%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV565+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 63.81s 64.04s
% Output : Proof 64.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV565+1 : TPTP v9.1.0. Released v9.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 07:41:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 63.81/64.04 % SZS status Theorem
% 63.81/64.04 % SZS output start Proof
% 63.81/64.04 tff(a_type, type, (
% 63.81/64.04 a: ( $i * $i ) > $i)).
% 63.81/64.04 tff(e_type, type, (
% 63.81/64.04 e: $i)).
% 63.81/64.04 tff(s_type, type, (
% 63.81/64.04 s: $i > $i)).
% 63.81/64.04 tff(n_type, type, (
% 63.81/64.04 n: $i > $i)).
% 63.81/64.04 tff(mem_type, type, (
% 63.81/64.04 mem: ( $i * $i ) > $o)).
% 63.81/64.04 tff(u_type, type, (
% 63.81/64.04 u: ( $i * $i ) > $i)).
% 63.81/64.04 tff(tptp_fun_Z_0_type, type, (
% 63.81/64.04 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 63.81/64.04 tff(subq_type, type, (
% 63.81/64.04 subq: ( $i * $i ) > $o)).
% 63.81/64.04 tff(m_type, type, (
% 63.81/64.04 m: ( $i * $i ) > $i)).
% 63.81/64.04 tff(p_type, type, (
% 63.81/64.04 p: $i > $i)).
% 63.81/64.04 tff(disj_type, type, (
% 63.81/64.04 disj: ( $i * $i ) > $o)).
% 63.81/64.04 tff(tptp_fun_Z_1_type, type, (
% 63.81/64.04 tptp_fun_Z_1: ( $i * $i ) > $i)).
% 63.81/64.04 tff(1,plain,
% 63.81/64.04 (^[X: $i, Y: $i] : refl((mem(X, s(Y)) <=> (X = Y)) <=> (mem(X, s(Y)) <=> (X = Y)))),
% 63.81/64.04 inference(bind,[status(th)],[])).
% 63.81/64.04 tff(2,plain,
% 63.81/64.04 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 63.81/64.04 inference(quant_intro,[status(thm)],[1])).
% 63.81/64.04 tff(3,plain,
% 63.81/64.04 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 63.81/64.04 inference(rewrite,[status(thm)],[])).
% 63.81/64.04 tff(4,axiom,(![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','s_ax')).
% 63.81/64.04 tff(5,plain,
% 63.81/64.04 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[4, 3])).
% 63.81/64.04 tff(6,plain,(
% 63.81/64.04 ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 63.81/64.04 inference(skolemize,[status(sab)],[5])).
% 63.81/64.04 tff(7,plain,
% 63.81/64.04 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[6, 2])).
% 63.81/64.04 tff(8,plain,
% 63.81/64.04 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(s(n(e)), s(n(e))), s(a(e, e))) <=> (a(s(n(e)), s(n(e))) = a(e, e)))),
% 63.81/64.04 inference(quant_inst,[status(thm)],[])).
% 63.81/64.04 tff(9,plain,
% 63.81/64.04 (mem(a(s(n(e)), s(n(e))), s(a(e, e))) <=> (a(s(n(e)), s(n(e))) = a(e, e))),
% 63.81/64.04 inference(unit_resolution,[status(thm)],[8, 7])).
% 63.81/64.04 tff(10,plain,
% 63.81/64.04 (^[X: $i] : refl((n(X) = a(X, X)) <=> (n(X) = a(X, X)))),
% 63.81/64.04 inference(bind,[status(th)],[])).
% 63.81/64.04 tff(11,plain,
% 63.81/64.04 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 63.81/64.04 inference(quant_intro,[status(thm)],[10])).
% 63.81/64.04 tff(12,plain,
% 63.81/64.04 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 63.81/64.04 inference(rewrite,[status(thm)],[])).
% 63.81/64.04 tff(13,axiom,(![X: $i] : (n(X) = a(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','n_def')).
% 63.81/64.04 tff(14,plain,
% 63.81/64.04 (![X: $i] : (n(X) = a(X, X))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[13, 12])).
% 63.81/64.04 tff(15,plain,(
% 63.81/64.04 ![X: $i] : (n(X) = a(X, X))),
% 63.81/64.04 inference(skolemize,[status(sab)],[14])).
% 63.81/64.04 tff(16,plain,
% 63.81/64.04 (![X: $i] : (n(X) = a(X, X))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[15, 11])).
% 63.81/64.04 tff(17,plain,
% 63.81/64.04 ((~![X: $i] : (n(X) = a(X, X))) | (n(s(n(e))) = a(s(n(e)), s(n(e))))),
% 63.81/64.04 inference(quant_inst,[status(thm)],[])).
% 63.81/64.04 tff(18,plain,
% 63.81/64.04 (n(s(n(e))) = a(s(n(e)), s(n(e)))),
% 63.81/64.04 inference(unit_resolution,[status(thm)],[17, 16])).
% 63.81/64.04 tff(19,plain,
% 63.81/64.04 (a(s(n(e)), s(n(e))) = n(s(n(e)))),
% 63.81/64.04 inference(symmetry,[status(thm)],[18])).
% 63.81/64.04 tff(20,plain,
% 63.81/64.04 (s(a(s(n(e)), s(n(e)))) = s(n(s(n(e))))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[19])).
% 63.81/64.04 tff(21,plain,
% 63.81/64.04 (mem(s(n(e)), s(a(s(n(e)), s(n(e))))) <=> mem(s(n(e)), s(n(s(n(e)))))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[20])).
% 63.81/64.04 tff(22,plain,
% 63.81/64.04 (mem(s(n(e)), s(n(s(n(e))))) <=> mem(s(n(e)), s(a(s(n(e)), s(n(e)))))),
% 63.81/64.04 inference(symmetry,[status(thm)],[21])).
% 63.81/64.04 tff(23,assumption,(~(mem(s(n(e)), s(a(n(e), n(e)))) <=> (s(n(e)) = a(n(e), n(e))))), introduced(assumption)).
% 63.81/64.04 tff(24,plain,
% 63.81/64.04 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(s(n(e)), s(a(n(e), n(e)))) <=> (s(n(e)) = a(n(e), n(e))))),
% 63.81/64.04 inference(quant_inst,[status(thm)],[])).
% 63.81/64.04 tff(25,plain,
% 63.81/64.04 ($false),
% 63.81/64.04 inference(unit_resolution,[status(thm)],[24, 7, 23])).
% 63.81/64.04 tff(26,plain,(mem(s(n(e)), s(a(n(e), n(e)))) <=> (s(n(e)) = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.04 tff(27,assumption,(mem(s(n(e)), s(a(n(e), n(e)))) <=> (s(n(e)) = a(n(e), n(e)))), introduced(assumption)).
% 63.81/64.04 tff(28,plain,
% 63.81/64.04 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(e)) = a(n(e), n(e)))),
% 63.81/64.04 inference(quant_inst,[status(thm)],[])).
% 63.81/64.04 tff(29,plain,
% 63.81/64.04 (n(n(e)) = a(n(e), n(e))),
% 63.81/64.04 inference(unit_resolution,[status(thm)],[28, 16])).
% 63.81/64.04 tff(30,plain,
% 63.81/64.04 (a(n(e), n(e)) = n(n(e))),
% 63.81/64.04 inference(symmetry,[status(thm)],[29])).
% 63.81/64.04 tff(31,plain,
% 63.81/64.04 (s(a(n(e), n(e))) = s(n(n(e)))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[30])).
% 63.81/64.04 tff(32,plain,
% 63.81/64.04 (mem(s(n(e)), s(a(n(e), n(e)))) <=> mem(s(n(e)), s(n(n(e))))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[31])).
% 63.81/64.04 tff(33,plain,
% 63.81/64.04 (mem(s(n(e)), s(n(n(e)))) <=> mem(s(n(e)), s(a(n(e), n(e))))),
% 63.81/64.04 inference(symmetry,[status(thm)],[32])).
% 63.81/64.04 tff(34,assumption,(mem(s(n(e)), s(n(n(e))))), introduced(assumption)).
% 63.81/64.04 tff(35,plain,
% 63.81/64.04 (mem(s(n(e)), s(a(n(e), n(e))))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[34, 33])).
% 63.81/64.04 tff(36,plain,
% 63.81/64.04 ((s(n(e)) = a(n(e), n(e))) <=> (a(n(e), n(e)) = s(n(e)))),
% 63.81/64.04 inference(commutativity,[status(thm)],[])).
% 63.81/64.04 tff(37,plain,
% 63.81/64.04 ((a(n(e), n(e)) = s(n(e))) <=> (s(n(e)) = a(n(e), n(e)))),
% 63.81/64.04 inference(symmetry,[status(thm)],[36])).
% 63.81/64.04 tff(38,plain,
% 63.81/64.04 ((~(a(n(e), n(e)) = s(n(e)))) <=> (~(s(n(e)) = a(n(e), n(e))))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[37])).
% 63.81/64.04 tff(39,assumption,(~(mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e)))))), introduced(assumption)).
% 63.81/64.04 tff(40,plain,
% 63.81/64.04 (^[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))))),
% 63.81/64.04 inference(bind,[status(th)],[])).
% 63.81/64.04 tff(41,plain,
% 63.81/64.04 (![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)))),
% 63.81/64.04 inference(quant_intro,[status(thm)],[40])).
% 63.81/64.04 tff(42,plain,
% 63.81/64.04 (![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)))),
% 63.81/64.04 inference(rewrite,[status(thm)],[])).
% 63.81/64.04 tff(43,plain,
% 63.81/64.04 (^[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))))),
% 63.81/64.04 inference(bind,[status(th)],[])).
% 63.81/64.04 tff(44,plain,
% 63.81/64.04 (![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)))),
% 63.81/64.04 inference(quant_intro,[status(thm)],[43])).
% 63.81/64.04 tff(45,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')).
% 63.81/64.04 tff(46,plain,
% 63.81/64.04 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[45, 44])).
% 63.81/64.04 tff(47,plain,
% 63.81/64.04 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[46, 42])).
% 63.81/64.04 tff(48,plain,(
% 63.81/64.04 ![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 63.81/64.04 inference(skolemize,[status(sab)],[47])).
% 63.81/64.04 tff(49,plain,
% 63.81/64.04 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[48, 41])).
% 63.81/64.04 tff(50,plain,
% 63.81/64.04 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), 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(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e))))))),
% 63.81/64.04 inference(rewrite,[status(thm)],[])).
% 63.81/64.04 tff(51,plain,
% 63.81/64.04 ((mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e)))))),
% 63.81/64.04 inference(rewrite,[status(thm)],[])).
% 63.81/64.04 tff(52,plain,
% 63.81/64.04 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e))))))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[51])).
% 63.81/64.04 tff(53,plain,
% 63.81/64.04 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e))))))),
% 63.81/64.04 inference(transitivity,[status(thm)],[52, 50])).
% 63.81/64.04 tff(54,plain,
% 63.81/64.04 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))))),
% 63.81/64.04 inference(quant_inst,[status(thm)],[])).
% 63.81/64.04 tff(55,plain,
% 63.81/64.04 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e)))))),
% 63.81/64.04 inference(modus_ponens,[status(thm)],[54, 53])).
% 63.81/64.04 tff(56,plain,
% 63.81/64.04 ($false),
% 63.81/64.04 inference(unit_resolution,[status(thm)],[55, 49, 39])).
% 63.81/64.04 tff(57,plain,(mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.04 tff(58,plain,
% 63.81/64.04 ((~![X: $i] : (n(X) = a(X, X))) | (n(e) = a(e, e))),
% 63.81/64.04 inference(quant_inst,[status(thm)],[])).
% 63.81/64.04 tff(59,plain,
% 63.81/64.04 (n(e) = a(e, e)),
% 63.81/64.04 inference(unit_resolution,[status(thm)],[58, 16])).
% 63.81/64.04 tff(60,plain,
% 63.81/64.04 (a(e, e) = n(e)),
% 63.81/64.04 inference(symmetry,[status(thm)],[59])).
% 63.81/64.04 tff(61,assumption,(e = a(e, e)), introduced(assumption)).
% 63.81/64.04 tff(62,plain,
% 63.81/64.04 (e = n(e)),
% 63.81/64.04 inference(transitivity,[status(thm)],[61, 60])).
% 63.81/64.04 tff(63,plain,
% 63.81/64.04 (n(e) = n(n(e))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[62])).
% 63.81/64.04 tff(64,plain,
% 63.81/64.04 (n(n(e)) = n(e)),
% 63.81/64.04 inference(symmetry,[status(thm)],[63])).
% 63.81/64.04 tff(65,plain,
% 63.81/64.04 (a(n(e), n(e)) = a(e, e)),
% 63.81/64.04 inference(transitivity,[status(thm)],[30, 64, 59])).
% 63.81/64.04 tff(66,plain,
% 63.81/64.04 ((e = a(n(e), n(e))) <=> (a(n(e), n(e)) = e)),
% 63.81/64.04 inference(commutativity,[status(thm)],[])).
% 63.81/64.04 tff(67,assumption,(a(n(e), n(e)) = a(e, e)), introduced(assumption)).
% 63.81/64.04 tff(68,plain,
% 63.81/64.04 (a(e, e) = a(n(e), n(e))),
% 63.81/64.04 inference(symmetry,[status(thm)],[67])).
% 63.81/64.04 tff(69,plain,
% 63.81/64.04 ((e = a(e, e)) <=> (e = a(n(e), n(e)))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[68])).
% 63.81/64.04 tff(70,plain,
% 63.81/64.04 ((e = a(e, e)) <=> (a(n(e), n(e)) = e)),
% 63.81/64.04 inference(transitivity,[status(thm)],[69, 66])).
% 63.81/64.04 tff(71,plain,
% 63.81/64.04 ((a(n(e), n(e)) = e) <=> (e = a(e, e))),
% 63.81/64.04 inference(symmetry,[status(thm)],[70])).
