(thm)],[])).
% 22.38/22.60 tff(263,plain,
% 22.38/22.60 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.60 inference(modus_ponens,[status(thm)],[262, 261])).
% 22.38/22.60 tff(264,plain,
% 22.38/22.60 (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[263, 32])).
% 22.38/22.60 tff(265,plain,
% 22.38/22.60 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(n(s(n(e)))), n(n(n(e)))) = u(s(n(s(n(e)))), s(n(n(n(e))))))),
% 22.38/22.60 inference(quant_inst,[status(thm)],[])).
% 22.38/22.60 tff(266,plain,
% 22.38/22.60 (a(s(n(s(n(e)))), n(n(n(e)))) = u(s(n(s(n(e)))), s(n(n(n(e)))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[265, 46])).
% 22.38/22.60 tff(267,plain,
% 22.38/22.60 (u(s(n(s(n(e)))), s(n(n(n(e))))) = a(s(n(s(n(e)))), n(n(n(e))))),
% 22.38/22.60 inference(symmetry,[status(thm)],[266])).
% 22.38/22.60 tff(268,plain,
% 22.38/22.60 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(n(e)), n(n(e))) = u(s(n(e)), s(n(n(e)))))),
% 22.38/22.60 inference(quant_inst,[status(thm)],[])).
% 22.38/22.60 tff(269,plain,
% 22.38/22.60 (a(s(n(e)), n(n(e))) = u(s(n(e)), s(n(n(e))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[268, 46])).
% 22.38/22.60 tff(270,plain,
% 22.38/22.60 (u(s(n(e)), s(n(n(e)))) = a(s(n(e)), n(n(e)))),
% 22.38/22.60 inference(symmetry,[status(thm)],[269])).
% 22.38/22.60 tff(271,plain,
% 22.38/22.60 (u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e)))))) = u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))),
% 22.38/22.60 inference(monotonicity,[status(thm)],[270, 267])).
% 22.38/22.60 tff(272,plain,
% 22.38/22.60 (mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))),
% 22.38/22.60 inference(monotonicity,[status(thm)],[271])).
% 22.38/22.60 tff(273,plain,
% 22.38/22.60 (mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) <=> mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e)))))))),
% 22.38/22.60 inference(symmetry,[status(thm)],[272])).
% 22.38/22.60 tff(274,plain,
% 22.38/22.60 ((~mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (~mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e))))))))),
% 22.38/22.60 inference(monotonicity,[status(thm)],[273])).
% 22.38/22.60 tff(275,assumption,(~mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), introduced(assumption)).
% 22.38/22.60 tff(276,plain,
% 22.38/22.60 (~mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e)))))))),
% 22.38/22.60 inference(modus_ponens,[status(thm)],[275, 274])).
% 22.38/22.60 tff(277,plain,
% 22.38/22.60 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(n(n(e)))))))),
% 22.38/22.60 inference(quant_inst,[status(thm)],[])).
% 22.38/22.60 tff(278,plain,
% 22.38/22.60 (mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(n(n(e))))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[277, 32])).
% 22.38/22.60 tff(279,plain,
% 22.38/22.60 ((mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))) | (~mem(a(e, e), s(n(e))))),
% 22.38/22.60 inference(tautology,[status(thm)],[])).
% 22.38/22.60 tff(280,plain,
% 22.38/22.60 (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[279, 197])).
% 22.38/22.60 tff(281,assumption,(~(mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))))), introduced(assumption)).
% 22.38/22.60 tff(282,plain,
% 22.38/22.60 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e)))))))),
% 22.38/22.60 inference(rewrite,[status(thm)],[])).
% 22.38/22.60 tff(283,plain,
% 22.38/22.60 ((mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(n(e)))) | mem(a(e, e), s(n(e))))) <=> (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))))),
% 22.38/22.60 inference(rewrite,[status(thm)],[])).
% 22.38/22.60 tff(284,plain,
% 22.38/22.60 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(n(e)))) | mem(a(e, e), s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e)))))))),
% 22.38/22.60 inference(monotonicity,[status(thm)],[283])).
% 22.38/22.60 tff(285,plain,
% 22.38/22.60 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(n(e)))) | mem(a(e, e), s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e)))))))),
% 22.38/22.60 inference(transitivity,[status(thm)],[284, 282])).
% 22.38/22.60 tff(286,plain,
% 22.38/22.60 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(n(e)))) | mem(a(e, e), s(n(e)))))),
% 22.38/22.60 inference(quant_inst,[status(thm)],[])).
% 22.38/22.60 tff(287,plain,
% 22.38/22.60 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))))),
% 22.38/22.60 inference(modus_ponens,[status(thm)],[286, 285])).
% 22.38/22.60 tff(288,plain,
% 22.38/22.60 ($false),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[287, 32, 281])).
% 22.38/22.60 tff(289,plain,(mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.60 tff(290,plain,
% 22.38/22.60 ((~(mem(a(e, e), u(s(n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))))) | mem(a(e, e), u(s(n(e)), s(n(n(e))))) | (~(mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))))),
% 22.38/22.60 inference(tautology,[status(thm)],[])).
% 22.38/22.60 tff(291,plain,
% 22.38/22.60 (mem(a(e, e), u(s(n(e)), s(n(n(e))))) | (~(mem(a(e, e), s(n(e))) | mem(a(e, e), s(n(n(e))))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[290, 289])).
% 22.38/22.60 tff(292,plain,
% 22.38/22.60 (mem(a(e, e), u(s(n(e)), s(n(n(e)))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[291, 280])).
% 22.38/22.60 tff(293,plain,
% 22.38/22.60 ((mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(n(n(e)))))) | (~mem(a(e, e), u(s(n(e)), s(n(n(e))))))),
% 22.38/22.60 inference(tautology,[status(thm)],[])).
% 22.38/22.60 tff(294,plain,
% 22.38/22.60 (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(n(n(e)))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[293, 292])).
% 22.38/22.60 tff(295,plain,
% 22.38/22.60 ((~(mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(n(n(e)))))))) | mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e))))))) | (~(mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(n(n(e)))))))),
% 22.38/22.60 inference(tautology,[status(thm)],[])).
% 22.38/22.60 tff(296,plain,
% 22.38/22.60 ((~(mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(n(n(e)))))))) | mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e)))))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[295, 294])).
% 22.38/22.60 tff(297,plain,
% 22.38/22.60 (mem(a(e, e), u(u(s(n(e)), s(n(n(e)))), u(s(n(s(n(e)))), s(n(n(n(e)))))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[296, 278])).
% 22.38/22.60 tff(298,plain,
% 22.38/22.60 ($false),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[297, 276])).
% 22.38/22.60 tff(299,plain,(mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.60 tff(300,plain,
% 22.38/22.60 ((mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) | (~mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.60 inference(tautology,[status(thm)],[])).
% 22.38/22.60 tff(301,plain,
% 22.38/22.60 (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[300, 299])).
% 22.38/22.60 tff(302,plain,
% 22.38/22.60 ((~(mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) | mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) | (~(mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.60 inference(tautology,[status(thm)],[])).
% 22.38/22.60 tff(303,plain,
% 22.38/22.60 ((~(mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))) | mem(a(e, e), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) | mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[302, 301])).
% 22.38/22.60 tff(304,plain,
% 22.38/22.60 (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[303, 264])).
% 22.38/22.60 tff(305,plain,
% 22.38/22.60 ($false),
% 22.38/22.60 inference(unit_resolution,[status(thm)],[304, 257])).
% 22.38/22.60 tff(306,plain,(mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.60 tff(307,assumption,(~mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))), introduced(assumption)).
% 22.38/22.60 tff(308,assumption,(mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))), introduced(assumption)).
% 22.38/22.60 tff(309,plain,
% 22.38/22.60 (^[X: $i, Y: $i] : refl((~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))))) <=> (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))))))),
% 22.38/22.60 inference(bind,[status(th)],[])).
% 22.38/22.60 tff(310,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))),
% 22.38/22.60 inference(quant_intro,[status(thm)],[309])).
% 22.38/22.60 tff(311,plain,
% 22.38/22.60 (^[X: $i, Y: $i] : rewrite((~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))))) <=> (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))))))),
% 22.38/22.60 inference(bind,[status(th)],[])).