% 63.81/64.04 tff(72,plain,
% 63.81/64.04 ((~(a(n(e), n(e)) = e)) <=> (~(e = a(e, e)))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[71])).
% 63.81/64.04 tff(73,assumption,(e = a(n(e), n(e))), introduced(assumption)).
% 63.81/64.04 tff(74,plain,
% 63.81/64.04 (a(n(e), n(e)) = e),
% 63.81/64.04 inference(symmetry,[status(thm)],[73])).
% 63.81/64.04 tff(75,plain,
% 63.81/64.04 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(n(e))) = a(n(n(e)), n(n(e))))),
% 63.81/64.04 inference(quant_inst,[status(thm)],[])).
% 63.81/64.04 tff(76,plain,
% 63.81/64.04 (n(n(n(e))) = a(n(n(e)), n(n(e)))),
% 63.81/64.04 inference(unit_resolution,[status(thm)],[75, 16])).
% 63.81/64.04 tff(77,plain,
% 63.81/64.04 (e = n(n(e))),
% 63.81/64.04 inference(transitivity,[status(thm)],[73, 30])).
% 63.81/64.04 tff(78,plain,
% 63.81/64.04 (n(e) = n(n(n(e)))),
% 63.81/64.04 inference(monotonicity,[status(thm)],[77])).
% 63.81/64.04 tff(79,plain,
% 63.81/64.04 (a(e, e) = a(n(n(e)), n(n(e)))),
% 63.81/64.04 inference(transitivity,[status(thm)],[60, 78, 76])).
% 63.81/64.05 tff(80,plain,
% 63.81/64.05 (mem(a(e, e), a(n(e), n(e))) <=> mem(a(n(n(e)), n(n(e))), e)),
% 63.81/64.05 inference(monotonicity,[status(thm)],[79, 74])).
% 63.81/64.05 tff(81,plain,
% 63.81/64.05 (mem(a(n(n(e)), n(n(e))), e) <=> mem(a(e, e), a(n(e), n(e)))),
% 63.81/64.05 inference(symmetry,[status(thm)],[80])).
% 63.81/64.05 tff(82,plain,
% 63.81/64.05 ((~mem(a(n(n(e)), n(n(e))), e)) <=> (~mem(a(e, e), a(n(e), n(e))))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[81])).
% 63.81/64.05 tff(83,plain,
% 63.81/64.05 (^[X: $i] : refl((~mem(X, e)) <=> (~mem(X, e)))),
% 63.81/64.05 inference(bind,[status(th)],[])).
% 63.81/64.05 tff(84,plain,
% 63.81/64.05 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 63.81/64.05 inference(quant_intro,[status(thm)],[83])).
% 63.81/64.05 tff(85,plain,
% 63.81/64.05 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(86,axiom,(![X: $i] : (~mem(X, e))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','e_ax')).
% 63.81/64.05 tff(87,plain,
% 63.81/64.05 (![X: $i] : (~mem(X, e))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[86, 85])).
% 63.81/64.05 tff(88,plain,(
% 63.81/64.05 ![X: $i] : (~mem(X, e))),
% 63.81/64.05 inference(skolemize,[status(sab)],[87])).
% 63.81/64.05 tff(89,plain,
% 63.81/64.05 (![X: $i] : (~mem(X, e))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[88, 84])).
% 63.81/64.05 tff(90,plain,
% 63.81/64.05 ((~![X: $i] : (~mem(X, e))) | (~mem(a(n(n(e)), n(n(e))), e))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(91,plain,
% 63.81/64.05 (~mem(a(n(n(e)), n(n(e))), e)),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[90, 89])).
% 63.81/64.05 tff(92,plain,
% 63.81/64.05 (~mem(a(e, e), a(n(e), n(e)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[91, 82])).
% 63.81/64.05 tff(93,plain,
% 63.81/64.05 (s(a(e, e)) = s(n(e))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[60])).
% 63.81/64.05 tff(94,plain,
% 63.81/64.05 (mem(a(e, e), s(a(e, e))) <=> mem(a(e, e), s(n(e)))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[93])).
% 63.81/64.05 tff(95,plain,
% 63.81/64.05 (mem(a(e, e), s(n(e))) <=> mem(a(e, e), s(a(e, e)))),
% 63.81/64.05 inference(symmetry,[status(thm)],[94])).
% 63.81/64.05 tff(96,plain,
% 63.81/64.05 ((~mem(a(e, e), s(n(e)))) <=> (~mem(a(e, e), s(a(e, e))))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[95])).
% 63.81/64.05 tff(97,assumption,(~mem(a(e, e), s(n(e)))), introduced(assumption)).
% 63.81/64.05 tff(98,plain,
% 63.81/64.05 (~mem(a(e, e), s(a(e, e)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[97, 96])).
% 63.81/64.05 tff(99,plain,
% 63.81/64.05 (((~![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))))),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(100,plain,
% 63.81/64.05 ((mem(a(e, e), s(a(e, e))) <=> $true) <=> mem(a(e, e), s(a(e, e)))),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(101,plain,
% 63.81/64.05 ((a(e, e) = a(e, e)) <=> $true),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(102,plain,
% 63.81/64.05 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> (mem(a(e, e), s(a(e, e))) <=> $true)),
% 63.81/64.05 inference(monotonicity,[status(thm)],[101])).
% 63.81/64.05 tff(103,plain,
% 63.81/64.05 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> mem(a(e, e), s(a(e, e)))),
% 63.81/64.05 inference(transitivity,[status(thm)],[102, 100])).
% 63.81/64.05 tff(104,plain,
% 63.81/64.05 (((~![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))))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[103])).
% 63.81/64.05 tff(105,plain,
% 63.81/64.05 (((~![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))))),
% 63.81/64.05 inference(transitivity,[status(thm)],[104, 99])).
% 63.81/64.05 tff(106,plain,
% 63.81/64.05 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e)))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(107,plain,
% 63.81/64.05 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[106, 105])).
% 63.81/64.05 tff(108,plain,
% 63.81/64.05 (mem(a(e, e), s(a(e, e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[107, 7])).
% 63.81/64.05 tff(109,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[108, 98])).
% 63.81/64.05 tff(110,plain,(mem(a(e, e), s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(111,plain,
% 63.81/64.05 (a(a(e, e), a(e, e)) = a(n(e), n(e))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[60, 60])).
% 63.81/64.05 tff(112,plain,
% 63.81/64.05 (^[X: $i, Y: $i] : refl((a(X, Y) = u(X, s(Y))) <=> (a(X, Y) = u(X, s(Y))))),
% 63.81/64.05 inference(bind,[status(th)],[])).
% 63.81/64.05 tff(113,plain,
% 63.81/64.05 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 63.81/64.05 inference(quant_intro,[status(thm)],[112])).
% 63.81/64.05 tff(114,plain,
% 63.81/64.05 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(115,axiom,(![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','a_def')).
% 63.81/64.05 tff(116,plain,
% 63.81/64.05 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[115, 114])).
% 63.81/64.05 tff(117,plain,(
% 63.81/64.05 ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 63.81/64.05 inference(skolemize,[status(sab)],[116])).
% 63.81/64.05 tff(118,plain,
% 63.81/64.05 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[117, 113])).
% 63.81/64.05 tff(119,plain,
% 63.81/64.05 ((~![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))))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(120,plain,
% 63.81/64.05 (a(a(e, e), a(e, e)) = u(a(e, e), s(a(e, e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[119, 118])).
% 63.81/64.05 tff(121,plain,
% 63.81/64.05 (u(a(e, e), s(a(e, e))) = a(a(e, e), a(e, e))),
% 63.81/64.05 inference(symmetry,[status(thm)],[120])).
% 63.81/64.05 tff(122,plain,
% 63.81/64.05 (s(n(e)) = s(a(e, e))),
% 63.81/64.05 inference(symmetry,[status(thm)],[93])).
% 63.81/64.05 tff(123,plain,
% 63.81/64.05 (u(a(e, e), s(n(e))) = u(a(e, e), s(a(e, e)))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[122])).
% 63.81/64.05 tff(124,plain,
% 63.81/64.05 (u(a(e, e), s(n(e))) = a(n(e), n(e))),
% 63.81/64.05 inference(transitivity,[status(thm)],[123, 121, 111])).
% 63.81/64.05 tff(125,plain,
% 63.81/64.05 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> mem(a(e, e), a(n(e), n(e)))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[124])).
% 63.81/64.05 tff(126,plain,
% 63.81/64.05 (mem(a(e, e), a(n(e), n(e))) <=> mem(a(e, e), u(a(e, e), s(n(e))))),
% 63.81/64.05 inference(symmetry,[status(thm)],[125])).
% 63.81/64.05 tff(127,plain,
% 63.81/64.05 ((~mem(a(e, e), a(n(e), n(e)))) <=> (~mem(a(e, e), u(a(e, e), s(n(e)))))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[126])).
% 63.81/64.05 tff(128,assumption,(~mem(a(e, e), a(n(e), n(e)))), introduced(assumption)).
% 63.81/64.05 tff(129,plain,
% 63.81/64.05 (~mem(a(e, e), u(a(e, e), s(n(e))))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[128, 127])).
% 63.81/64.05 tff(130,plain,
% 63.81/64.05 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(131,plain,
% 63.81/64.05 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[130, 49])).
% 63.81/64.05 tff(132,assumption,(mem(a(e, e), s(n(e)))), introduced(assumption)).
% 63.81/64.05 tff(133,plain,
% 63.81/64.05 ((mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))) | (~mem(a(e, e), s(n(e))))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(134,plain,
% 63.81/64.05 (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[133, 132])).
% 63.81/64.05 tff(135,plain,
% 63.81/64.05 ((~(mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))) | mem(a(e, e), u(a(e, e), s(n(e)))) | (~(mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(136,plain,
% 63.81/64.05 ((~(mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))) | mem(a(e, e), u(a(e, e), s(n(e))))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[135, 134])).
% 63.81/64.05 tff(137,plain,
% 63.81/64.05 (mem(a(e, e), u(a(e, e), s(n(e))))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[136, 131])).
% 63.81/64.05 tff(138,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[137, 129])).
% 63.81/64.05 tff(139,plain,(mem(a(e, e), a(n(e), n(e))) | (~mem(a(e, e), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(140,plain,
% 63.81/64.05 (mem(a(e, e), a(n(e), n(e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[139, 110])).
% 63.81/64.05 tff(141,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[140, 92])).
% 63.81/64.05 tff(142,plain,(~(e = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(143,assumption,(a(n(e), n(e)) = e), introduced(assumption)).
% 63.81/64.05 tff(144,plain,
% 63.81/64.05 (e = a(n(e), n(e))),
% 63.81/64.05 inference(symmetry,[status(thm)],[143])).
% 63.81/64.05 tff(145,assumption,(~(e = a(n(e), n(e)))), introduced(assumption)).
% 63.81/64.05 tff(146,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[145, 144])).
% 63.81/64.05 tff(147,plain,((~(a(n(e), n(e)) = e)) | (e = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(148,plain,
% 63.81/64.05 (~(a(n(e), n(e)) = e)),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[147, 142])).
% 63.81/64.05 tff(149,plain,
% 63.81/64.05 (~(e = a(e, e))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[148, 72])).
% 63.81/64.05 tff(150,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[61, 149])).
% 63.81/64.05 tff(151,plain,((~(a(n(e), n(e)) = a(e, e))) | (~(e = a(e, e)))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(152,plain,
% 63.81/64.05 (~(a(n(e), n(e)) = a(e, e))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[151, 61])).
% 63.81/64.05 tff(153,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[152, 65])).
% 63.81/64.05 tff(154,plain,(~(e = a(e, e))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(155,assumption,(~(mem(e, s(a(e, e))) <=> (e = a(e, e)))), introduced(assumption)).
% 63.81/64.05 tff(156,plain,
% 63.81/64.05 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(a(e, e))) <=> (e = a(e, e)))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(157,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[156, 7, 155])).
% 63.81/64.05 tff(158,plain,(mem(e, s(a(e, e))) <=> (e = a(e, e))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(159,plain,
% 63.81/64.05 ((~(mem(e, s(a(e, e))) <=> (e = a(e, e)))) | (~mem(e, s(a(e, e)))) | (e = a(e, e))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(160,plain,
% 63.81/64.05 ((~mem(e, s(a(e, e)))) | (e = a(e, e))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[159, 158])).
% 63.81/64.05 tff(161,plain,
% 63.81/64.05 (~mem(e, s(a(e, e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[160, 154])).
% 63.81/64.05 tff(162,plain,
% 63.81/64.05 (mem(e, s(a(e, e))) <=> mem(e, s(n(e)))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[93])).
% 63.81/64.05 tff(163,plain,
% 63.81/64.05 (mem(e, s(n(e))) <=> mem(e, s(a(e, e)))),
% 63.81/64.05 inference(symmetry,[status(thm)],[162])).
% 63.81/64.05 tff(164,assumption,(mem(e, s(n(e)))), introduced(assumption)).
% 63.81/64.05 tff(165,plain,
% 63.81/64.05 (mem(e, s(a(e, e)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[164, 163])).
% 63.81/64.05 tff(166,assumption,(~mem(e, s(a(e, e)))), introduced(assumption)).
% 63.81/64.05 tff(167,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[166, 165])).
% 63.81/64.05 tff(168,plain,(mem(e, s(a(e, e))) | (~mem(e, s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(169,plain,
% 63.81/64.05 (~mem(e, s(n(e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[168, 161])).
% 63.81/64.05 tff(170,assumption,(~(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))), introduced(assumption)).
% 63.81/64.05 tff(171,plain,
% 63.81/64.05 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(172,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[171, 49, 170])).
% 63.81/64.05 tff(173,plain,(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(174,assumption,(~mem(e, s(e))), introduced(assumption)).