% 22.38/22.60 tff(312,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))),
% 22.38/22.60 inference(quant_intro,[status(thm)],[311])).
% 22.38/22.60 tff(313,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))),
% 22.38/22.60 inference(transitivity,[status(thm)],[312, 310])).
% 22.38/22.60 tff(314,plain,
% 22.38/22.60 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))) <=> ((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))), rewrite((subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))) <=> (subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))), ((((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))) & (subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))) <=> (((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))) & (subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))))), rewrite((((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))) & (subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))) <=> (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))), ((((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))) & (subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))) <=> (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))))),
% 22.38/22.60 inference(bind,[status(th)],[])).
% 22.38/22.60 tff(315,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))) & (subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y))))) <=> ![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))),
% 22.38/22.60 inference(quant_intro,[status(thm)],[314])).
% 22.38/22.60 tff(316,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))) <=> ![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 22.38/22.60 inference(rewrite,[status(thm)],[])).
% 22.38/22.60 tff(317,plain,
% 22.38/22.60 (^[X: $i, Y: $i] : rewrite((subq(X, Y) <=> ![Z: $i] : (mem(Z, X) => mem(Z, Y))) <=> (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))))),
% 22.38/22.60 inference(bind,[status(th)],[])).
% 22.38/22.60 tff(318,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : (mem(Z, X) => mem(Z, Y))) <=> ![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 22.38/22.60 inference(quant_intro,[status(thm)],[317])).
% 22.38/22.60 tff(319,axiom,(![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : (mem(Z, X) => mem(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','subq_def')).
% 22.38/22.60 tff(320,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 22.38/22.60 inference(modus_ponens,[status(thm)],[319, 318])).
% 22.38/22.60 tff(321,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 22.38/22.60 inference(modus_ponens,[status(thm)],[320, 316])).
% 22.38/22.60 tff(322,plain,(
% 22.38/22.60 ![X: $i, Y: $i] : (((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y))) & (subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))),
% 22.38/22.60 inference(skolemize,[status(sab)],[321])).
% 22.38/22.60 tff(323,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))),
% 22.38/22.60 inference(modus_ponens,[status(thm)],[322, 315])).
% 22.38/22.60 tff(324,plain,
% 22.38/22.60 (![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))),
% 22.38/22.60 inference(modus_ponens,[status(thm)],[323, 313])).
% 22.38/22.60 tff(325,plain,
% 22.38/22.60 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))) | (~(subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) | (~((~mem(tptp_fun_Z_0(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(tptp_fun_Z_0(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))))))),
% 22.38/22.61 inference(quant_inst,[status(thm)],[])).
% 22.38/22.61 tff(326,plain,
% 22.38/22.61 (~((~((~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))) | (~(subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) | (~((~mem(tptp_fun_Z_0(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(tptp_fun_Z_0(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[325, 324])).
% 22.38/22.61 tff(327,plain,
% 22.38/22.61 (((~((~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))) | (~(subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) | (~((~mem(tptp_fun_Z_0(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(tptp_fun_Z_0(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))))) | ((~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(328,plain,
% 22.38/22.61 ((~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[327, 326])).
% 22.38/22.61 tff(329,plain,
% 22.38/22.61 (subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.61 inference(rewrite,[status(thm)],[])).
% 22.38/22.61 tff(330,plain,
% 22.38/22.61 ((~(~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) <=> subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.61 inference(rewrite,[status(thm)],[])).
% 22.38/22.61 tff(331,axiom,(~(~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nsubq_2762_2760')).
% 22.38/22.61 tff(332,plain,
% 22.38/22.61 (subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.61 inference(modus_ponens,[status(thm)],[331, 330])).
% 22.38/22.61 tff(333,plain,
% 22.38/22.61 (subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.61 inference(modus_ponens,[status(thm)],[332, 329])).
% 22.38/22.61 tff(334,plain,
% 22.38/22.61 ((~((~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))) | (~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(335,plain,
% 22.38/22.61 ((~((~subq(u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))))) | ![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[334, 333])).
% 22.38/22.61 tff(336,plain,
% 22.38/22.61 (![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[335, 328])).
% 22.38/22.61 tff(337,plain,
% 22.38/22.61 (((~![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) | ((~mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) <=> ((~![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) | (~mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.61 inference(rewrite,[status(thm)],[])).
% 22.38/22.61 tff(338,plain,
% 22.38/22.61 ((~![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) | ((~mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))),
% 22.38/22.61 inference(quant_inst,[status(thm)],[])).
% 22.38/22.61 tff(339,plain,
% 22.38/22.61 ((~![Z: $i] : ((~mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(Z, u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))))) | (~mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.61 inference(modus_ponens,[status(thm)],[338, 337])).
% 22.38/22.61 tff(340,plain,
% 22.38/22.61 ($false),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[339, 336, 308, 307])).
% 22.38/22.61 tff(341,plain,((~mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(a(s(n(e)), n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.61 tff(342,plain,
% 22.38/22.61 (mem(a(e, e), u(a(s(u(n(e), n(s(n(e))))), a(n(e), n(n(e)))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[341, 306])).
% 22.38/22.61 tff(343,plain,
% 22.38/22.61 (mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))),
% 22.38/22.61 inference(modus_ponens,[status(thm)],[342, 251])).
% 22.38/22.61 tff(344,plain,
% 22.38/22.61 ((~(mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))))) | (~mem(a(e, e), u(u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))))) | (mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(345,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[344, 343, 245])).
% 22.38/22.61 tff(346,plain,
% 22.38/22.61 ((~(mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e)))))))) | mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(347,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) | mem(a(e, e), u(s(u(n(e), n(s(n(e))))), s(a(n(e), n(n(e))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[346, 345])).
% 22.38/22.61 tff(348,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[347, 243])).
% 22.38/22.61 tff(349,plain,
% 22.38/22.61 (u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e)))))) = u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))),
% 22.38/22.61 inference(monotonicity,[status(thm)],[267])).
% 22.38/22.61 tff(350,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))),
% 22.38/22.61 inference(monotonicity,[status(thm)],[349])).
% 22.38/22.61 tff(351,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e)))))) <=> mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e)))))))),
% 22.38/22.61 inference(symmetry,[status(thm)],[350])).
% 22.38/22.61 tff(352,assumption,(mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))), introduced(assumption)).
% 22.38/22.61 tff(353,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e)))))))),
% 22.38/22.61 inference(modus_ponens,[status(thm)],[352, 351])).
% 22.38/22.61 tff(354,plain,
% 22.38/22.61 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), s(n(n(e))))))),
% 22.38/22.61 inference(quant_inst,[status(thm)],[])).
% 22.38/22.61 tff(355,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), s(n(n(e)))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[354, 32])).
% 22.38/22.61 tff(356,assumption,(~mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e))))))), introduced(assumption)).
% 22.38/22.61 tff(357,assumption,(~mem(a(e, e), s(n(n(e))))), introduced(assumption)).
% 22.38/22.61 tff(358,plain,
% 22.38/22.61 ((~(mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), s(n(n(e)))))) | mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), s(n(n(e))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(359,plain,
% 22.38/22.61 (~(mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), s(n(n(e)))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[358, 357, 356])).
% 22.38/22.61 tff(360,plain,
% 22.38/22.61 ((~(mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), s(n(n(e))))))) | (~mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e)))))))) | (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), s(n(n(e)))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(361,plain,
% 22.38/22.61 ((~(mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), s(n(n(e))))))) | (~mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e))))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[360, 359])).
% 22.38/22.61 tff(362,plain,
% 22.38/22.61 (~mem(a(e, e), u(s(n(n(e))), u(s(n(s(n(e)))), s(n(n(n(e)))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[361, 355])).
% 22.38/22.61 tff(363,plain,
% 22.38/22.61 ($false),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[362, 353])).
% 22.38/22.61 tff(364,plain,((~mem(a(e, e), u(s(n(n(e))), a(s(n(s(n(e)))), n(n(n(e))))))) | mem(a(e, e), s(n(n(e)))) | mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.61 tff(365,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[364, 348, 110])).
% 22.38/22.61 tff(366,assumption,(~(mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) <=> (mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e)))))))), introduced(assumption)).