% 63.81/64.05 tff(175,plain,
% 63.81/64.05 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(e, s(e))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(e, s(e)))),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(176,plain,
% 63.81/64.05 ((mem(e, s(e)) <=> $true) <=> mem(e, s(e))),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(177,plain,
% 63.81/64.05 ((e = e) <=> $true),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(178,plain,
% 63.81/64.05 ((mem(e, s(e)) <=> (e = e)) <=> (mem(e, s(e)) <=> $true)),
% 63.81/64.05 inference(monotonicity,[status(thm)],[177])).
% 63.81/64.05 tff(179,plain,
% 63.81/64.05 ((mem(e, s(e)) <=> (e = e)) <=> mem(e, s(e))),
% 63.81/64.05 inference(transitivity,[status(thm)],[178, 176])).
% 63.81/64.05 tff(180,plain,
% 63.81/64.05 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(e)) <=> (e = e))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(e, s(e)))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[179])).
% 63.81/64.05 tff(181,plain,
% 63.81/64.05 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(e)) <=> (e = e))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(e, s(e)))),
% 63.81/64.05 inference(transitivity,[status(thm)],[180, 175])).
% 63.81/64.05 tff(182,plain,
% 63.81/64.05 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(e)) <=> (e = e))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(183,plain,
% 63.81/64.05 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(e, s(e))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[182, 181])).
% 63.81/64.05 tff(184,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[183, 7, 174])).
% 63.81/64.05 tff(185,plain,(mem(e, s(e))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(186,plain,
% 63.81/64.05 ((mem(e, s(e)) | mem(e, e)) | (~mem(e, s(e)))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(187,plain,
% 63.81/64.05 (mem(e, s(e)) | mem(e, e)),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[186, 185])).
% 63.81/64.05 tff(188,plain,
% 63.81/64.05 ((~(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))) | mem(e, u(e, s(e))) | (~(mem(e, s(e)) | mem(e, e)))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(189,plain,
% 63.81/64.05 ((~(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))) | mem(e, u(e, s(e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[188, 187])).
% 63.81/64.05 tff(190,plain,
% 63.81/64.05 (mem(e, u(e, s(e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[189, 173])).
% 63.81/64.05 tff(191,plain,
% 63.81/64.05 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(e, e) = u(e, s(e)))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(192,plain,
% 63.81/64.05 (a(e, e) = u(e, s(e))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[191, 118])).
% 63.81/64.05 tff(193,plain,
% 63.81/64.05 (u(e, s(e)) = a(e, e)),
% 63.81/64.05 inference(symmetry,[status(thm)],[192])).
% 63.81/64.05 tff(194,plain,
% 63.81/64.05 (mem(e, u(e, s(e))) <=> mem(e, a(e, e))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[193])).
% 63.81/64.05 tff(195,plain,
% 63.81/64.05 (mem(e, a(e, e)) <=> mem(e, u(e, s(e)))),
% 63.81/64.05 inference(symmetry,[status(thm)],[194])).
% 63.81/64.05 tff(196,plain,
% 63.81/64.05 ((~mem(e, a(e, e))) <=> (~mem(e, u(e, s(e))))),
% 63.81/64.05 inference(monotonicity,[status(thm)],[195])).
% 63.81/64.05 tff(197,assumption,(~mem(e, a(e, e))), introduced(assumption)).
% 63.81/64.05 tff(198,plain,
% 63.81/64.05 (~mem(e, u(e, s(e)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[197, 196])).
% 63.81/64.05 tff(199,assumption,(mem(e, u(e, s(e)))), introduced(assumption)).
% 63.81/64.05 tff(200,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[199, 198])).
% 63.81/64.05 tff(201,plain,((~mem(e, u(e, s(e)))) | mem(e, a(e, e))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(202,plain,
% 63.81/64.05 (mem(e, a(e, e))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[201, 190])).
% 63.81/64.05 tff(203,assumption,(mem(e, a(e, e))), introduced(assumption)).
% 63.81/64.05 tff(204,assumption,(~mem(e, s(n(e)))), introduced(assumption)).
% 63.81/64.05 tff(205,assumption,(![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))), introduced(assumption)).
% 63.81/64.05 tff(206,plain,
% 63.81/64.05 (((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))) | ((~mem(e, a(e, e))) | mem(e, s(n(e))))) <=> ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))) | (~mem(e, a(e, e))) | mem(e, s(n(e))))),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(207,plain,
% 63.81/64.05 ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))) | ((~mem(e, a(e, e))) | mem(e, s(n(e))))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(208,plain,
% 63.81/64.05 ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))) | (~mem(e, a(e, e))) | mem(e, s(n(e)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[207, 206])).
% 63.81/64.05 tff(209,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[208, 205, 204, 203])).
% 63.81/64.05 tff(210,plain,((~mem(e, a(e, e))) | (~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))) | mem(e, s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(211,plain,
% 63.81/64.05 ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))) | mem(e, s(n(e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[210, 202])).
% 63.81/64.05 tff(212,plain,
% 63.81/64.05 (~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[211, 169])).
% 63.81/64.05 tff(213,assumption,((~((~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e)))))) | (~(subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))))))), introduced(assumption)).
% 63.81/64.05 tff(214,plain,
% 63.81/64.05 (^[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))))))))),
% 63.81/64.05 inference(bind,[status(th)],[])).
% 63.81/64.05 tff(215,plain,
% 63.81/64.05 (![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)))))))),
% 63.81/64.05 inference(quant_intro,[status(thm)],[214])).
% 63.81/64.05 tff(216,plain,
% 63.81/64.05 (^[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))))))))),
% 63.81/64.05 inference(bind,[status(th)],[])).
% 63.81/64.05 tff(217,plain,
% 63.81/64.05 (![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)))))))),
% 63.81/64.05 inference(quant_intro,[status(thm)],[216])).
% 63.81/64.05 tff(218,plain,
% 63.81/64.05 (![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)))))))),
% 63.81/64.05 inference(transitivity,[status(thm)],[217, 215])).
% 63.81/64.05 tff(219,plain,
% 63.81/64.05 (^[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)))))))))),
% 63.81/64.05 inference(bind,[status(th)],[])).
% 63.81/64.05 tff(220,plain,
% 63.81/64.05 (![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)))))))),
% 63.81/64.05 inference(quant_intro,[status(thm)],[219])).
% 63.81/64.05 tff(221,plain,
% 63.81/64.05 (![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)))),
% 63.81/64.05 inference(rewrite,[status(thm)],[])).
% 63.81/64.05 tff(222,plain,
% 63.81/64.05 (^[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))))),
% 63.81/64.05 inference(bind,[status(th)],[])).
% 63.81/64.05 tff(223,plain,
% 63.81/64.05 (![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)))),
% 63.81/64.05 inference(quant_intro,[status(thm)],[222])).
% 63.81/64.05 tff(224,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')).
% 63.81/64.05 tff(225,plain,
% 63.81/64.05 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[224, 223])).
% 63.81/64.05 tff(226,plain,
% 63.81/64.05 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[225, 221])).
% 63.81/64.05 tff(227,plain,(
% 63.81/64.05 ![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)))))),
% 63.81/64.05 inference(skolemize,[status(sab)],[226])).
% 63.81/64.05 tff(228,plain,
% 63.81/64.05 (![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)))))))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[227, 220])).
% 63.81/64.05 tff(229,plain,
% 63.81/64.05 (![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)))))))),
% 63.81/64.05 inference(modus_ponens,[status(thm)],[228, 218])).
% 63.81/64.05 tff(230,plain,
% 63.81/64.05 ((~![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(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e)))))) | (~(subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))))))))),
% 63.81/64.05 inference(quant_inst,[status(thm)],[])).
% 63.81/64.05 tff(231,plain,
% 63.81/64.05 ($false),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[230, 229, 213])).
% 63.81/64.05 tff(232,plain,(~((~((~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e)))))) | (~(subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e))))))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.05 tff(233,plain,
% 63.81/64.05 (((~((~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e)))))) | (~(subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))))))) | ((~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e)))))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(234,plain,
% 63.81/64.05 ((~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[233, 232])).
% 63.81/64.05 tff(235,plain,
% 63.81/64.05 ((~((~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e)))))) | (~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(236,plain,
% 63.81/64.05 ((~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e))))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[235, 234])).
% 63.81/64.05 tff(237,plain,
% 63.81/64.05 (~subq(a(e, e), s(n(e)))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[236, 212])).
% 63.81/64.05 tff(238,plain,
% 63.81/64.05 (((~((~subq(a(e, e), s(n(e)))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(e)))))) | (~(subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))))))) | (subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e))))))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(239,plain,
% 63.81/64.05 (subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[238, 232])).
% 63.81/64.05 tff(240,plain,
% 63.81/64.05 ((~(subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e))))))) | subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))))),
% 63.81/64.05 inference(tautology,[status(thm)],[])).
% 63.81/64.05 tff(241,plain,
% 63.81/64.05 (subq(a(e, e), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))))),
% 63.81/64.05 inference(unit_resolution,[status(thm)],[240, 239])).
% 63.81/64.06 tff(242,plain,
% 63.81/64.06 (~((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[241, 237])).
% 63.81/64.06 tff(243,plain,
% 63.81/64.06 (((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(244,plain,
% 63.81/64.06 (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[243, 242])).
% 63.81/64.06 tff(245,plain,
% 63.81/64.06 ((mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e)))) | (~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)))),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(246,plain,
% 63.81/64.06 (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e)))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[245, 244])).
% 63.81/64.06 tff(247,plain,
% 63.81/64.06 ((~(mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) | (~(mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e)))))),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(248,plain,
% 63.81/64.06 ((~(mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e)) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(n(e), n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[247, 246])).
% 63.81/64.06 tff(249,plain,
% 63.81/64.06 (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[248, 57])).
% 63.81/64.06 tff(250,assumption,(a(n(e), n(e)) = s(n(e))), introduced(assumption)).
% 63.81/64.06 tff(251,plain,
% 63.81/64.06 (a(n(e), n(e)) = s(a(e, e))),
% 63.81/64.06 inference(transitivity,[status(thm)],[250, 122])).
% 63.81/64.06 tff(252,plain,
% 63.81/64.06 (u(a(e, e), a(n(e), n(e))) = u(a(e, e), s(a(e, e)))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[251])).
% 63.81/64.06 tff(253,plain,
% 63.81/64.06 (u(a(e, e), a(n(e), n(e))) = s(n(e))),
% 63.81/64.06 inference(transitivity,[status(thm)],[252, 121, 111, 250])).
% 63.81/64.06 tff(254,plain,
% 63.81/64.06 (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))) <=> mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[253])).
% 63.81/64.06 tff(255,plain,
% 63.81/64.06 (mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e))) <=> mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e))))),
% 63.81/64.06 inference(symmetry,[status(thm)],[254])).
% 63.81/64.06 tff(256,plain,
% 63.81/64.06 ((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))) <=> (~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e)))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[255])).
% 63.81/64.06 tff(257,plain,
% 63.81/64.06 (((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))) | (~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e))))),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(258,plain,
% 63.81/64.06 (~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), s(n(e)))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[257, 242])).
% 63.81/64.06 tff(259,plain,
% 63.81/64.06 (~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e))))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[258, 256])).
% 63.81/64.06 tff(260,assumption,(mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e))))), introduced(assumption)).
% 63.81/64.06 tff(261,plain,
% 63.81/64.06 ($false),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[260, 259])).
% 63.81/64.06 tff(262,plain,((~mem(tptp_fun_Z_0(s(n(e)), a(e, e)), u(a(e, e), a(n(e), n(e))))) | (~(a(n(e), n(e)) = s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.06 tff(263,plain,
% 63.81/64.06 (~(a(n(e), n(e)) = s(n(e)))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[262, 249])).
% 63.81/64.06 tff(264,plain,
% 63.81/64.06 (~(s(n(e)) = a(n(e), n(e)))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[263, 38])).
% 63.81/64.06 tff(265,plain,
% 63.81/64.06 ((~(mem(s(n(e)), s(a(n(e), n(e)))) <=> (s(n(e)) = a(n(e), n(e))))) | (~mem(s(n(e)), s(a(n(e), n(e))))) | (s(n(e)) = a(n(e), n(e)))),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(266,plain,
% 63.81/64.06 ($false),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[265, 264, 35, 27])).
% 63.81/64.06 tff(267,plain,((~(mem(s(n(e)), s(a(n(e), n(e)))) <=> (s(n(e)) = a(n(e), n(e))))) | (~mem(s(n(e)), s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.06 tff(268,plain,
% 63.81/64.06 (~mem(s(n(e)), s(n(n(e))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[267, 26])).
% 63.81/64.06 tff(269,assumption,(~(mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))))), introduced(assumption)).
% 63.81/64.06 tff(270,plain,
% 63.81/64.06 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(271,plain,
% 63.81/64.06 ($false),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[270, 49, 269])).
% 63.81/64.06 tff(272,plain,(mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.06 tff(273,plain,
% 63.81/64.06 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(n(n(e))), n(s(n(e)))) = u(s(n(n(e))), s(n(s(n(e))))))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(274,plain,
% 63.81/64.06 (a(s(n(n(e))), n(s(n(e)))) = u(s(n(n(e))), s(n(s(n(e)))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[273, 118])).
% 63.81/64.06 tff(275,plain,
% 63.81/64.06 (u(s(n(n(e))), s(n(s(n(e))))) = a(s(n(n(e))), n(s(n(e))))),
% 63.81/64.06 inference(symmetry,[status(thm)],[274])).
% 63.81/64.06 tff(276,plain,
% 63.81/64.06 (u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))) = u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[275])).
% 63.81/64.06 tff(277,plain,
% 63.81/64.06 (mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[276])).
% 63.81/64.06 tff(278,plain,
% 63.81/64.06 (mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) <=> mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))))),
% 63.81/64.06 inference(symmetry,[status(thm)],[277])).
% 63.81/64.06 tff(279,plain,
% 63.81/64.06 (a(n(n(e)), n(n(e))) = n(n(n(e)))),
% 63.81/64.06 inference(symmetry,[status(thm)],[76])).