% 22.38/22.61 tff(367,plain,
% 22.38/22.61 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) <=> (mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e)))))))),
% 22.38/22.61 inference(quant_inst,[status(thm)],[])).
% 22.38/22.61 tff(368,plain,
% 22.38/22.61 ($false),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[367, 32, 366])).
% 22.38/22.61 tff(369,plain,(mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) <=> (mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.61 tff(370,plain,
% 22.38/22.61 ((~(mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e)))))) <=> (mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e)))))))) | (~mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e))))))) | (mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e))))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(371,plain,
% 22.38/22.61 ((~mem(a(e, e), u(s(n(s(n(e)))), s(n(n(n(e))))))) | (mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[370, 369])).
% 22.38/22.61 tff(372,plain,
% 22.38/22.61 (mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e)))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[371, 365])).
% 22.38/22.61 tff(373,plain,
% 22.38/22.61 ((~(mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e))))))) | mem(a(e, e), s(n(n(n(e))))) | mem(a(e, e), s(n(s(n(e)))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(374,plain,
% 22.38/22.61 (mem(a(e, e), s(n(s(n(e)))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[373, 372, 79])).
% 22.38/22.61 tff(375,plain,
% 22.38/22.61 (s(a(s(n(e)), s(n(e)))) = s(n(s(n(e))))),
% 22.38/22.61 inference(monotonicity,[status(thm)],[136])).
% 22.38/22.61 tff(376,plain,
% 22.38/22.61 (mem(a(e, e), s(a(s(n(e)), s(n(e))))) <=> mem(a(e, e), s(n(s(n(e)))))),
% 22.38/22.61 inference(monotonicity,[status(thm)],[375])).
% 22.38/22.61 tff(377,plain,
% 22.38/22.61 (mem(a(e, e), s(n(s(n(e))))) <=> mem(a(e, e), s(a(s(n(e)), s(n(e)))))),
% 22.38/22.61 inference(symmetry,[status(thm)],[376])).
% 22.38/22.61 tff(378,assumption,(mem(a(e, e), s(n(s(n(e)))))), introduced(assumption)).
% 22.38/22.61 tff(379,plain,
% 22.38/22.61 (mem(a(e, e), s(a(s(n(e)), s(n(e)))))),
% 22.38/22.61 inference(modus_ponens,[status(thm)],[378, 377])).
% 22.38/22.61 tff(380,plain,
% 22.38/22.61 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(s(n(e)), s(n(e))))) <=> (a(e, e) = a(s(n(e)), s(n(e)))))),
% 22.38/22.61 inference(quant_inst,[status(thm)],[])).
% 22.38/22.61 tff(381,plain,
% 22.38/22.61 (mem(a(e, e), s(a(s(n(e)), s(n(e))))) <=> (a(e, e) = a(s(n(e)), s(n(e))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[380, 8])).
% 22.38/22.61 tff(382,assumption,(~(a(e, e) = a(s(n(e)), s(n(e))))), introduced(assumption)).
% 22.38/22.61 tff(383,plain,
% 22.38/22.61 ((~(mem(a(e, e), s(a(s(n(e)), s(n(e))))) <=> (a(e, e) = a(s(n(e)), s(n(e)))))) | (~mem(a(e, e), s(a(s(n(e)), s(n(e)))))) | (a(e, e) = a(s(n(e)), s(n(e))))),
% 22.38/22.61 inference(tautology,[status(thm)],[])).
% 22.38/22.61 tff(384,plain,
% 22.38/22.61 ((~(mem(a(e, e), s(a(s(n(e)), s(n(e))))) <=> (a(e, e) = a(s(n(e)), s(n(e)))))) | (~mem(a(e, e), s(a(s(n(e)), s(n(e))))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[383, 382])).
% 22.38/22.61 tff(385,plain,
% 22.38/22.61 (~mem(a(e, e), s(a(s(n(e)), s(n(e)))))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[384, 381])).
% 22.38/22.61 tff(386,plain,
% 22.38/22.61 ($false),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[385, 379])).
% 22.38/22.61 tff(387,plain,((~mem(a(e, e), s(n(s(n(e)))))) | (a(e, e) = a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.61 tff(388,plain,
% 22.38/22.61 (a(e, e) = a(s(n(e)), s(n(e)))),
% 22.38/22.61 inference(unit_resolution,[status(thm)],[387, 374])).
% 22.38/22.61 tff(389,assumption,(a(e, e) = a(s(n(e)), s(n(e)))), introduced(assumption)).
% 22.38/22.61 tff(390,plain,
% 22.38/22.61 (a(s(n(e)), s(n(e))) = a(e, e)),
% 22.38/22.61 inference(symmetry,[status(thm)],[389])).
% 22.38/22.61 tff(391,plain,
% 22.38/22.61 (u(s(n(e)), s(s(n(e)))) = a(s(n(e)), s(n(e)))),
% 22.38/22.61 inference(symmetry,[status(thm)],[169])).
% 22.38/22.61 tff(392,plain,
% 22.38/22.61 (u(s(n(e)), s(s(n(e)))) = a(e, e)),
% 22.38/22.61 inference(transitivity,[status(thm)],[391, 390])).
% 22.38/22.61 tff(393,plain,
% 22.38/22.61 (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> mem(a(e, e), a(e, e))),
% 22.38/22.61 inference(monotonicity,[status(thm)],[392])).
% 22.38/22.61 tff(394,plain,
% 22.38/22.61 (mem(a(e, e), a(e, e)) <=> mem(a(e, e), u(s(n(e)), s(s(n(e)))))),
% 22.38/22.61 inference(symmetry,[status(thm)],[393])).
% 22.38/22.61 tff(395,plain,
% 22.38/22.61 ((~mem(a(e, e), a(e, e))) <=> (~mem(a(e, e), u(s(n(e)), s(s(n(e))))))),
% 22.38/22.61 inference(monotonicity,[status(thm)],[394])).
% 22.38/22.61 tff(396,assumption,(~mem(a(e, e), a(e, e))), introduced(assumption)).
% 22.38/22.61 tff(397,plain,
% 22.38/22.61 (~mem(a(e, e), u(s(n(e)), s(s(n(e)))))),
% 22.38/22.61 inference(modus_ponens,[status(thm)],[396, 395])).
% 22.38/22.61 tff(398,assumption,(mem(a(e, e), u(s(n(e)), s(s(n(e)))))), introduced(assumption)).
% 22.38/22.61 tff(399,plain,
% 22.38/22.61 ($false),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[398, 397])).
% 22.38/22.62 tff(400,plain,((~mem(a(e, e), u(s(n(e)), s(s(n(e)))))) | mem(a(e, e), a(e, e)) | (~(a(e, e) = a(s(n(e)), s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.62 tff(401,plain,
% 22.38/22.62 (mem(a(e, e), a(e, e)) | (~(a(e, e) = a(s(n(e)), s(n(e)))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[400, 202])).
% 22.38/22.62 tff(402,plain,
% 22.38/22.62 (mem(a(e, e), a(e, e))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[401, 388])).
% 22.38/22.62 tff(403,plain,
% 22.38/22.62 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(a(e, e))) <=> (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = a(e, e)))),
% 22.38/22.62 inference(quant_inst,[status(thm)],[])).
% 22.38/22.62 tff(404,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(a(e, e))) <=> (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = a(e, e))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[403, 8])).
% 22.38/22.62 tff(405,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(a(e, e))) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e)))),
% 22.38/22.62 inference(monotonicity,[status(thm)],[78])).
% 22.38/22.62 tff(406,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(a(e, e)))),
% 22.38/22.62 inference(symmetry,[status(thm)],[405])).
% 22.38/22.62 tff(407,assumption,(~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))), introduced(assumption)).
% 22.38/22.62 tff(408,plain,
% 22.38/22.62 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))))),
% 22.38/22.62 inference(quant_inst,[status(thm)],[])).
% 22.38/22.62 tff(409,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e)))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[408, 32])).
% 22.38/22.62 tff(410,plain,
% 22.38/22.62 (a(a(e, e), a(e, e)) = a(n(e), n(e))),
% 22.38/22.62 inference(monotonicity,[status(thm)],[77, 77])).
% 22.38/22.62 tff(411,plain,
% 22.38/22.62 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(a(e, e), a(e, e)) = u(a(e, e), s(a(e, e))))),
% 22.38/22.62 inference(quant_inst,[status(thm)],[])).