% 63.81/64.06 tff(280,plain,
% 63.81/64.06 (s(a(n(n(e)), n(n(e)))) = s(n(n(n(e))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[279])).
% 63.81/64.06 tff(281,plain,
% 63.81/64.06 (mem(s(n(e)), s(a(n(n(e)), n(n(e))))) <=> mem(s(n(e)), s(n(n(n(e)))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[280])).
% 63.81/64.06 tff(282,plain,
% 63.81/64.06 (mem(s(n(e)), s(n(n(n(e))))) <=> mem(s(n(e)), s(a(n(n(e)), n(n(e)))))),
% 63.81/64.06 inference(symmetry,[status(thm)],[281])).
% 63.81/64.06 tff(283,assumption,(mem(s(n(e)), s(n(n(n(e)))))), introduced(assumption)).
% 63.81/64.06 tff(284,plain,
% 63.81/64.06 (mem(s(n(e)), s(a(n(n(e)), n(n(e)))))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[283, 282])).
% 63.81/64.06 tff(285,plain,
% 63.81/64.06 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(s(n(e)), s(a(n(n(e)), n(n(e))))) <=> (s(n(e)) = a(n(n(e)), n(n(e)))))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(286,plain,
% 63.81/64.06 (mem(s(n(e)), s(a(n(n(e)), n(n(e))))) <=> (s(n(e)) = a(n(n(e)), n(n(e))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[285, 7])).
% 63.81/64.06 tff(287,assumption,(s(n(e)) = a(n(n(e)), n(n(e)))), introduced(assumption)).
% 63.81/64.06 tff(288,plain,
% 63.81/64.06 (subq(s(n(e)), u(n(e), n(s(n(e))))) <=> subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[287])).
% 63.81/64.06 tff(289,plain,
% 63.81/64.06 (subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e))))) <=> subq(s(n(e)), u(n(e), n(s(n(e)))))),
% 63.81/64.06 inference(symmetry,[status(thm)],[288])).
% 63.81/64.06 tff(290,plain,
% 63.81/64.06 ((~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) <=> (~subq(s(n(e)), u(n(e), n(s(n(e))))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[289])).
% 63.81/64.06 tff(291,assumption,((~((~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(n(e)), n(n(e)))), u(n(e), n(s(n(e)))))))))), introduced(assumption)).
% 63.81/64.06 tff(292,plain,
% 63.81/64.06 ((~![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(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(n(e)), n(n(e)))), u(n(e), n(s(n(e)))))))))))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(293,plain,
% 63.81/64.06 ($false),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[292, 229, 291])).
% 63.81/64.06 tff(294,plain,(~((~((~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(n(e)), n(n(e)))), u(n(e), n(s(n(e))))))))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.06 tff(295,plain,
% 63.81/64.06 (((~((~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(n(e)), n(n(e)))), u(n(e), n(s(n(e)))))))))) | ((~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e)))))))),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(296,plain,
% 63.81/64.06 ((~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e))))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[295, 294])).
% 63.81/64.06 tff(297,assumption,(![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e))))))), introduced(assumption)).
% 63.81/64.06 tff(298,plain,
% 63.81/64.06 (u(a(e, e), a(s(n(e)), s(n(e)))) = u(n(e), n(s(n(e))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[60, 19])).
% 63.81/64.06 tff(299,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> mem(a(n(e), n(e)), u(n(e), n(s(n(e)))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[298])).
% 63.81/64.06 tff(300,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(n(e), n(s(n(e))))) <=> mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.81/64.06 inference(symmetry,[status(thm)],[299])).
% 63.81/64.06 tff(301,assumption,(mem(a(n(e), n(e)), u(n(e), n(s(n(e)))))), introduced(assumption)).
% 63.81/64.06 tff(302,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[301, 300])).
% 63.81/64.06 tff(303,plain,
% 63.81/64.06 ((~![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), a(s(n(e)), s(n(e))))) <=> (mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) | mem(a(n(e), n(e)), a(e, e))))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(304,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) | mem(a(n(e), n(e)), a(e, e)))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[303, 49])).
% 63.81/64.06 tff(305,assumption,(~(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))), introduced(assumption)).
% 63.81/64.06 tff(306,plain,
% 63.81/64.06 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(307,plain,
% 63.81/64.06 ($false),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[306, 7, 305])).
% 63.81/64.06 tff(308,plain,(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e)), inference(lemma,lemma(discharge,[]))).
% 63.81/64.06 tff(309,plain,
% 63.81/64.06 ((~(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)),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(310,plain,
% 63.81/64.06 ((~mem(a(n(e), n(e)), s(e))) | (a(n(e), n(e)) = e)),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[309, 308])).
% 63.81/64.06 tff(311,plain,
% 63.81/64.06 (~mem(a(n(e), n(e)), s(e))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[310, 148])).
% 63.81/64.06 tff(312,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(e, s(e))) <=> mem(a(n(e), n(e)), a(e, e))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[193])).
% 63.81/64.06 tff(313,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), a(e, e)) <=> mem(a(n(e), n(e)), u(e, s(e)))),
% 63.81/64.06 inference(symmetry,[status(thm)],[312])).
% 63.81/64.06 tff(314,assumption,(mem(a(n(e), n(e)), a(e, e))), introduced(assumption)).
% 63.81/64.06 tff(315,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(e, s(e)))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[314, 313])).
% 63.81/64.06 tff(316,plain,
% 63.81/64.06 (((~![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)))))),
% 63.81/64.06 inference(rewrite,[status(thm)],[])).
% 63.81/64.06 tff(317,plain,
% 63.81/64.06 ((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))))),
% 63.81/64.06 inference(rewrite,[status(thm)],[])).
% 63.81/64.06 tff(318,plain,
% 63.81/64.06 (((~![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)))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[317])).
% 63.81/64.06 tff(319,plain,
% 63.81/64.06 (((~![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)))))),
% 63.81/64.06 inference(transitivity,[status(thm)],[318, 316])).
% 63.81/64.06 tff(320,plain,
% 63.81/64.06 ((~![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)))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(321,plain,
% 63.81/64.06 ((~![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))))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[320, 319])).
% 63.81/64.06 tff(322,plain,
% 63.81/64.06 (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)))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[321, 49])).
% 63.81/64.06 tff(323,assumption,(~mem(a(n(e), n(e)), s(e))), introduced(assumption)).
% 63.81/64.06 tff(324,assumption,(mem(a(n(e), n(e)), e)), introduced(assumption)).
% 63.81/64.06 tff(325,plain,
% 63.81/64.06 ((~![X: $i] : (~mem(X, e))) | (~mem(a(n(e), n(e)), e))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(326,plain,
% 63.81/64.06 ($false),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[325, 89, 324])).
% 63.81/64.06 tff(327,plain,(~mem(a(n(e), n(e)), e)), inference(lemma,lemma(discharge,[]))).
% 63.81/64.06 tff(328,plain,
% 63.81/64.06 ((~(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))),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(329,plain,
% 63.81/64.06 (~(mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[328, 327, 323])).
% 63.81/64.06 tff(330,plain,
% 63.81/64.06 ((~(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)))),
% 63.81/64.06 inference(tautology,[status(thm)],[])).
% 63.81/64.06 tff(331,plain,
% 63.81/64.06 ((~(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))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[330, 329])).
% 63.81/64.06 tff(332,plain,
% 63.81/64.06 (~mem(a(n(e), n(e)), u(e, s(e)))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[331, 322])).
% 63.81/64.06 tff(333,plain,
% 63.81/64.06 ($false),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[332, 315])).
% 63.81/64.06 tff(334,plain,((~mem(a(n(e), n(e)), a(e, e))) | mem(a(n(e), n(e)), s(e))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.06 tff(335,plain,
% 63.81/64.06 (~mem(a(n(e), n(e)), a(e, e))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[334, 311])).
% 63.81/64.06 tff(336,plain,
% 63.81/64.06 ((~![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)))))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(337,plain,
% 63.81/64.06 (a(s(n(e)), s(n(e))) = u(s(n(e)), s(s(n(e))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[336, 118])).
% 63.81/64.06 tff(338,plain,
% 63.81/64.06 (u(s(n(e)), s(s(n(e)))) = a(s(n(e)), s(n(e)))),
% 63.81/64.06 inference(symmetry,[status(thm)],[337])).
% 63.81/64.06 tff(339,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> mem(a(n(e), n(e)), a(s(n(e)), s(n(e))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[338])).
% 63.81/64.06 tff(340,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) <=> mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e)))))),
% 63.81/64.06 inference(symmetry,[status(thm)],[339])).
% 63.81/64.06 tff(341,assumption,(mem(a(n(e), n(e)), a(s(n(e)), s(n(e))))), introduced(assumption)).
% 63.81/64.06 tff(342,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e)))))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[341, 340])).
% 63.81/64.06 tff(343,plain,
% 63.81/64.06 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(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(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e)))))))),
% 63.81/64.06 inference(rewrite,[status(thm)],[])).
% 63.81/64.06 tff(344,plain,
% 63.81/64.06 ((mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(s(n(e)))) | mem(a(n(e), n(e)), s(n(e))))) <=> (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e))))))),
% 63.81/64.06 inference(rewrite,[status(thm)],[])).
% 63.81/64.06 tff(345,plain,
% 63.81/64.06 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(s(n(e)))) | mem(a(n(e), n(e)), s(n(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(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e)))))))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[344])).
% 63.81/64.06 tff(346,plain,
% 63.81/64.06 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(s(n(e)))) | mem(a(n(e), n(e)), s(n(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(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e)))))))),
% 63.81/64.06 inference(transitivity,[status(thm)],[345, 343])).
% 63.81/64.06 tff(347,plain,
% 63.81/64.06 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(s(n(e)))) | mem(a(n(e), n(e)), s(n(e)))))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(348,plain,
% 63.81/64.06 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e))))))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[347, 346])).
% 63.81/64.06 tff(349,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e)))))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[348, 49])).
% 63.81/64.06 tff(350,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), s(a(e, e))) <=> mem(a(n(e), n(e)), s(n(e)))),
% 63.81/64.06 inference(monotonicity,[status(thm)],[93])).
% 63.81/64.06 tff(351,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), s(n(e))) <=> mem(a(n(e), n(e)), s(a(e, e)))),
% 63.81/64.06 inference(symmetry,[status(thm)],[350])).
% 63.81/64.06 tff(352,assumption,(mem(a(n(e), n(e)), s(n(e)))), introduced(assumption)).
% 63.81/64.06 tff(353,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), s(a(e, e)))),
% 63.81/64.06 inference(modus_ponens,[status(thm)],[352, 351])).
% 63.81/64.06 tff(354,plain,
% 63.81/64.06 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(a(e, e))) <=> (a(n(e), n(e)) = a(e, e)))),
% 63.81/64.06 inference(quant_inst,[status(thm)],[])).
% 63.81/64.06 tff(355,plain,
% 63.81/64.06 (mem(a(n(e), n(e)), s(a(e, e))) <=> (a(n(e), n(e)) = a(e, e))),
% 63.81/64.06 inference(unit_resolution,[status(thm)],[354, 7])).
% 63.81/64.06 tff(356,plain,
% 63.81/64.07 (mem(a(e, e), a(n(e), n(e))) <=> mem(a(n(e), n(e)), a(e, e))),
% 63.81/64.07 inference(monotonicity,[status(thm)],[68, 67])).
% 63.81/64.07 tff(357,plain,
% 63.81/64.07 (mem(a(n(e), n(e)), a(e, e)) <=> mem(a(e, e), a(n(e), n(e)))),
% 63.81/64.07 inference(symmetry,[status(thm)],[356])).
% 63.81/64.07 tff(358,plain,
% 63.81/64.07 ((~mem(a(n(e), n(e)), a(e, e))) <=> (~mem(a(e, e), a(n(e), n(e))))),
% 63.81/64.07 inference(monotonicity,[status(thm)],[357])).
% 63.81/64.07 tff(359,plain,
% 63.81/64.07 (~mem(a(e, e), a(n(e), n(e)))),
% 63.81/64.07 inference(modus_ponens,[status(thm)],[335, 358])).
% 63.81/64.07 tff(360,plain,
% 63.81/64.07 ($false),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[140, 359])).
% 63.81/64.07 tff(361,plain,(~(a(n(e), n(e)) = a(e, e))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.07 tff(362,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), s(a(e, e))) <=> (a(n(e), n(e)) = a(e, e)))) | (~mem(a(n(e), n(e)), s(a(e, e)))) | (a(n(e), n(e)) = a(e, e))),
% 63.81/64.07 inference(tautology,[status(thm)],[])).
% 63.81/64.07 tff(363,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), s(a(e, e))) <=> (a(n(e), n(e)) = a(e, e)))) | (~mem(a(n(e), n(e)), s(a(e, e))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[362, 361])).
% 63.81/64.07 tff(364,plain,
% 63.81/64.07 (~mem(a(n(e), n(e)), s(a(e, e)))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[363, 355])).
% 63.81/64.07 tff(365,plain,
% 63.81/64.07 ($false),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[364, 353])).
% 63.81/64.07 tff(366,plain,(~mem(a(n(e), n(e)), s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.07 tff(367,assumption,(~(mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e))))), introduced(assumption)).
% 63.81/64.07 tff(368,plain,
% 63.81/64.07 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e))))),
% 63.81/64.07 inference(quant_inst,[status(thm)],[])).
% 63.81/64.07 tff(369,plain,
% 63.81/64.07 ($false),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[368, 7, 367])).
% 63.81/64.07 tff(370,plain,(mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.07 tff(371,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e))))) | (~mem(a(n(e), n(e)), s(s(n(e))))) | (a(n(e), n(e)) = s(n(e)))),
% 63.81/64.07 inference(tautology,[status(thm)],[])).
% 63.81/64.07 tff(372,plain,
% 63.81/64.07 ((~mem(a(n(e), n(e)), s(s(n(e))))) | (a(n(e), n(e)) = s(n(e)))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[371, 370])).
% 63.81/64.07 tff(373,plain,
% 63.81/64.07 (~mem(a(n(e), n(e)), s(s(n(e))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[372, 263])).
% 63.81/64.07 tff(374,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e)))))) | mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e))))),
% 63.81/64.07 inference(tautology,[status(thm)],[])).
% 63.81/64.07 tff(375,plain,
% 63.81/64.07 (~(mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e)))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[374, 373, 366])).
% 63.81/64.07 tff(376,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e))))))) | (~mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e)))))) | (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e)))))),
% 63.81/64.07 inference(tautology,[status(thm)],[])).
% 63.81/64.07 tff(377,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(a(n(e), n(e)), s(n(e))) | mem(a(n(e), n(e)), s(s(n(e))))))) | (~mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e))))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[376, 375])).
% 63.81/64.07 tff(378,plain,
% 63.81/64.07 (~mem(a(n(e), n(e)), u(s(n(e)), s(s(n(e)))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[377, 349])).
% 63.81/64.07 tff(379,plain,
% 63.81/64.07 ($false),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[378, 342])).
% 63.81/64.07 tff(380,plain,(~mem(a(n(e), n(e)), a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.07 tff(381,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) | mem(a(n(e), n(e)), a(e, e)))) | mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) | mem(a(n(e), n(e)), a(e, e))),
% 63.81/64.07 inference(tautology,[status(thm)],[])).
% 63.81/64.07 tff(382,plain,
% 63.81/64.07 (~(mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) | mem(a(n(e), n(e)), a(e, e)))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[381, 380, 335])).
% 63.81/64.07 tff(383,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) | mem(a(n(e), n(e)), a(e, e))))) | (~mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e)))))) | (mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) | mem(a(n(e), n(e)), a(e, e)))),
% 63.81/64.07 inference(tautology,[status(thm)],[])).
% 63.81/64.07 tff(384,plain,
% 63.81/64.07 ((~(mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(n(e), n(e)), a(s(n(e)), s(n(e)))) | mem(a(n(e), n(e)), a(e, e))))) | (~mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e))))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[383, 382])).
% 63.81/64.07 tff(385,plain,
% 63.81/64.07 (~mem(a(n(e), n(e)), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[384, 304])).
% 63.81/64.07 tff(386,plain,
% 63.81/64.07 ($false),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[385, 302])).
% 63.81/64.07 tff(387,plain,(~mem(a(n(e), n(e)), u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.81/64.07 tff(388,plain,
% 63.81/64.07 (a(a(n(e), n(e)), a(n(e), n(e))) = a(n(n(e)), n(n(e)))),
% 63.81/64.07 inference(monotonicity,[status(thm)],[30, 30])).
% 63.81/64.07 tff(389,plain,
% 63.81/64.07 ((~![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)))))),
% 63.81/64.07 inference(quant_inst,[status(thm)],[])).
% 63.81/64.07 tff(390,plain,
% 63.81/64.07 (a(a(n(e), n(e)), a(n(e), n(e))) = u(a(n(e), n(e)), s(a(n(e), n(e))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[389, 118])).
% 63.81/64.07 tff(391,plain,
% 63.81/64.07 (u(a(n(e), n(e)), s(a(n(e), n(e)))) = a(a(n(e), n(e)), a(n(e), n(e)))),
% 63.81/64.07 inference(symmetry,[status(thm)],[390])).
% 63.81/64.07 tff(392,plain,
% 63.81/64.07 (s(n(n(e))) = s(a(n(e), n(e)))),
% 63.81/64.07 inference(symmetry,[status(thm)],[31])).
% 63.81/64.07 tff(393,plain,
% 63.81/64.07 (u(a(n(e), n(e)), s(n(n(e)))) = u(a(n(e), n(e)), s(a(n(e), n(e))))),
% 63.81/64.07 inference(monotonicity,[status(thm)],[392])).
% 63.81/64.07 tff(394,plain,
% 63.81/64.07 (u(a(n(e), n(e)), s(n(n(e)))) = a(n(n(e)), n(n(e)))),
% 63.81/64.07 inference(transitivity,[status(thm)],[393, 391, 388])).
% 63.81/64.07 tff(395,plain,
% 63.81/64.07 (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))),
% 63.81/64.07 inference(monotonicity,[status(thm)],[394])).
% 63.81/64.07 tff(396,plain,
% 63.81/64.07 (mem(a(n(e), n(e)), a(n(n(e)), n(n(e)))) <=> mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e)))))),
% 63.81/64.07 inference(symmetry,[status(thm)],[395])).
% 63.81/64.07 tff(397,plain,
% 63.81/64.07 ((~mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))) <=> (~mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))))),
% 63.81/64.07 inference(monotonicity,[status(thm)],[396])).
% 63.81/64.07 tff(398,assumption,(~mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))), introduced(assumption)).
% 63.81/64.07 tff(399,plain,
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% 63.81/64.07 inference(modus_ponens,[status(thm)],[398, 397])).
% 63.81/64.07 tff(400,plain,
% 63.81/64.07 ((~![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(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))))),
% 63.81/64.07 inference(quant_inst,[status(thm)],[])).
% 63.81/64.07 tff(401,plain,
% 63.81/64.07 (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e))))),
% 63.81/64.07 inference(unit_resolution,[status(thm)],[400, 49])).
% 63.81/64.07 tff(402,plain,
% 63.81/64.07 (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> mem(a(n(e), n(e)), s(n(n(e))))),
% 63.81/64.07 inference(monotonicity,[status(thm)],[31])).
% 63.81/64.07 tff(403,plain,
% 63.81/64.07 (mem(a(n(e), n(e)), s(n(n(e)))) <=> mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 63.81/64.07 inference(symmetry,[status(thm)],[402])).
% 63.81/64.07 tff(404,plain,
% 63.81/64.07 ((~mem(a(n(e), n(e)), s(n(n(e))))) <=> (~mem(a(n(e), n(e)), s(a(n(e), n(e)))))),
% 63.81/64.07 inference(monotonicity,[status(thm)],[403])).
% 63.81/64.07 tff(405,assumption,(~mem(a(n(e), n(e)), s(n(n(e))))), introduced(assumption)).
% 63.81/64.07 tff(406,plain,
% 63.81/64.07 (~mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 63.81/64.07 inference(modus_ponens,[status(thm)],[405, 404])).
% 63.81/64.07 tff(407,plain,
% 63.81/64.07 (((~![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)))))),
% 63.81/64.07 inference(rewrite,[status(thm)],[])).
% 63.81/64.07 tff(408,plain,
% 63.81/64.07 ((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))))),
% 63.81/64.07 inference(rewrite,[status(thm)],[])).
% 63.81/64.07 tff(409,plain,
% 63.81/64.07 ((a(n(e), n(e)) = a(n(e), n(e))) <=> $true),
% 63.81/64.07 inference(rewrite,[status(thm)],[])).
% 63.81/64.07 tff(410,plain,
% 63.81/64.07 ((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)),
% 63.81/64.07 inference(monotonicity,[status(thm)],[409])).
% 63.90/64.07 tff(411,plain,
% 63.90/64.07 ((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))))),
% 63.90/64.07 inference(transitivity,[status(thm)],[410, 408])).
% 63.90/64.07 tff(412,plain,
% 63.90/64.07 (((~![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)))))),
% 63.90/64.07 inference(monotonicity,[status(thm)],[411])).
% 63.90/64.07 tff(413,plain,
% 63.90/64.07 (((~![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)))))),
% 63.90/64.07 inference(transitivity,[status(thm)],[412, 407])).
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% 63.90/64.07 ((~![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))))),
% 63.90/64.07 inference(quant_inst,[status(thm)],[])).
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% 63.90/64.07 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 63.90/64.07 inference(modus_ponens,[status(thm)],[414, 413])).
% 63.90/64.07 tff(416,plain,
% 63.90/64.07 (mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[415, 7])).
% 63.90/64.07 tff(417,plain,
% 63.90/64.07 ($false),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[416, 406])).
% 63.90/64.07 tff(418,plain,(mem(a(n(e), n(e)), s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.07 tff(419,plain,
% 63.90/64.07 ((mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))) | (~mem(a(n(e), n(e)), s(n(n(e)))))),
% 63.90/64.07 inference(tautology,[status(thm)],[])).
% 63.90/64.07 tff(420,plain,
% 63.90/64.07 (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[419, 418])).
% 63.90/64.07 tff(421,plain,
% 63.90/64.07 ((~(mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))))) | mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) | (~(mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))))),
% 63.90/64.07 inference(tautology,[status(thm)],[])).
% 63.90/64.07 tff(422,plain,
% 63.90/64.07 ((~(mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))))) | mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e)))))),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[421, 420])).
% 63.90/64.07 tff(423,plain,
% 63.90/64.07 (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e)))))),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[422, 401])).
% 63.90/64.07 tff(424,plain,
% 63.90/64.07 ($false),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[423, 399])).
% 63.90/64.07 tff(425,plain,(mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.07 tff(426,plain,
% 63.90/64.07 (((~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e))))))) | ((~mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))) | mem(a(n(e), n(e)), u(n(e), n(s(n(e))))))) <=> ((~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e))))))) | (~mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))) | mem(a(n(e), n(e)), u(n(e), n(s(n(e))))))),
% 63.90/64.07 inference(rewrite,[status(thm)],[])).
% 63.90/64.07 tff(427,plain,
% 63.90/64.07 ((~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e))))))) | ((~mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))) | mem(a(n(e), n(e)), u(n(e), n(s(n(e))))))),
% 63.90/64.07 inference(quant_inst,[status(thm)],[])).
% 63.90/64.07 tff(428,plain,
% 63.90/64.07 ((~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e))))))) | (~mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))) | mem(a(n(e), n(e)), u(n(e), n(s(n(e)))))),
% 63.90/64.07 inference(modus_ponens,[status(thm)],[427, 426])).
% 63.90/64.07 tff(429,plain,
% 63.90/64.07 ($false),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[428, 425, 387, 297])).
% 63.90/64.07 tff(430,plain,(~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.07 tff(431,plain,
% 63.90/64.07 ((~((~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e))))))),
% 63.90/64.07 inference(tautology,[status(thm)],[])).
% 63.90/64.07 tff(432,plain,
% 63.90/64.07 ((~((~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e))))))),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[431, 430])).
% 63.90/64.07 tff(433,plain,
% 63.90/64.07 (~subq(a(n(n(e)), n(n(e))), u(n(e), n(s(n(e)))))),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[432, 296])).
% 63.90/64.07 tff(434,plain,
% 63.90/64.07 (~subq(s(n(e)), u(n(e), n(s(n(e)))))),
% 63.90/64.07 inference(modus_ponens,[status(thm)],[433, 290])).
% 63.90/64.07 tff(435,plain,
% 63.90/64.07 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e))))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e))))),
% 63.90/64.07 inference(monotonicity,[status(thm)],[338])).
% 63.90/64.07 tff(436,plain,
% 63.90/64.07 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e)))))),
% 63.90/64.07 inference(symmetry,[status(thm)],[435])).
% 63.90/64.07 tff(437,plain,
% 63.90/64.07 ((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e))))) <=> (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e))))))),
% 63.90/64.07 inference(monotonicity,[status(thm)],[436])).
% 63.90/64.07 tff(438,plain,
% 63.90/64.07 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))),
% 63.90/64.07 inference(monotonicity,[status(thm)],[298])).
% 63.90/64.07 tff(439,plain,
% 63.90/64.07 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e))))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.90/64.07 inference(symmetry,[status(thm)],[438])).
% 63.90/64.07 tff(440,plain,
% 63.90/64.07 ((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))) <=> (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e))))))),
% 63.90/64.07 inference(monotonicity,[status(thm)],[439])).
% 63.90/64.07 tff(441,assumption,(~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e))))))), introduced(assumption)).
% 63.90/64.07 tff(442,plain,
% 63.90/64.07 (((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e))))))),
% 63.90/64.07 inference(tautology,[status(thm)],[])).
% 63.90/64.07 tff(443,plain,
% 63.90/64.07 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[442, 441])).
% 63.90/64.07 tff(444,plain,
% 63.90/64.07 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.90/64.07 inference(modus_ponens,[status(thm)],[443, 440])).
% 63.90/64.07 tff(445,assumption,(~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(e, e))))), introduced(assumption)).
% 63.90/64.07 tff(446,plain,
% 63.90/64.07 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(e, e))))),
% 63.90/64.07 inference(quant_inst,[status(thm)],[])).
% 63.90/64.07 tff(447,plain,
% 63.90/64.07 ($false),
% 63.90/64.07 inference(unit_resolution,[status(thm)],[446, 49, 445])).
% 63.90/64.07 tff(448,plain,(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(e, e)))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.07 tff(449,plain,
% 63.90/64.07 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(e, e))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) | (~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(e, e))))),
% 63.90/64.07 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(450,plain,
% 63.90/64.08 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) | (~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(e, e))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[449, 448])).
% 63.90/64.08 tff(451,plain,
% 63.90/64.08 (~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(e, e)))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[450, 444])).
% 63.90/64.08 tff(452,plain,
% 63.90/64.08 ((mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(e, e))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e)))))),
% 63.90/64.08 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(453,plain,
% 63.90/64.08 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), a(s(n(e)), s(n(e))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[452, 451])).
% 63.90/64.08 tff(454,plain,
% 63.90/64.08 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e)))))),
% 63.90/64.08 inference(modus_ponens,[status(thm)],[453, 437])).
% 63.90/64.08 tff(455,plain,
% 63.90/64.08 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))))),
% 63.90/64.08 inference(quant_inst,[status(thm)],[])).
% 63.90/64.08 tff(456,plain,
% 63.90/64.08 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[455, 49])).