% 22.38/22.62 tff(412,plain,
% 22.38/22.62 (a(a(e, e), a(e, e)) = u(a(e, e), s(a(e, e)))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[411, 46])).
% 22.38/22.62 tff(413,plain,
% 22.38/22.62 (u(a(e, e), s(a(e, e))) = a(a(e, e), a(e, e))),
% 22.38/22.62 inference(symmetry,[status(thm)],[412])).
% 22.38/22.62 tff(414,plain,
% 22.38/22.62 (s(n(e)) = s(a(e, e))),
% 22.38/22.62 inference(symmetry,[status(thm)],[78])).
% 22.38/22.62 tff(415,plain,
% 22.38/22.62 (u(a(e, e), s(n(e))) = u(a(e, e), s(a(e, e)))),
% 22.38/22.62 inference(monotonicity,[status(thm)],[414])).
% 22.38/22.62 tff(416,plain,
% 22.38/22.62 (u(a(e, e), s(n(e))) = a(n(e), n(e))),
% 22.38/22.62 inference(transitivity,[status(thm)],[415, 413, 410])).
% 22.38/22.62 tff(417,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(a(e, e), s(n(e)))) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))),
% 22.38/22.62 inference(monotonicity,[status(thm)],[416])).
% 22.38/22.62 tff(418,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e))) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(a(e, e), s(n(e))))),
% 22.38/22.62 inference(symmetry,[status(thm)],[417])).
% 22.38/22.62 tff(419,assumption,(~mem(a(e, e), s(u(n(e), n(s(n(e))))))), introduced(assumption)).
% 22.38/22.62 tff(420,plain,
% 22.38/22.62 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> mem(a(e, e), a(n(e), n(e)))),
% 22.38/22.62 inference(monotonicity,[status(thm)],[416])).
% 22.38/22.62 tff(421,plain,
% 22.38/22.62 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e))))))),
% 22.38/22.62 inference(rewrite,[status(thm)],[])).
% 22.38/22.62 tff(422,plain,
% 22.38/22.62 ((mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e)))) <=> (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))),
% 22.38/22.62 inference(rewrite,[status(thm)],[])).
% 22.38/22.62 tff(423,plain,
% 22.38/22.62 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e))))))),
% 22.38/22.62 inference(monotonicity,[status(thm)],[422])).
% 22.38/22.62 tff(424,plain,
% 22.38/22.62 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e))))))),
% 22.38/22.62 inference(transitivity,[status(thm)],[423, 421])).
% 22.38/22.62 tff(425,plain,
% 22.38/22.62 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))),
% 22.38/22.62 inference(quant_inst,[status(thm)],[])).
% 22.38/22.62 tff(426,plain,
% 22.38/22.62 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))),
% 22.38/22.62 inference(modus_ponens,[status(thm)],[425, 424])).
% 22.38/22.62 tff(427,plain,
% 22.38/22.62 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[426, 32])).
% 22.38/22.62 tff(428,plain,
% 22.38/22.62 ((mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))) | (~mem(a(e, e), s(n(e))))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(429,plain,
% 22.38/22.62 (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[428, 197])).
% 22.38/22.62 tff(430,plain,
% 22.38/22.62 ((~(mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))) | mem(a(e, e), u(a(e, e), s(n(e)))) | (~(mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(431,plain,
% 22.38/22.62 ((~(mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))) | mem(a(e, e), u(a(e, e), s(n(e))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[430, 429])).
% 22.38/22.62 tff(432,plain,
% 22.38/22.62 (mem(a(e, e), u(a(e, e), s(n(e))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[431, 427])).
% 22.38/22.62 tff(433,plain,
% 22.38/22.62 (mem(a(e, e), a(n(e), n(e)))),
% 22.38/22.62 inference(modus_ponens,[status(thm)],[432, 420])).
% 22.38/22.62 tff(434,assumption,(![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))), introduced(assumption)).
% 22.38/22.62 tff(435,plain,
% 22.38/22.62 (((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))) | ((~mem(a(e, e), a(n(e), n(e)))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))) <=> ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))) | (~mem(a(e, e), a(n(e), n(e)))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))),
% 22.38/22.62 inference(rewrite,[status(thm)],[])).
% 22.38/22.62 tff(436,plain,
% 22.38/22.62 ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))) | ((~mem(a(e, e), a(n(e), n(e)))) | mem(a(e, e), s(u(n(e), n(s(n(e)))))))),
% 22.38/22.62 inference(quant_inst,[status(thm)],[])).
% 22.38/22.62 tff(437,plain,
% 22.38/22.62 ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))) | (~mem(a(e, e), a(n(e), n(e)))) | mem(a(e, e), s(u(n(e), n(s(n(e))))))),
% 22.38/22.62 inference(modus_ponens,[status(thm)],[436, 435])).
% 22.38/22.62 tff(438,plain,
% 22.38/22.62 ($false),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[437, 434, 433, 419])).
% 22.38/22.62 tff(439,plain,((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))) | mem(a(e, e), s(u(n(e), n(s(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.62 tff(440,plain,
% 22.38/22.62 (~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[439, 233])).
% 22.38/22.62 tff(441,plain,
% 22.38/22.62 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e))))))))) | (~(subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e))))))))))))),
% 22.38/22.62 inference(quant_inst,[status(thm)],[])).
% 22.38/22.62 tff(442,plain,
% 22.38/22.62 (~((~((~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e))))))))) | (~(subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e)))))))))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[441, 324])).
% 22.38/22.62 tff(443,plain,
% 22.38/22.62 (((~((~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e))))))))) | (~(subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e))))))))))) | ((~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e))))))))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(444,plain,
% 22.38/22.62 ((~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[443, 442])).
% 22.38/22.62 tff(445,plain,
% 22.38/22.62 ((~((~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e))))))))) | (~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(446,plain,
% 22.38/22.62 ((~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e)))))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[445, 444])).
% 22.38/22.62 tff(447,plain,
% 22.38/22.62 (~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[446, 440])).
% 22.38/22.62 tff(448,plain,
% 22.38/22.62 (((~((~subq(a(n(e), n(e)), s(u(n(e), n(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, s(u(n(e), n(s(n(e))))))))) | (~(subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e))))))))))) | (subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e)))))))))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(449,plain,
% 22.38/22.62 (subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e))))))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[448, 442])).
% 22.38/22.62 tff(450,plain,
% 22.38/22.62 ((~(subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e)))))))))) | subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e))))))))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(451,plain,
% 22.38/22.62 (subq(a(n(e), n(e)), s(u(n(e), n(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e))))))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[450, 449])).
% 22.38/22.62 tff(452,plain,
% 22.38/22.62 (~((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e)))))))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[451, 447])).
% 22.38/22.62 tff(453,plain,
% 22.38/22.62 (((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(454,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(n(e), n(e)))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[453, 452])).
% 22.38/22.62 tff(455,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(a(e, e), s(n(e))))),
% 22.38/22.62 inference(modus_ponens,[status(thm)],[454, 418])).
% 22.38/22.62 tff(456,plain,
% 22.38/22.62 ((~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))))) | (~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(a(e, e), s(n(e))))) | (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e)))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(457,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[456, 455, 409])).
% 22.38/22.62 tff(458,plain,
% 22.38/22.62 ((~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e)))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(459,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[458, 457])).
% 22.38/22.62 tff(460,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e)))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[459, 407])).
% 22.38/22.62 tff(461,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(a(e, e)))),
% 22.38/22.62 inference(modus_ponens,[status(thm)],[460, 406])).
% 22.38/22.62 tff(462,plain,
% 22.38/22.62 ((~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(a(e, e))) <=> (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = a(e, e)))) | (~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(a(e, e)))) | (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = a(e, e))),
% 22.38/22.62 inference(tautology,[status(thm)],[])).
% 22.38/22.62 tff(463,plain,
% 22.38/22.62 (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = a(e, e)),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[462, 461, 404])).
% 22.38/22.62 tff(464,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e)) <=> mem(a(e, e), a(e, e))),
% 22.38/22.62 inference(monotonicity,[status(thm)],[463])).
% 22.38/22.62 tff(465,plain,
% 22.38/22.62 (mem(a(e, e), a(e, e)) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))),
% 22.38/22.62 inference(symmetry,[status(thm)],[464])).
% 22.38/22.62 tff(466,assumption,(mem(a(e, e), a(e, e))), introduced(assumption)).
% 22.38/22.62 tff(467,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))),
% 22.38/22.62 inference(modus_ponens,[status(thm)],[466, 465])).
% 22.38/22.62 tff(468,plain,
% 22.38/22.62 ($false),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[407, 467])).
% 22.38/22.62 tff(469,plain,(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e)) | (~mem(a(e, e), a(e, e)))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.62 tff(470,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))),
% 22.38/22.62 inference(unit_resolution,[status(thm)],[469, 402])).
% 22.38/22.62 tff(471,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e))) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))),
% 22.38/22.62 inference(monotonicity,[status(thm)],[49])).
% 22.38/22.62 tff(472,plain,
% 22.38/22.62 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e)) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e)))),
% 22.38/22.62 inference(symmetry,[status(thm)],[471])).
% 22.38/22.62 tff(473,assumption,(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))), introduced(assumption)).
% 22.38/22.63 tff(474,plain,
% 22.38/22.63 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e)))),
% 22.38/22.63 inference(modus_ponens,[status(thm)],[473, 472])).
% 22.38/22.63 tff(475,plain,
% 22.38/22.63 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e)))),
% 22.38/22.63 inference(quant_inst,[status(thm)],[])).
% 22.38/22.63 tff(476,plain,
% 22.38/22.63 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e))),
% 22.38/22.63 inference(unit_resolution,[status(thm)],[475, 32])).
% 22.38/22.63 tff(477,assumption,(~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e))), introduced(assumption)).
% 22.38/22.63 tff(478,assumption,(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e)), introduced(assumption)).
% 22.38/22.63 tff(479,plain,
% 22.38/22.63 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e))),
% 22.38/22.63 inference(quant_inst,[status(thm)],[])).
% 22.38/22.63 tff(480,plain,
% 22.38/22.63 ($false),
% 22.38/22.63 inference(unit_resolution,[status(thm)],[479, 19, 478])).
% 22.38/22.63 tff(481,plain,(~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e)), inference(lemma,lemma(discharge,[]))).
% 22.38/22.63 tff(482,plain,
% 22.38/22.63 ((~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e)),
% 22.38/22.63 inference(tautology,[status(thm)],[])).
% 22.38/22.63 tff(483,plain,
% 22.38/22.63 (~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e))),
% 22.38/22.63 inference(unit_resolution,[status(thm)],[482, 481, 477])).
% 22.38/22.63 tff(484,plain,
% 22.38/22.63 ((~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e)))) | (~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e)))) | (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e))),
% 22.38/22.63 inference(tautology,[status(thm)],[])).
% 22.38/22.63 tff(485,plain,
% 22.38/22.63 ((~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), e)))) | (~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e))))),
% 22.38/22.63 inference(unit_resolution,[status(thm)],[484, 483])).
% 22.38/22.63 tff(486,plain,
% 22.38/22.63 (~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), u(e, s(e)))),
% 22.38/22.63 inference(unit_resolution,[status(thm)],[485, 476])).
% 22.38/22.63 tff(487,plain,
% 22.38/22.63 ($false),
% 22.38/22.63 inference(unit_resolution,[status(thm)],[486, 474])).
% 22.38/22.63 tff(488,plain,((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))) | mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e))), inference(lemma,lemma(discharge,[]))).
% 22.38/22.63 tff(489,plain,
% 22.38/22.63 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e))),
% 22.38/22.63 inference(unit_resolution,[status(thm)],[488, 470])).
% 22.38/22.63 tff(490,assumption,(~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) <=> (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = e))), introduced(assumption)).
% 22.38/22.63 tff(491,plain,
% 22.38/22.63 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) <=> (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = e))),
% 22.38/22.63 inference(quant_inst,[status(thm)],[])).
% 22.38/22.63 tff(492,plain,
% 22.38/22.63 ($false),
% 22.38/22.63 inference(unit_resolution,[status(thm)],[491, 8, 490])).
% 22.38/22.63 tff(493,plain,(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) <=> (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = e)), inference(lemma,lemma(discharge,[]))).
% 22.38/22.63 tff(494,plain,
% 22.38/22.63 ((~(mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e)) <=> (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = e))) | (~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e))) | (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = e)),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(495,plain,
% 22.48/22.63 ((~mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(e))) | (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = e)),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[494, 493])).
% 22.48/22.63 tff(496,plain,
% 22.48/22.63 (tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))) = e),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[495, 489])).
% 22.48/22.63 tff(497,plain,
% 22.48/22.63 (e = tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e)))),
% 22.48/22.63 inference(symmetry,[status(thm)],[496])).
% 22.48/22.63 tff(498,plain,
% 22.48/22.63 (mem(e, s(a(e, e))) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e)))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[497, 78])).
% 22.48/22.63 tff(499,plain,
% 22.48/22.63 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e))) <=> mem(e, s(a(e, e)))),
% 22.48/22.63 inference(symmetry,[status(thm)],[498])).
% 22.48/22.63 tff(500,plain,
% 22.48/22.63 (mem(e, s(n(e))) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e)))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[497])).
% 22.48/22.63 tff(501,plain,
% 22.48/22.63 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(n(e))) | mem(e, s(s(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(n(e))) | mem(e, s(s(n(e)))))))),
% 22.48/22.63 inference(rewrite,[status(thm)],[])).
% 22.48/22.63 tff(502,plain,
% 22.48/22.63 ((mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e))))) <=> (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(n(e))) | mem(e, s(s(n(e))))))),
% 22.48/22.63 inference(rewrite,[status(thm)],[])).
% 22.48/22.63 tff(503,plain,
% 22.48/22.63 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(n(e))) | mem(e, s(s(n(e)))))))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[502])).
% 22.48/22.63 tff(504,plain,
% 22.48/22.63 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(n(e))) | mem(e, s(s(n(e)))))))),
% 22.48/22.63 inference(transitivity,[status(thm)],[503, 501])).
% 22.48/22.63 tff(505,plain,
% 22.48/22.63 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e)))))),
% 22.48/22.63 inference(quant_inst,[status(thm)],[])).
% 22.48/22.63 tff(506,plain,
% 22.48/22.63 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(n(e))) | mem(e, s(s(n(e))))))),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[505, 504])).
% 22.48/22.63 tff(507,plain,
% 22.48/22.63 (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(n(e))) | mem(e, s(s(n(e)))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[506, 32])).
% 22.48/22.63 tff(508,plain,
% 22.48/22.63 (a(s(n(e)), s(n(e))) = a(e, e)),
% 22.48/22.63 inference(symmetry,[status(thm)],[388])).
% 22.48/22.63 tff(509,plain,
% 22.48/22.63 (u(s(n(e)), s(s(n(e)))) = a(e, e)),
% 22.48/22.63 inference(transitivity,[status(thm)],[391, 508])).
% 22.48/22.63 tff(510,plain,
% 22.48/22.63 (mem(e, u(s(n(e)), s(s(n(e))))) <=> mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[497, 509])).
% 22.48/22.63 tff(511,plain,
% 22.48/22.63 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), a(e, e)) <=> mem(e, u(s(n(e)), s(s(n(e)))))),
% 22.48/22.63 inference(symmetry,[status(thm)],[510])).
% 22.48/22.63 tff(512,plain,
% 22.48/22.63 (mem(e, u(s(n(e)), s(s(n(e)))))),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[470, 511])).
% 22.48/22.63 tff(513,plain,
% 22.48/22.63 ((~(mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(n(e))) | mem(e, s(s(n(e))))))) | (~mem(e, u(s(n(e)), s(s(n(e)))))) | (mem(e, s(n(e))) | mem(e, s(s(n(e)))))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(514,plain,
% 22.48/22.63 (mem(e, s(n(e))) | mem(e, s(s(n(e))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[513, 512, 507])).
% 22.48/22.63 tff(515,assumption,(~(mem(e, s(s(n(e)))) <=> (e = s(n(e))))), introduced(assumption)).
% 22.48/22.63 tff(516,plain,
% 22.48/22.63 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(s(n(e)))) <=> (e = s(n(e))))),
% 22.48/22.63 inference(quant_inst,[status(thm)],[])).