% 63.90/64.08 tff(457,plain,
% 63.90/64.08 (((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))),
% 63.90/64.08 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(458,plain,
% 63.90/64.08 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[457, 441])).
% 63.90/64.08 tff(459,plain,
% 63.90/64.08 ((mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e))))),
% 63.90/64.08 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(460,plain,
% 63.90/64.08 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[459, 458])).
% 63.90/64.08 tff(461,plain,
% 63.90/64.08 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e))))) | (~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))))),
% 63.90/64.08 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(462,plain,
% 63.90/64.08 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e)))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[461, 460])).
% 63.90/64.08 tff(463,plain,
% 63.90/64.08 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(s(n(e)), s(s(n(e)))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[462, 456])).
% 63.90/64.08 tff(464,plain,
% 63.90/64.08 ($false),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[463, 454])).
% 63.90/64.08 tff(465,plain,((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.08 tff(466,assumption,((~((~subq(s(n(e)), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))))))), introduced(assumption)).
% 63.90/64.08 tff(467,plain,
% 63.90/64.08 ((~![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(s(n(e)), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))))))))),
% 63.90/64.08 inference(quant_inst,[status(thm)],[])).
% 63.90/64.08 tff(468,plain,
% 63.90/64.08 ($false),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[467, 229, 466])).
% 63.90/64.08 tff(469,plain,(~((~((~subq(s(n(e)), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e))))))))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.08 tff(470,plain,
% 63.90/64.08 (((~((~subq(s(n(e)), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))))))) | (subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e))))))))),
% 63.90/64.08 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(471,plain,
% 63.90/64.08 (subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[470, 469])).
% 63.90/64.08 tff(472,plain,
% 63.90/64.08 ((~(subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e))))))))) | subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))))),
% 63.90/64.08 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(473,plain,
% 63.90/64.08 (subq(s(n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), s(n(e))), u(n(e), n(s(n(e)))))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[472, 471])).
% 63.90/64.08 tff(474,plain,
% 63.90/64.08 (subq(s(n(e)), u(n(e), n(s(n(e)))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[473, 465])).
% 63.90/64.08 tff(475,plain,
% 63.90/64.08 ($false),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[474, 434])).
% 63.90/64.08 tff(476,plain,(~(s(n(e)) = a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.08 tff(477,plain,
% 63.90/64.08 ((~(mem(s(n(e)), s(a(n(n(e)), n(n(e))))) <=> (s(n(e)) = a(n(n(e)), n(n(e)))))) | (~mem(s(n(e)), s(a(n(n(e)), n(n(e)))))) | (s(n(e)) = a(n(n(e)), n(n(e))))),
% 63.90/64.08 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(478,plain,
% 63.90/64.08 ((~(mem(s(n(e)), s(a(n(n(e)), n(n(e))))) <=> (s(n(e)) = a(n(n(e)), n(n(e)))))) | (~mem(s(n(e)), s(a(n(n(e)), n(n(e))))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[477, 476])).
% 63.90/64.08 tff(479,plain,
% 63.90/64.08 (~mem(s(n(e)), s(a(n(n(e)), n(n(e)))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[478, 286])).
% 63.90/64.08 tff(480,plain,
% 63.90/64.08 ($false),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[479, 284])).
% 63.90/64.08 tff(481,plain,(~mem(s(n(e)), s(n(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.08 tff(482,plain,
% 63.90/64.08 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))),
% 63.90/64.08 inference(quant_inst,[status(thm)],[])).
% 63.90/64.08 tff(483,plain,
% 63.90/64.08 (mem(s(n(e)), u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[482, 49])).
% 63.90/64.08 tff(484,plain,
% 63.90/64.08 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))) = u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.90/64.08 inference(quant_inst,[status(thm)],[])).
% 63.90/64.08 tff(485,plain,
% 63.90/64.08 (a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))) = u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[484, 118])).
% 63.90/64.08 tff(486,plain,
% 63.90/64.08 (u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))) = a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e)))))),
% 63.90/64.08 inference(symmetry,[status(thm)],[485])).
% 63.90/64.08 tff(487,plain,
% 63.90/64.08 (u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e))))) = u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))),
% 63.90/64.08 inference(monotonicity,[status(thm)],[486])).
% 63.90/64.08 tff(488,plain,
% 63.90/64.08 (mem(s(n(e)), u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.90/64.08 inference(monotonicity,[status(thm)],[487])).
% 63.90/64.08 tff(489,plain,
% 63.90/64.08 (mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))) <=> mem(s(n(e)), u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e))))))),
% 63.90/64.08 inference(symmetry,[status(thm)],[488])).
% 63.90/64.08 tff(490,assumption,(~(mem(a(e, e), p(s(n(e)))) <=> subq(a(e, e), s(n(e))))), introduced(assumption)).
% 63.90/64.08 tff(491,plain,
% 63.90/64.08 (^[X: $i, Y: $i] : refl((mem(X, p(Y)) <=> subq(X, Y)) <=> (mem(X, p(Y)) <=> subq(X, Y)))),
% 63.90/64.08 inference(bind,[status(th)],[])).
% 63.90/64.08 tff(492,plain,
% 63.90/64.08 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y)) <=> ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 63.90/64.08 inference(quant_intro,[status(thm)],[491])).
% 63.90/64.08 tff(493,plain,
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% 63.90/64.08 tff(524,plain,(mem(s(n(e)), p(p(s(n(e))))) <=> subq(s(n(e)), p(s(n(e))))), inference(lemma,lemma(discharge,[]))).
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% 63.90/64.08 inference(unit_resolution,[status(thm)],[526, 520])).
% 63.90/64.08 tff(528,assumption,(~(mem(s(n(e)), p(u(n(e), n(s(n(e)))))) <=> subq(s(n(e)), u(n(e), n(s(n(e))))))), introduced(assumption)).
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% 63.90/64.08 inference(tautology,[status(thm)],[])).
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% 63.90/64.08 inference(unit_resolution,[status(thm)],[532, 531])).
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% 63.90/64.08 inference(tautology,[status(thm)],[])).
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% 63.90/64.08 inference(unit_resolution,[status(thm)],[535, 534])).
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% 63.90/64.08 tff(538,assumption,(((~mem(s(n(e)), p(u(n(e), n(s(n(e))))))) | mem(s(n(e)), p(p(s(n(e)))))) <=> mem(s(n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))), introduced(assumption)).
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% 63.90/64.08 inference(quant_intro,[status(thm)],[539])).
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% 63.90/64.08 inference(quant_intro,[status(thm)],[541])).
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% 63.90/64.08 tff(557,assumption,(~(mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) <=> (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))), introduced(assumption)).
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% 63.90/64.08 tff(560,plain,(mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) <=> (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.08 tff(561,plain,
% 63.90/64.08 ((~(mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) <=> (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))) | mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) | (~(mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.90/64.08 inference(tautology,[status(thm)],[])).
% 63.90/64.08 tff(562,plain,
% 63.90/64.08 (mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) | (~(mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[561, 560])).
% 63.90/64.08 tff(563,plain,
% 63.90/64.08 (mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))),
% 63.90/64.08 inference(unit_resolution,[status(thm)],[562, 556])).
% 63.90/64.08 tff(564,assumption,(~mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))), introduced(assumption)).
% 63.90/64.08 tff(565,assumption,(mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))), introduced(assumption)).
% 63.90/64.08 tff(566,plain,
% 63.90/64.08 ((~![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(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))))) | (~(subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))))))))),
% 63.90/64.08 inference(quant_inst,[status(thm)],[])).
% 63.90/64.08 tff(567,plain,
% 63.90/64.08 (~((~((~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))))) | (~(subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[566, 229])).
% 63.90/64.09 tff(568,plain,
% 63.90/64.09 (((~((~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))))) | (~(subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))))))) | ((~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))))),
% 63.90/64.09 inference(tautology,[status(thm)],[])).
% 63.90/64.09 tff(569,plain,
% 63.90/64.09 ((~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[568, 567])).
% 63.90/64.09 tff(570,plain,
% 63.90/64.09 (subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))) <=> subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.90/64.09 inference(rewrite,[status(thm)],[])).
% 63.90/64.09 tff(571,plain,
% 63.90/64.09 ((~(~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) <=> subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.90/64.09 inference(rewrite,[status(thm)],[])).
% 63.90/64.09 tff(572,axiom,(~(~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nsubq_2252_2248')).
% 63.90/64.09 tff(573,plain,
% 63.90/64.09 (subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.90/64.09 inference(modus_ponens,[status(thm)],[572, 571])).
% 63.90/64.09 tff(574,plain,
% 63.90/64.09 (subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.90/64.09 inference(modus_ponens,[status(thm)],[573, 570])).
% 63.90/64.09 tff(575,plain,
% 63.90/64.09 ((~((~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))))) | (~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))),
% 63.90/64.09 inference(tautology,[status(thm)],[])).
% 63.90/64.09 tff(576,plain,
% 63.90/64.09 ((~((~subq(u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))))) | ![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[575, 574])).
% 63.90/64.09 tff(577,plain,
% 63.90/64.09 (![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[576, 569])).
% 63.90/64.09 tff(578,plain,
% 63.90/64.09 (((~![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) | ((~mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) <=> ((~![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) | (~mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))),
% 63.90/64.09 inference(rewrite,[status(thm)],[])).
% 63.90/64.09 tff(579,plain,
% 63.90/64.09 ((~![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) | ((~mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))),
% 63.90/64.09 inference(quant_inst,[status(thm)],[])).
% 63.90/64.09 tff(580,plain,
% 63.90/64.09 ((~![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) | (~mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.90/64.09 inference(modus_ponens,[status(thm)],[579, 578])).
% 63.90/64.09 tff(581,plain,
% 63.90/64.09 ($false),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[580, 577, 565, 564])).
% 63.90/64.09 tff(582,plain,(mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))) | (~mem(s(n(e)), u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.09 tff(583,plain,
% 63.90/64.09 (mem(s(n(e)), u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[582, 563])).
% 63.90/64.09 tff(584,plain,
% 63.90/64.09 (mem(s(n(e)), u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e))))))),
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% 63.90/64.09 tff(585,plain,
% 63.90/64.09 ((~(mem(s(n(e)), u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))) | (~mem(s(n(e)), u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e))))))) | (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))),
% 63.90/64.09 inference(tautology,[status(thm)],[])).
% 63.90/64.09 tff(586,plain,
% 63.90/64.09 (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[585, 584, 483])).
% 63.90/64.09 tff(587,plain,
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% 63.90/64.09 inference(tautology,[status(thm)],[])).
% 63.90/64.09 tff(588,plain,
% 63.90/64.09 (mem(s(n(e)), s(n(n(n(e))))) | mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[587, 586])).
% 63.90/64.09 tff(589,plain,
% 63.90/64.09 (mem(s(n(e)), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[588, 481])).
% 63.90/64.09 tff(590,plain,
% 63.90/64.09 (mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))))),
% 63.90/64.09 inference(modus_ponens,[status(thm)],[589, 278])).
% 63.90/64.09 tff(591,assumption,(~mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))))), introduced(assumption)).
% 63.90/64.09 tff(592,plain,
% 63.90/64.09 ($false),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[591, 590])).
% 63.90/64.09 tff(593,plain,(mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.09 tff(594,plain,
% 63.90/64.09 ((~(mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))))) | (~mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))))) | (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))))),
% 63.90/64.09 inference(tautology,[status(thm)],[])).
% 63.90/64.09 tff(595,plain,
% 63.90/64.09 ((~(mem(s(n(e)), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))))) | (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[594, 593])).
% 63.90/64.09 tff(596,plain,
% 63.90/64.09 (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[595, 272])).
% 63.90/64.09 tff(597,assumption,(~(mem(s(n(e)), s(u(n(e), n(s(n(e)))))) <=> (s(n(e)) = u(n(e), n(s(n(e))))))), introduced(assumption)).
% 63.90/64.09 tff(598,plain,
% 63.90/64.09 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(s(n(e)), s(u(n(e), n(s(n(e)))))) <=> (s(n(e)) = u(n(e), n(s(n(e))))))),
% 63.90/64.09 inference(quant_inst,[status(thm)],[])).
% 63.90/64.09 tff(599,plain,
% 63.90/64.09 ($false),
% 63.90/64.09 inference(unit_resolution,[status(thm)],[598, 7, 597])).
% 63.90/64.09 tff(600,plain,(mem(s(n(e)), s(u(n(e), n(s(n(e)))))) <=> (s(n(e)) = u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.90/64.09 tff(601,plain,
% 63.90/64.09 ((s(n(e)) = u(n(e), n(s(n(e))))) <=> (u(n(e), n(s(n(e)))) = s(n(e)))),
% 63.90/64.09 inference(commutativity,[status(thm)],[])).
% 63.90/64.09 tff(602,plain,
% 63.90/64.09 ((u(n(e), n(s(n(e)))) = s(n(e))) <=> (s(n(e)) = u(n(e), n(s(n(e)))))),
% 63.90/64.09 inference(symmetry,[status(thm)],[601])).
% 63.90/64.09 tff(603,plain,
% 63.90/64.09 ((~(u(n(e), n(s(n(e)))) = s(n(e)))) <=> (~(s(n(e)) = u(n(e), n(s(n(e))))))),
% 63.90/64.09 inference(monotonicity,[status(thm)],[602])).
% 63.90/64.09 tff(604,assumption,(u(n(e), n(s(n(e)))) = s(n(e))), introduced(assumption)).
% 63.90/64.09 tff(605,plain,
% 63.90/64.09 (subq(a(e, e), u(n(e), n(s(n(e))))) <=> subq(a(e, e), s(n(e)))),
% 63.90/64.09 inference(monotonicity,[status(thm)],[604])).
% 63.90/64.09 tff(606,plain,
% 63.90/64.09 (subq(a(e, e), s(n(e))) <=> subq(a(e, e), u(n(e), n(s(n(e)))))),
% 63.90/64.09 inference(symmetry,[status(thm)],[605])).
% 63.90/64.09 tff(607,plain,
% 63.90/64.09 ((~subq(a(e, e), s(n(e)))) <=> (~subq(a(e, e), u(n(e), n(s(n(e))))))),
% 63.90/64.09 inference(monotonicity,[status(thm)],[606])).
% 63.90/64.09 tff(608,plain,
% 63.90/64.09 (~subq(a(e, e), u(n(e), n(s(n(e)))))),
% 63.90/64.09 inference(modus_ponens,[status(thm)],[237, 607])).
% 63.90/64.09 tff(609,assumption,((~((~subq(a(e, e), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))))))), introduced(assumption)).
% 63.90/64.09 tff(610,plain,
% 63.90/64.09 ((~![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(e, e), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))))))))),
% 63.93/64.09 inference(quant_inst,[status(thm)],[])).
% 63.93/64.09 tff(611,plain,
% 63.93/64.09 ($false),
% 63.93/64.09 inference(unit_resolution,[status(thm)],[610, 229, 609])).
% 63.93/64.09 tff(612,plain,(~((~((~subq(a(e, e), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e))))))))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.09 tff(613,plain,
% 63.93/64.09 (((~((~subq(a(e, e), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))))))) | (subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e))))))))),
% 63.93/64.09 inference(tautology,[status(thm)],[])).
% 63.93/64.09 tff(614,plain,
% 63.93/64.09 (subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))))),
% 63.93/64.09 inference(unit_resolution,[status(thm)],[613, 612])).
% 63.93/64.09 tff(615,plain,
% 63.93/64.09 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))),
% 63.93/64.09 inference(monotonicity,[status(thm)],[298])).
% 63.93/64.09 tff(616,plain,
% 63.93/64.09 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e))))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.09 inference(symmetry,[status(thm)],[615])).
% 63.93/64.09 tff(617,plain,
% 63.93/64.09 ((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))) <=> (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e))))))),
% 63.93/64.09 inference(monotonicity,[status(thm)],[616])).
% 63.93/64.09 tff(618,assumption,(~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e))))))), introduced(assumption)).
% 63.93/64.09 tff(619,plain,
% 63.93/64.09 (((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e))))))),
% 63.93/64.09 inference(tautology,[status(thm)],[])).
% 63.93/64.09 tff(620,plain,
% 63.93/64.09 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))),
% 63.93/64.09 inference(unit_resolution,[status(thm)],[619, 618])).
% 63.93/64.09 tff(621,plain,
% 63.93/64.09 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.09 inference(modus_ponens,[status(thm)],[620, 617])).
% 63.93/64.09 tff(622,plain,
% 63.93/64.09 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))))),
% 63.93/64.09 inference(quant_inst,[status(thm)],[])).
% 63.93/64.09 tff(623,plain,
% 63.93/64.09 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e)))),
% 63.93/64.09 inference(unit_resolution,[status(thm)],[622, 49])).
% 63.93/64.09 tff(624,plain,
% 63.93/64.09 (((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))),
% 63.93/64.09 inference(tautology,[status(thm)],[])).
% 63.93/64.09 tff(625,plain,
% 63.93/64.09 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))),
% 63.93/64.09 inference(unit_resolution,[status(thm)],[624, 618])).
% 63.93/64.09 tff(626,plain,
% 63.93/64.09 ((mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e)))),
% 63.93/64.09 inference(tautology,[status(thm)],[])).
% 63.93/64.09 tff(627,plain,
% 63.93/64.09 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[626, 625])).
% 63.93/64.10 tff(628,plain,
% 63.93/64.10 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e))))) | (~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(629,plain,
% 63.93/64.10 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[628, 627])).
% 63.93/64.10 tff(630,plain,
% 63.93/64.10 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[629, 623])).
% 63.93/64.10 tff(631,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[630, 621])).
% 63.93/64.10 tff(632,plain,((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(633,plain,
% 63.93/64.10 ((~(subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e))))))))) | subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e)))))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(634,plain,
% 63.93/64.10 ((~(subq(a(e, e), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(e, e)), u(n(e), n(s(n(e))))))))) | subq(a(e, e), u(n(e), n(s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[633, 632])).
% 63.93/64.10 tff(635,plain,
% 63.93/64.10 (subq(a(e, e), u(n(e), n(s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[634, 614])).
% 63.93/64.10 tff(636,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[635, 608])).
% 63.93/64.10 tff(637,plain,(~(u(n(e), n(s(n(e)))) = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(638,plain,
% 63.93/64.10 (~(s(n(e)) = u(n(e), n(s(n(e)))))),
% 63.93/64.10 inference(modus_ponens,[status(thm)],[637, 603])).
% 63.93/64.10 tff(639,plain,
% 63.93/64.10 ((~(mem(s(n(e)), s(u(n(e), n(s(n(e)))))) <=> (s(n(e)) = u(n(e), n(s(n(e))))))) | (~mem(s(n(e)), s(u(n(e), n(s(n(e))))))) | (s(n(e)) = u(n(e), n(s(n(e)))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(640,plain,
% 63.93/64.10 ((~(mem(s(n(e)), s(u(n(e), n(s(n(e)))))) <=> (s(n(e)) = u(n(e), n(s(n(e))))))) | (~mem(s(n(e)), s(u(n(e), n(s(n(e)))))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[639, 638])).
% 63.93/64.10 tff(641,plain,
% 63.93/64.10 (~mem(s(n(e)), s(u(n(e), n(s(n(e))))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[640, 600])).
% 63.93/64.10 tff(642,plain,
% 63.93/64.10 ((~(mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))))) | mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(643,plain,
% 63.93/64.10 ((~(mem(s(n(e)), s(u(n(e), n(s(n(e)))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))))) | mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[642, 641])).
% 63.93/64.10 tff(644,plain,
% 63.93/64.10 (mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[643, 596])).
% 63.93/64.10 tff(645,assumption,(~(mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e)))))))), introduced(assumption)).
% 63.93/64.10 tff(646,plain,
% 63.93/64.10 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e))))))))),
% 63.93/64.10 inference(rewrite,[status(thm)],[])).
% 63.93/64.10 tff(647,plain,
% 63.93/64.10 ((mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(s(n(e))))) | mem(s(n(e)), s(n(n(e)))))) <=> (mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e)))))))),
% 63.93/64.10 inference(rewrite,[status(thm)],[])).
% 63.93/64.10 tff(648,plain,
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% 63.93/64.10 inference(monotonicity,[status(thm)],[647])).
% 63.93/64.10 tff(649,plain,
% 63.93/64.10 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(s(n(e))))) | mem(s(n(e)), s(n(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e))))))))),
% 63.93/64.10 inference(transitivity,[status(thm)],[648, 646])).
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% 63.93/64.10 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(s(n(e))))) | mem(s(n(e)), s(n(n(e))))))),
% 63.93/64.10 inference(quant_inst,[status(thm)],[])).
% 63.93/64.10 tff(651,plain,
% 63.93/64.10 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e)))))))),
% 63.93/64.10 inference(modus_ponens,[status(thm)],[650, 649])).
% 63.93/64.10 tff(652,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[651, 49, 645])).
% 63.93/64.10 tff(653,plain,(mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(654,plain,
% 63.93/64.10 ((~(mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e)))))))) | (~mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))) | (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e))))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(655,plain,
% 63.93/64.10 ((~mem(s(n(e)), u(s(n(n(e))), s(n(s(n(e))))))) | (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e))))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[654, 653])).
% 63.93/64.10 tff(656,plain,
% 63.93/64.10 (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[655, 644])).
% 63.93/64.10 tff(657,plain,
% 63.93/64.10 ((~(mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e))))))) | mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e)))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(658,plain,
% 63.93/64.10 (mem(s(n(e)), s(n(n(e)))) | mem(s(n(e)), s(n(s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[657, 656])).
% 63.93/64.10 tff(659,plain,
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% 63.93/64.10 inference(unit_resolution,[status(thm)],[658, 268])).
% 63.93/64.10 tff(660,plain,
% 63.93/64.10 (mem(s(n(e)), s(a(s(n(e)), s(n(e)))))),
% 63.93/64.10 inference(modus_ponens,[status(thm)],[659, 22])).
% 63.93/64.10 tff(661,assumption,(~(mem(s(n(e)), s(a(s(n(e)), s(n(e))))) <=> (s(n(e)) = a(s(n(e)), s(n(e)))))), introduced(assumption)).
% 63.93/64.10 tff(662,plain,
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% 63.93/64.10 inference(quant_inst,[status(thm)],[])).
% 63.93/64.10 tff(663,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[662, 7, 661])).
% 63.93/64.10 tff(664,plain,(mem(s(n(e)), s(a(s(n(e)), s(n(e))))) <=> (s(n(e)) = a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(665,plain,
% 63.93/64.10 ((~(mem(s(n(e)), s(a(s(n(e)), s(n(e))))) <=> (s(n(e)) = a(s(n(e)), s(n(e)))))) | (~mem(s(n(e)), s(a(s(n(e)), s(n(e)))))) | (s(n(e)) = a(s(n(e)), s(n(e))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(666,plain,
% 63.93/64.10 ((~mem(s(n(e)), s(a(s(n(e)), s(n(e)))))) | (s(n(e)) = a(s(n(e)), s(n(e))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[665, 664])).
% 63.93/64.10 tff(667,plain,
% 63.93/64.10 (s(n(e)) = a(s(n(e)), s(n(e)))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[666, 660])).
% 63.93/64.10 tff(668,plain,
% 63.93/64.10 (s(a(e, e)) = a(s(n(e)), s(n(e)))),
% 63.93/64.10 inference(transitivity,[status(thm)],[93, 667])).
% 63.93/64.10 tff(669,plain,
% 63.93/64.10 (a(s(n(e)), s(n(e))) = s(n(e))),
% 63.93/64.10 inference(symmetry,[status(thm)],[667])).
% 63.93/64.10 tff(670,plain,
% 63.93/64.10 (mem(a(s(n(e)), s(n(e))), s(a(e, e))) <=> mem(s(n(e)), a(s(n(e)), s(n(e))))),
% 63.93/64.10 inference(monotonicity,[status(thm)],[669, 668])).
% 63.93/64.10 tff(671,plain,
% 63.93/64.10 (mem(s(n(e)), a(s(n(e)), s(n(e)))) <=> mem(a(s(n(e)), s(n(e))), s(a(e, e)))),
% 63.93/64.10 inference(symmetry,[status(thm)],[670])).
% 63.93/64.10 tff(672,plain,
% 63.93/64.10 (mem(s(n(e)), u(s(n(e)), s(s(n(e))))) <=> mem(s(n(e)), a(s(n(e)), s(n(e))))),
% 63.93/64.10 inference(monotonicity,[status(thm)],[338])).
% 63.93/64.10 tff(673,plain,
% 63.93/64.10 (mem(s(n(e)), a(s(n(e)), s(n(e)))) <=> mem(s(n(e)), u(s(n(e)), s(s(n(e)))))),
% 63.93/64.10 inference(symmetry,[status(thm)],[672])).
% 63.93/64.10 tff(674,plain,
% 63.93/64.10 ((~mem(s(n(e)), a(s(n(e)), s(n(e))))) <=> (~mem(s(n(e)), u(s(n(e)), s(s(n(e))))))),
% 63.93/64.10 inference(monotonicity,[status(thm)],[673])).
% 63.93/64.10 tff(675,assumption,(~mem(s(n(e)), a(s(n(e)), s(n(e))))), introduced(assumption)).
% 63.93/64.10 tff(676,plain,
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% 63.93/64.10 inference(modus_ponens,[status(thm)],[675, 674])).
% 63.93/64.10 tff(677,plain,
% 63.93/64.10 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(s(n(e)), s(s(n(e)))) | mem(s(n(e)), s(n(e)))))),
% 63.93/64.10 inference(quant_inst,[status(thm)],[])).
% 63.93/64.10 tff(678,plain,
% 63.93/64.10 (mem(s(n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(s(n(e)), s(s(n(e)))) | mem(s(n(e)), s(n(e))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[677, 49])).
% 63.93/64.10 tff(679,assumption,(~mem(s(n(e)), s(s(n(e))))), introduced(assumption)).
% 63.93/64.10 tff(680,plain,
% 63.93/64.10 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(s(n(e)), s(s(n(e))))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(s(n(e)), s(s(n(e)))))),
% 63.93/64.10 inference(rewrite,[status(thm)],[])).
% 63.93/64.10 tff(681,plain,
% 63.93/64.10 ((mem(s(n(e)), s(s(n(e)))) <=> $true) <=> mem(s(n(e)), s(s(n(e))))),
% 63.93/64.10 inference(rewrite,[status(thm)],[])).
% 63.93/64.10 tff(682,plain,
% 63.93/64.10 ((s(n(e)) = s(n(e))) <=> $true),
% 63.93/64.10 inference(rewrite,[status(thm)],[])).
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% 63.93/64.10 ((mem(s(n(e)), s(s(n(e)))) <=> (s(n(e)) = s(n(e)))) <=> (mem(s(n(e)), s(s(n(e)))) <=> $true)),
% 63.93/64.10 inference(monotonicity,[status(thm)],[682])).
% 63.93/64.10 tff(684,plain,
% 63.93/64.10 ((mem(s(n(e)), s(s(n(e)))) <=> (s(n(e)) = s(n(e)))) <=> mem(s(n(e)), s(s(n(e))))),
% 63.93/64.10 inference(transitivity,[status(thm)],[683, 681])).
% 63.93/64.10 tff(685,plain,
% 63.93/64.10 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(s(n(e)), s(s(n(e)))) <=> (s(n(e)) = s(n(e))))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(s(n(e)), s(s(n(e)))))),
% 63.93/64.10 inference(monotonicity,[status(thm)],[684])).