% 22.48/22.63 tff(517,plain,
% 22.48/22.63 ($false),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[516, 8, 515])).
% 22.48/22.63 tff(518,plain,(mem(e, s(s(n(e)))) <=> (e = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 22.48/22.63 tff(519,assumption,(e = s(n(e))), introduced(assumption)).
% 22.48/22.63 tff(520,plain,
% 22.48/22.63 (mem(a(e, e), e) <=> mem(a(e, e), s(n(e)))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[519])).
% 22.48/22.63 tff(521,plain,
% 22.48/22.63 (mem(a(e, e), s(n(e))) <=> mem(a(e, e), e)),
% 22.48/22.63 inference(symmetry,[status(thm)],[520])).
% 22.48/22.63 tff(522,plain,
% 22.48/22.63 (mem(a(e, e), e)),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[197, 521])).
% 22.48/22.63 tff(523,plain,
% 22.48/22.63 ($false),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[166, 522])).
% 22.48/22.63 tff(524,plain,(~(e = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 22.48/22.63 tff(525,plain,
% 22.48/22.63 ((~(mem(e, s(s(n(e)))) <=> (e = s(n(e))))) | (~mem(e, s(s(n(e))))) | (e = s(n(e)))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(526,plain,
% 22.48/22.63 ((~(mem(e, s(s(n(e)))) <=> (e = s(n(e))))) | (~mem(e, s(s(n(e)))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[525, 524])).
% 22.48/22.63 tff(527,plain,
% 22.48/22.63 (~mem(e, s(s(n(e))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[526, 518])).
% 22.48/22.63 tff(528,plain,
% 22.48/22.63 ((~(mem(e, s(n(e))) | mem(e, s(s(n(e)))))) | mem(e, s(n(e))) | mem(e, s(s(n(e))))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(529,plain,
% 22.48/22.63 ((~(mem(e, s(n(e))) | mem(e, s(s(n(e)))))) | mem(e, s(n(e)))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[528, 527])).
% 22.48/22.63 tff(530,plain,
% 22.48/22.63 (mem(e, s(n(e)))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[529, 514])).
% 22.48/22.63 tff(531,plain,
% 22.48/22.63 (mem(tptp_fun_Z_0(s(u(n(e), n(s(n(e))))), a(n(e), n(e))), s(n(e)))),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[530, 500])).
% 22.48/22.63 tff(532,plain,
% 22.48/22.63 (mem(e, s(a(e, e)))),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[531, 499])).
% 22.48/22.63 tff(533,plain,
% 22.48/22.63 ((~(mem(e, s(a(e, e))) <=> (e = a(e, e)))) | (~mem(e, s(a(e, e)))) | (e = a(e, e))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(534,plain,
% 22.48/22.63 (e = a(e, e)),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[533, 532, 74])).
% 22.48/22.63 tff(535,plain,
% 22.48/22.63 (a(e, e) = e),
% 22.48/22.63 inference(symmetry,[status(thm)],[534])).
% 22.48/22.63 tff(536,plain,
% 22.48/22.63 (n(e) = e),
% 22.48/22.63 inference(transitivity,[status(thm)],[76, 535])).
% 22.48/22.63 tff(537,plain,
% 22.48/22.63 (n(n(e)) = n(e)),
% 22.48/22.63 inference(monotonicity,[status(thm)],[536])).
% 22.48/22.63 tff(538,plain,
% 22.48/22.63 (n(e) = n(n(e))),
% 22.48/22.63 inference(symmetry,[status(thm)],[537])).
% 22.48/22.63 tff(539,plain,
% 22.48/22.63 (a(e, e) = a(n(e), n(e))),
% 22.48/22.63 inference(transitivity,[status(thm)],[77, 538, 60])).
% 22.48/22.63 tff(540,plain,
% 22.48/22.63 ($false),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[96, 539])).
% 22.48/22.63 tff(541,plain,((a(e, e) = u(n(e), s(n(n(e))))) | mem(a(e, e), s(n(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.48/22.63 tff(542,plain,
% 22.48/22.63 (mem(a(e, e), s(n(n(n(e)))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[541, 72])).
% 22.48/22.63 tff(543,plain,
% 22.48/22.63 (a(n(n(e)), n(n(e))) = n(n(n(e)))),
% 22.48/22.63 inference(symmetry,[status(thm)],[88])).
% 22.48/22.63 tff(544,plain,
% 22.48/22.63 (s(a(n(n(e)), n(n(e)))) = s(n(n(n(e))))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[543])).
% 22.48/22.63 tff(545,plain,
% 22.48/22.63 (mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> mem(a(e, e), s(n(n(n(e)))))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[544])).
% 22.48/22.63 tff(546,plain,
% 22.48/22.63 (mem(a(e, e), s(n(n(n(e))))) <=> mem(a(e, e), s(a(n(n(e)), n(n(e)))))),
% 22.48/22.63 inference(symmetry,[status(thm)],[545])).
% 22.48/22.63 tff(547,assumption,(mem(a(e, e), s(n(n(n(e)))))), introduced(assumption)).
% 22.48/22.63 tff(548,plain,
% 22.48/22.63 (mem(a(e, e), s(a(n(n(e)), n(n(e)))))),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[547, 546])).
% 22.48/22.63 tff(549,plain,
% 22.48/22.63 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> (a(e, e) = a(n(n(e)), n(n(e)))))),
% 22.48/22.63 inference(quant_inst,[status(thm)],[])).
% 22.48/22.63 tff(550,plain,
% 22.48/22.63 (mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> (a(e, e) = a(n(n(e)), n(n(e))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[549, 8])).
% 22.48/22.63 tff(551,assumption,(~(a(e, e) = a(n(n(e)), n(n(e))))), introduced(assumption)).
% 22.48/22.63 tff(552,plain,
% 22.48/22.63 ((~(mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> (a(e, e) = a(n(n(e)), n(n(e)))))) | (~mem(a(e, e), s(a(n(n(e)), n(n(e)))))) | (a(e, e) = a(n(n(e)), n(n(e))))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(553,plain,
% 22.48/22.63 ((~(mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> (a(e, e) = a(n(n(e)), n(n(e)))))) | (~mem(a(e, e), s(a(n(n(e)), n(n(e))))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[552, 551])).
% 22.48/22.63 tff(554,plain,
% 22.48/22.63 (~mem(a(e, e), s(a(n(n(e)), n(n(e)))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[553, 550])).
% 22.48/22.63 tff(555,plain,
% 22.48/22.63 ($false),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[554, 548])).
% 22.48/22.63 tff(556,plain,((~mem(a(e, e), s(n(n(n(e)))))) | (a(e, e) = a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 22.48/22.63 tff(557,plain,
% 22.48/22.63 (a(e, e) = a(n(n(e)), n(n(e)))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[556, 542])).
% 22.48/22.63 tff(558,assumption,(a(e, e) = a(n(n(e)), n(n(e)))), introduced(assumption)).
% 22.48/22.63 tff(559,plain,
% 22.48/22.63 (a(n(n(e)), n(n(e))) = a(e, e)),
% 22.48/22.63 inference(symmetry,[status(thm)],[558])).
% 22.48/22.63 tff(560,plain,
% 22.48/22.63 (a(a(n(e), n(e)), a(n(e), n(e))) = a(n(n(e)), n(n(e)))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[82, 82])).
% 22.48/22.63 tff(561,plain,
% 22.48/22.63 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(a(n(e), n(e)), a(n(e), n(e))) = u(a(n(e), n(e)), s(a(n(e), n(e)))))),
% 22.48/22.63 inference(quant_inst,[status(thm)],[])).
% 22.48/22.63 tff(562,plain,
% 22.48/22.63 (a(a(n(e), n(e)), a(n(e), n(e))) = u(a(n(e), n(e)), s(a(n(e), n(e))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[561, 46])).
% 22.48/22.63 tff(563,plain,
% 22.48/22.63 (u(a(n(e), n(e)), s(a(n(e), n(e)))) = a(a(n(e), n(e)), a(n(e), n(e)))),
% 22.48/22.63 inference(symmetry,[status(thm)],[562])).
% 22.48/22.63 tff(564,plain,
% 22.48/22.63 (s(n(n(e))) = s(a(n(e), n(e)))),
% 22.48/22.63 inference(symmetry,[status(thm)],[97])).
% 22.48/22.63 tff(565,plain,
% 22.48/22.63 (u(a(n(e), n(e)), s(n(n(e)))) = u(a(n(e), n(e)), s(a(n(e), n(e))))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[564])).
% 22.48/22.63 tff(566,plain,
% 22.48/22.63 (u(a(n(e), n(e)), s(n(n(e)))) = a(e, e)),
% 22.48/22.63 inference(transitivity,[status(thm)],[565, 563, 560, 559])).
% 22.48/22.63 tff(567,plain,
% 22.48/22.63 (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> mem(a(e, e), a(e, e))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[566])).
% 22.48/22.63 tff(568,plain,
% 22.48/22.63 (mem(a(e, e), a(e, e)) <=> mem(a(e, e), u(a(n(e), n(e)), s(n(n(e)))))),
% 22.48/22.63 inference(symmetry,[status(thm)],[567])).
% 22.48/22.63 tff(569,plain,
% 22.48/22.63 ((~mem(a(e, e), a(e, e))) <=> (~mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[568])).
% 22.48/22.63 tff(570,plain,
% 22.48/22.63 (~mem(a(e, e), u(a(n(e), n(e)), s(n(n(e)))))),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[396, 569])).
% 22.48/22.63 tff(571,plain,
% 22.48/22.63 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e)))))))),
% 22.48/22.63 inference(rewrite,[status(thm)],[])).
% 22.48/22.63 tff(572,plain,
% 22.48/22.63 ((mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(n(e)))) | mem(a(e, e), a(n(e), n(e))))) <=> (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e))))))),
% 22.48/22.63 inference(rewrite,[status(thm)],[])).
% 22.48/22.63 tff(573,plain,
% 22.48/22.63 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(n(e)))) | mem(a(e, e), a(n(e), n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e)))))))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[572])).
% 22.48/22.63 tff(574,plain,
% 22.48/22.63 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(n(e)))) | mem(a(e, e), a(n(e), n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e)))))))),
% 22.48/22.63 inference(transitivity,[status(thm)],[573, 571])).
% 22.48/22.63 tff(575,plain,
% 22.48/22.63 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), s(n(n(e)))) | mem(a(e, e), a(n(e), n(e)))))),
% 22.48/22.63 inference(quant_inst,[status(thm)],[])).
% 22.48/22.63 tff(576,plain,
% 22.48/22.63 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e))))))),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[575, 574])).
% 22.48/22.63 tff(577,plain,
% 22.48/22.63 (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e)))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[576, 32])).
% 22.48/22.63 tff(578,plain,
% 22.48/22.63 ((mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e))))) | (~mem(a(e, e), a(n(e), n(e))))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(579,plain,
% 22.48/22.63 (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[578, 433])).
% 22.48/22.63 tff(580,plain,
% 22.48/22.63 ((~(mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e))))))) | mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) | (~(mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e))))))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(581,plain,
% 22.48/22.63 ((~(mem(a(e, e), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(e, e), a(n(e), n(e))) | mem(a(e, e), s(n(n(e))))))) | mem(a(e, e), u(a(n(e), n(e)), s(n(n(e)))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[580, 579])).
% 22.48/22.63 tff(582,plain,
% 22.48/22.63 (mem(a(e, e), u(a(n(e), n(e)), s(n(n(e)))))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[581, 577])).
% 22.48/22.63 tff(583,plain,
% 22.48/22.63 ($false),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[582, 570])).
% 22.48/22.63 tff(584,plain,(mem(a(e, e), a(e, e)) | (~(a(e, e) = a(n(n(e)), n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 22.48/22.63 tff(585,plain,
% 22.48/22.63 (mem(a(e, e), a(e, e))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[584, 557])).
% 22.48/22.63 tff(586,plain,
% 22.48/22.63 (mem(a(e, e), u(e, s(e)))),
% 22.48/22.63 inference(modus_ponens,[status(thm)],[585, 71])).
% 22.48/22.63 tff(587,plain,
% 22.48/22.63 ((~(mem(a(e, e), u(e, s(e))) <=> (mem(a(e, e), e) | mem(a(e, e), s(e))))) | (~mem(a(e, e), u(e, s(e)))) | (mem(a(e, e), e) | mem(a(e, e), s(e)))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(588,plain,
% 22.48/22.63 (mem(a(e, e), e) | mem(a(e, e), s(e))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[587, 586, 69])).
% 22.48/22.63 tff(589,plain,
% 22.48/22.63 ((~(mem(a(e, e), e) | mem(a(e, e), s(e)))) | mem(a(e, e), e) | mem(a(e, e), s(e))),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(590,plain,
% 22.48/22.63 ((~(mem(a(e, e), e) | mem(a(e, e), s(e)))) | mem(a(e, e), s(e))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[589, 166])).
% 22.48/22.63 tff(591,plain,
% 22.48/22.63 (mem(a(e, e), s(e))),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[590, 588])).
% 22.48/22.63 tff(592,plain,
% 22.48/22.63 ((~(mem(a(e, e), s(e)) <=> (a(e, e) = e))) | (~mem(a(e, e), s(e))) | (a(e, e) = e)),
% 22.48/22.63 inference(tautology,[status(thm)],[])).
% 22.48/22.63 tff(593,plain,
% 22.48/22.63 ((~(mem(a(e, e), s(e)) <=> (a(e, e) = e))) | (a(e, e) = e)),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[592, 591])).
% 22.48/22.63 tff(594,plain,
% 22.48/22.63 (a(e, e) = e),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[593, 62])).
% 22.48/22.63 tff(595,plain,
% 22.48/22.63 (n(e) = e),
% 22.48/22.63 inference(transitivity,[status(thm)],[76, 594])).
% 22.48/22.63 tff(596,plain,
% 22.48/22.63 (n(n(e)) = n(e)),
% 22.48/22.63 inference(monotonicity,[status(thm)],[595])).
% 22.48/22.63 tff(597,plain,
% 22.48/22.63 (n(e) = n(n(e))),
% 22.48/22.63 inference(symmetry,[status(thm)],[596])).
% 22.48/22.63 tff(598,plain,
% 22.48/22.63 (a(e, e) = a(n(e), n(e))),
% 22.48/22.63 inference(transitivity,[status(thm)],[77, 597, 60])).
% 22.48/22.63 tff(599,plain,
% 22.48/22.63 ($false),
% 22.48/22.63 inference(unit_resolution,[status(thm)],[96, 598])).
% 22.48/22.63 tff(600,plain,(a(e, e) = u(n(e), s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 22.48/22.63 tff(601,plain,
% 22.48/22.63 (u(n(e), s(n(n(e)))) = a(e, e)),
% 22.48/22.63 inference(symmetry,[status(thm)],[600])).
% 22.48/22.63 tff(602,plain,
% 22.48/22.63 (u(a(e, e), s(n(n(e)))) = u(n(e), s(n(n(e))))),
% 22.48/22.63 inference(monotonicity,[status(thm)],[77])).
% 22.48/22.63 tff(603,plain,
% 22.48/22.63 (u(a(e, e), s(n(n(e)))) = a(e, e)),
% 22.48/22.63 inference(transitivity,[status(thm)],[602, 601])).
% 22.48/22.64 tff(604,plain,
% 22.48/22.64 (mem(a(n(e), n(e)), u(a(e, e), s(n(n(e))))) <=> mem(a(n(e), n(e)), a(e, e))),
% 22.48/22.64 inference(monotonicity,[status(thm)],[603])).
% 22.48/22.64 tff(605,plain,
% 22.48/22.64 (mem(a(n(e), n(e)), a(e, e)) <=> mem(a(n(e), n(e)), u(a(e, e), s(n(n(e)))))),
% 22.48/22.64 inference(symmetry,[status(thm)],[604])).
% 22.48/22.64 tff(606,plain,
% 22.48/22.64 ((~mem(a(n(e), n(e)), a(e, e))) <=> (~mem(a(n(e), n(e)), u(a(e, e), s(n(n(e))))))),
% 22.48/22.64 inference(monotonicity,[status(thm)],[605])).
% 22.48/22.64 tff(607,assumption,(~mem(a(n(e), n(e)), a(e, e))), introduced(assumption)).
% 22.48/22.64 tff(608,plain,
% 22.48/22.64 (~mem(a(n(e), n(e)), u(a(e, e), s(n(n(e)))))),
% 22.48/22.64 inference(modus_ponens,[status(thm)],[607, 606])).
% 22.48/22.64 tff(609,plain,
% 22.48/22.64 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(e, e), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(e, e))))),
% 22.48/22.64 inference(quant_inst,[status(thm)],[])).
% 22.48/22.64 tff(610,plain,
% 22.48/22.64 (mem(a(n(e), n(e)), u(a(e, e), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(e, e)))),
% 22.48/22.64 inference(unit_resolution,[status(thm)],[609, 32])).
% 22.48/22.64 tff(611,plain,
% 22.48/22.64 (mem(a(n(e), n(e)), s(n(n(e)))) <=> mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 22.48/22.64 inference(monotonicity,[status(thm)],[564])).
% 22.48/22.64 tff(612,plain,
% 22.48/22.64 (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> mem(a(n(e), n(e)), s(n(n(e))))),
% 22.48/22.64 inference(symmetry,[status(thm)],[611])).
% 22.48/22.64 tff(613,plain,
% 22.48/22.64 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e))))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e)))))),
% 22.48/22.64 inference(rewrite,[status(thm)],[])).
% 22.48/22.64 tff(614,plain,
% 22.48/22.64 ((mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> $true) <=> mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 22.48/22.64 inference(rewrite,[status(thm)],[])).
% 22.48/22.64 tff(615,plain,
% 22.48/22.64 ((a(n(e), n(e)) = a(n(e), n(e))) <=> $true),
% 22.48/22.64 inference(rewrite,[status(thm)],[])).
% 22.48/22.64 tff(616,plain,
% 22.48/22.64 ((mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> (a(n(e), n(e)) = a(n(e), n(e)))) <=> (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> $true)),
% 22.48/22.64 inference(monotonicity,[status(thm)],[615])).
% 22.48/22.64 tff(617,plain,
% 22.48/22.64 ((mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> (a(n(e), n(e)) = a(n(e), n(e)))) <=> mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 22.48/22.64 inference(transitivity,[status(thm)],[616, 614])).
% 22.48/22.64 tff(618,plain,
% 22.48/22.64 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> (a(n(e), n(e)) = a(n(e), n(e))))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e)))))),
% 22.48/22.64 inference(monotonicity,[status(thm)],[617])).
% 22.48/22.64 tff(619,plain,
% 22.48/22.64 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> (a(n(e), n(e)) = a(n(e), n(e))))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e)))))),
% 22.48/22.64 inference(transitivity,[status(thm)],[618, 613])).
% 22.48/22.64 tff(620,plain,
% 22.48/22.64 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> (a(n(e), n(e)) = a(n(e), n(e))))),
% 22.48/22.64 inference(quant_inst,[status(thm)],[])).
% 22.48/22.64 tff(621,plain,
% 22.48/22.64 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 22.48/22.64 inference(modus_ponens,[status(thm)],[620, 619])).
% 22.48/22.64 tff(622,plain,
% 22.48/22.64 (mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 22.48/22.64 inference(unit_resolution,[status(thm)],[621, 8])).
% 22.48/22.64 tff(623,plain,
% 22.48/22.64 (mem(a(n(e), n(e)), s(n(n(e))))),
% 22.48/22.64 inference(modus_ponens,[status(thm)],[622, 612])).
% 22.48/22.64 tff(624,assumption,(~mem(a(n(e), n(e)), s(n(n(e))))), introduced(assumption)).
% 22.48/22.64 tff(625,plain,
% 22.48/22.64 ($false),
% 22.48/22.64 inference(unit_resolution,[status(thm)],[624, 623])).
% 22.48/22.64 tff(626,plain,(mem(a(n(e), n(e)), s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 22.48/22.64 tff(627,plain,
% 22.48/22.64 ((mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(e, e))) | (~mem(a(n(e), n(e)), s(n(n(e)))))),
% 22.48/22.64 inference(tautology,[status(thm)],[])).
% 22.48/22.64 tff(628,plain,
% 22.48/22.64 (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(e, e))),
% 22.48/22.64 inference(unit_resolution,[status(thm)],[627, 626])).
% 22.48/22.64 tff(629,plain,
% 22.48/22.64 ((~(mem(a(n(e), n(e)), u(a(e, e), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(e, e))))) | mem(a(n(e), n(e)), u(a(e, e), s(n(n(e))))) | (~(mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(e, e))))),
% 22.48/22.65 inference(tautology,[status(thm)],[])).
% 22.48/22.65 tff(630,plain,
% 22.48/22.65 ((~(mem(a(n(e), n(e)), u(a(e, e), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(e, e))))) | mem(a(n(e), n(e)), u(a(e, e), s(n(n(e)))))),
% 22.48/22.65 inference(unit_resolution,[status(thm)],[629, 628])).
% 22.48/22.65 tff(631,plain,
% 22.48/22.65 (mem(a(n(e), n(e)), u(a(e, e), s(n(n(e)))))),
% 22.48/22.65 inference(unit_resolution,[status(thm)],[630, 610])).
% 22.48/22.65 tff(632,plain,
% 22.48/22.65 ($false),
% 22.48/22.65 inference(unit_resolution,[status(thm)],[631, 608])).
% 22.48/22.65 tff(633,plain,(mem(a(n(e), n(e)), a(e, e))), inference(lemma,lemma(discharge,[]))).
% 22.48/22.65 tff(634,plain,
% 22.48/22.65 (mem(a(n(e), n(e)), u(e, s(e)))),
% 22.48/22.65 inference(modus_ponens,[status(thm)],[633, 51])).
% 22.48/22.65 tff(635,plain,
% 22.48/22.65 ((~(mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))) | (~mem(a(n(e), n(e)), u(e, s(e)))) | (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))),
% 22.48/22.65 inference(tautology,[status(thm)],[])).
% 22.48/22.65 tff(636,plain,
% 22.48/22.65 (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))),
% 22.48/22.65 inference(unit_resolution,[status(thm)],[635, 634, 39])).
% 22.48/22.65 tff(637,plain,
% 22.48/22.65 ((~(mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))) | mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))),
% 22.48/22.65 inference(tautology,[status(thm)],[])).
% 22.48/22.65 tff(638,plain,
% 22.48/22.65 (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))),
% 22.48/22.65 inference(unit_resolution,[status(thm)],[637, 636])).
% 22.48/22.65 tff(639,plain,
% 22.48/22.65 (mem(a(n(e), n(e)), s(e))),
% 22.48/22.65 inference(unit_resolution,[status(thm)],[638, 22])).
% 22.48/22.65 tff(640,plain,
% 22.48/22.65 ((~(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))) | (~mem(a(n(e), n(e)), s(e))) | (a(n(e), n(e)) = e)),
% 22.48/22.65 inference(tautology,[status(thm)],[])).
% 22.48/22.65 tff(641,plain,
% 22.48/22.65 (a(n(e), n(e)) = e),
% 22.48/22.65 inference(unit_resolution,[status(thm)],[640, 639, 11])).
% 22.48/22.65 tff(642,plain,
% 22.48/22.65 (e = a(n(e), n(e))),
% 22.48/22.65 inference(symmetry,[status(thm)],[641])).
% 22.48/22.65 tff(643,plain,
% 22.48/22.65 (mem(a(e, e), e) <=> mem(a(e, e), a(n(e), n(e)))),
% 22.48/22.65 inference(monotonicity,[status(thm)],[642])).
% 22.48/22.65 tff(644,plain,
% 22.48/22.65 (mem(a(e, e), a(n(e), n(e))) <=> mem(a(e, e), e)),
% 22.48/22.65 inference(symmetry,[status(thm)],[643])).
% 22.48/22.65 tff(645,plain,
% 22.48/22.65 (mem(a(e, e), e)),
% 22.48/22.65 inference(modus_ponens,[status(thm)],[433, 644])).
% 22.48/22.65 tff(646,plain,
% 22.48/22.65 ($false),
% 22.48/22.65 inference(unit_resolution,[status(thm)],[166, 645])).
% 22.48/22.65 % SZS output end Proof
% 22.48/22.65 % E exiting
%------------------------------------------------------------------------------