% 63.93/64.10 tff(686,plain,
% 63.93/64.10 (((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(s(n(e)), s(s(n(e)))) <=> (s(n(e)) = s(n(e))))) <=> ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(s(n(e)), s(s(n(e)))))),
% 63.93/64.10 inference(transitivity,[status(thm)],[685, 680])).
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% 63.93/64.10 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(s(n(e)), s(s(n(e)))) <=> (s(n(e)) = s(n(e))))),
% 63.93/64.10 inference(quant_inst,[status(thm)],[])).
% 63.93/64.10 tff(688,plain,
% 63.93/64.10 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(s(n(e)), s(s(n(e))))),
% 63.93/64.10 inference(modus_ponens,[status(thm)],[687, 686])).
% 63.93/64.10 tff(689,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[688, 7, 679])).
% 63.93/64.10 tff(690,plain,(mem(s(n(e)), s(s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(691,plain,
% 63.93/64.10 ((mem(s(n(e)), s(s(n(e)))) | mem(s(n(e)), s(n(e)))) | (~mem(s(n(e)), s(s(n(e)))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(692,plain,
% 63.93/64.10 (mem(s(n(e)), s(s(n(e)))) | mem(s(n(e)), s(n(e)))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[691, 690])).
% 63.93/64.10 tff(693,plain,
% 63.93/64.10 ((~(mem(s(n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(s(n(e)), s(s(n(e)))) | mem(s(n(e)), s(n(e)))))) | mem(s(n(e)), u(s(n(e)), s(s(n(e))))) | (~(mem(s(n(e)), s(s(n(e)))) | mem(s(n(e)), s(n(e)))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(694,plain,
% 63.93/64.10 ((~(mem(s(n(e)), u(s(n(e)), s(s(n(e))))) <=> (mem(s(n(e)), s(s(n(e)))) | mem(s(n(e)), s(n(e)))))) | mem(s(n(e)), u(s(n(e)), s(s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[693, 692])).
% 63.93/64.10 tff(695,plain,
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% 63.93/64.10 inference(unit_resolution,[status(thm)],[694, 678])).
% 63.93/64.10 tff(696,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[695, 676])).
% 63.93/64.10 tff(697,plain,(mem(s(n(e)), a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(698,plain,
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% 63.93/64.10 inference(modus_ponens,[status(thm)],[697, 671])).
% 63.93/64.10 tff(699,plain,
% 63.93/64.10 ((a(s(n(e)), s(n(e))) = a(e, e)) <=> (a(e, e) = a(s(n(e)), s(n(e))))),
% 63.93/64.10 inference(commutativity,[status(thm)],[])).
% 63.93/64.10 tff(700,plain,
% 63.93/64.10 ((a(e, e) = a(s(n(e)), s(n(e)))) <=> (a(s(n(e)), s(n(e))) = a(e, e))),
% 63.93/64.10 inference(symmetry,[status(thm)],[699])).
% 63.93/64.10 tff(701,plain,
% 63.93/64.10 ((~(a(e, e) = a(s(n(e)), s(n(e))))) <=> (~(a(s(n(e)), s(n(e))) = a(e, e)))),
% 63.93/64.10 inference(monotonicity,[status(thm)],[700])).
% 63.93/64.10 tff(702,assumption,(a(e, e) = a(s(n(e)), s(n(e)))), introduced(assumption)).
% 63.93/64.10 tff(703,plain,
% 63.93/64.10 (mem(a(e, e), p(p(s(n(e))))) <=> mem(a(s(n(e)), s(n(e))), p(p(s(n(e)))))),
% 63.93/64.10 inference(monotonicity,[status(thm)],[702])).
% 63.93/64.10 tff(704,plain,
% 63.93/64.10 (mem(a(s(n(e)), s(n(e))), p(p(s(n(e))))) <=> mem(a(e, e), p(p(s(n(e)))))),
% 63.93/64.10 inference(symmetry,[status(thm)],[703])).
% 63.93/64.10 tff(705,plain,
% 63.93/64.10 ((~mem(a(s(n(e)), s(n(e))), p(p(s(n(e)))))) <=> (~mem(a(e, e), p(p(s(n(e))))))),
% 63.93/64.10 inference(monotonicity,[status(thm)],[704])).
% 63.93/64.10 tff(706,assumption,(~(mem(a(s(n(e)), s(n(e))), p(p(s(n(e))))) <=> subq(a(s(n(e)), s(n(e))), p(s(n(e)))))), introduced(assumption)).
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% 63.93/64.10 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(a(s(n(e)), s(n(e))), p(p(s(n(e))))) <=> subq(a(s(n(e)), s(n(e))), p(s(n(e)))))),
% 63.93/64.10 inference(quant_inst,[status(thm)],[])).
% 63.93/64.10 tff(708,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[707, 497, 706])).
% 63.93/64.10 tff(709,plain,(mem(a(s(n(e)), s(n(e))), p(p(s(n(e))))) <=> subq(a(s(n(e)), s(n(e))), p(s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(710,assumption,((~((~subq(a(s(n(e)), s(n(e))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e))))))) | (~(subq(a(s(n(e)), s(n(e))), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(s(n(e)), s(n(e)))), a(s(n(e)), s(n(e))))) | mem(tptp_fun_Z_0(p(s(n(e))), a(s(n(e)), s(n(e)))), p(s(n(e))))))))), introduced(assumption)).
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% 63.93/64.10 inference(quant_inst,[status(thm)],[])).
% 63.93/64.10 tff(712,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[711, 229, 710])).
% 63.93/64.10 tff(713,plain,(~((~((~subq(a(s(n(e)), s(n(e))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e))))))) | (~(subq(a(s(n(e)), s(n(e))), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(s(n(e)), s(n(e)))), a(s(n(e)), s(n(e))))) | mem(tptp_fun_Z_0(p(s(n(e))), a(s(n(e)), s(n(e)))), p(s(n(e)))))))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(714,plain,
% 63.93/64.10 (((~((~subq(a(s(n(e)), s(n(e))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e))))))) | (~(subq(a(s(n(e)), s(n(e))), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(s(n(e)), s(n(e)))), a(s(n(e)), s(n(e))))) | mem(tptp_fun_Z_0(p(s(n(e))), a(s(n(e)), s(n(e)))), p(s(n(e))))))))) | ((~subq(a(s(n(e)), s(n(e))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e))))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(715,plain,
% 63.93/64.10 ((~subq(a(s(n(e)), s(n(e))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[714, 713])).
% 63.93/64.10 tff(716,assumption,(![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e)))))), introduced(assumption)).
% 63.93/64.10 tff(717,plain,
% 63.93/64.10 (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> mem(a(e, e), a(s(n(e)), s(n(e))))),
% 63.93/64.10 inference(monotonicity,[status(thm)],[338])).
% 63.93/64.10 tff(718,plain,
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% 63.93/64.10 inference(symmetry,[status(thm)],[717])).
% 63.93/64.10 tff(719,plain,
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% 63.93/64.10 inference(monotonicity,[status(thm)],[718])).
% 63.93/64.10 tff(720,assumption,(~mem(a(e, e), a(s(n(e)), s(n(e))))), introduced(assumption)).
% 63.93/64.10 tff(721,plain,
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% 63.93/64.10 inference(modus_ponens,[status(thm)],[720, 719])).
% 63.93/64.10 tff(722,plain,
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% 63.93/64.10 inference(quant_inst,[status(thm)],[])).
% 63.93/64.10 tff(723,plain,
% 63.93/64.10 (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))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[722, 49])).
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% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(725,plain,
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% 63.93/64.10 inference(unit_resolution,[status(thm)],[724, 110])).
% 63.93/64.10 tff(726,plain,
% 63.93/64.10 ((~(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(s(n(e)))) | mem(a(e, e), s(n(e)))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(727,plain,
% 63.93/64.10 ((~(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)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[726, 725])).
% 63.93/64.10 tff(728,plain,
% 63.93/64.10 (mem(a(e, e), u(s(n(e)), s(s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[727, 723])).
% 63.93/64.10 tff(729,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[728, 721])).
% 63.93/64.10 tff(730,plain,(mem(a(e, e), a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(731,plain,
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% 63.93/64.10 inference(rewrite,[status(thm)],[])).
% 63.93/64.10 tff(732,plain,
% 63.93/64.10 ((~![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e)))))) | ((~mem(a(e, e), a(s(n(e)), s(n(e))))) | mem(a(e, e), p(s(n(e)))))),
% 63.93/64.10 inference(quant_inst,[status(thm)],[])).
% 63.93/64.10 tff(733,plain,
% 63.93/64.10 ((~![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e)))))) | (~mem(a(e, e), a(s(n(e)), s(n(e))))) | mem(a(e, e), p(s(n(e))))),
% 63.93/64.10 inference(modus_ponens,[status(thm)],[732, 731])).
% 63.93/64.10 tff(734,plain,
% 63.93/64.10 ($false),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[733, 730, 503, 716])).
% 63.93/64.10 tff(735,plain,(~![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.10 tff(736,plain,
% 63.93/64.10 ((~((~subq(a(s(n(e)), s(n(e))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e))))))) | (~subq(a(s(n(e)), s(n(e))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e)))))),
% 63.93/64.10 inference(tautology,[status(thm)],[])).
% 63.93/64.10 tff(737,plain,
% 63.93/64.10 ((~((~subq(a(s(n(e)), s(n(e))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(s(n(e)), s(n(e))))) | mem(Z, p(s(n(e))))))) | (~subq(a(s(n(e)), s(n(e))), p(s(n(e)))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[736, 735])).
% 63.93/64.10 tff(738,plain,
% 63.93/64.10 (~subq(a(s(n(e)), s(n(e))), p(s(n(e))))),
% 63.93/64.10 inference(unit_resolution,[status(thm)],[737, 715])).
% 63.93/64.10 tff(739,plain,
% 63.93/64.10 ((~(mem(a(s(n(e)), s(n(e))), p(p(s(n(e))))) <=> subq(a(s(n(e)), s(n(e))), p(s(n(e)))))) | (~mem(a(s(n(e)), s(n(e))), p(p(s(n(e)))))) | subq(a(s(n(e)), s(n(e))), p(s(n(e))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(740,plain,
% 63.93/64.11 ((~(mem(a(s(n(e)), s(n(e))), p(p(s(n(e))))) <=> subq(a(s(n(e)), s(n(e))), p(s(n(e)))))) | (~mem(a(s(n(e)), s(n(e))), p(p(s(n(e))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[739, 738])).
% 63.93/64.11 tff(741,plain,
% 63.93/64.11 (~mem(a(s(n(e)), s(n(e))), p(p(s(n(e)))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[740, 709])).
% 63.93/64.11 tff(742,plain,
% 63.93/64.11 (~mem(a(e, e), p(p(s(n(e)))))),
% 63.93/64.11 inference(modus_ponens,[status(thm)],[741, 705])).
% 63.93/64.11 tff(743,assumption,(~subq(a(e, e), p(s(n(e))))), introduced(assumption)).
% 63.93/64.11 tff(744,assumption,(~(mem(a(e, e), p(p(s(n(e))))) <=> subq(a(e, e), p(s(n(e)))))), introduced(assumption)).
% 63.93/64.11 tff(745,plain,
% 63.93/64.11 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(a(e, e), p(p(s(n(e))))) <=> subq(a(e, e), p(s(n(e)))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(746,plain,
% 63.93/64.11 ($false),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[745, 497, 744])).
% 63.93/64.11 tff(747,plain,(mem(a(e, e), p(p(s(n(e))))) <=> subq(a(e, e), p(s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.11 tff(748,plain,
% 63.93/64.11 ((~(mem(a(e, e), p(p(s(n(e))))) <=> subq(a(e, e), p(s(n(e)))))) | (~mem(a(e, e), p(p(s(n(e)))))) | subq(a(e, e), p(s(n(e))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(749,plain,
% 63.93/64.11 ((~mem(a(e, e), p(p(s(n(e)))))) | subq(a(e, e), p(s(n(e))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[748, 747])).
% 63.93/64.11 tff(750,plain,
% 63.93/64.11 (~mem(a(e, e), p(p(s(n(e)))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[749, 743])).
% 63.93/64.11 tff(751,assumption,(~(mem(a(e, e), p(u(n(e), n(s(n(e)))))) <=> subq(a(e, e), u(n(e), n(s(n(e))))))), introduced(assumption)).
% 63.93/64.11 tff(752,plain,
% 63.93/64.11 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(a(e, e), p(u(n(e), n(s(n(e)))))) <=> subq(a(e, e), u(n(e), n(s(n(e))))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(753,plain,
% 63.93/64.11 ($false),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[752, 497, 751])).
% 63.93/64.11 tff(754,plain,(mem(a(e, e), p(u(n(e), n(s(n(e)))))) <=> subq(a(e, e), u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.11 tff(755,plain,
% 63.93/64.11 ((~(mem(a(e, e), p(u(n(e), n(s(n(e)))))) <=> subq(a(e, e), u(n(e), n(s(n(e))))))) | mem(a(e, e), p(u(n(e), n(s(n(e)))))) | (~subq(a(e, e), u(n(e), n(s(n(e))))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(756,plain,
% 63.93/64.11 ((~(mem(a(e, e), p(u(n(e), n(s(n(e)))))) <=> subq(a(e, e), u(n(e), n(s(n(e))))))) | mem(a(e, e), p(u(n(e), n(s(n(e))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[755, 635])).
% 63.93/64.11 tff(757,plain,
% 63.93/64.11 (mem(a(e, e), p(u(n(e), n(s(n(e))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[756, 754])).
% 63.93/64.11 tff(758,plain,
% 63.93/64.11 ((~((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e))))))) | (~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e)))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(759,plain,
% 63.93/64.11 ((~((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e))))))) | mem(a(e, e), p(p(s(n(e)))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[758, 757])).
% 63.93/64.11 tff(760,plain,
% 63.93/64.11 (~((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[759, 750])).
% 63.93/64.11 tff(761,assumption,(((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e)))))) <=> mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))), introduced(assumption)).
% 63.93/64.11 tff(762,plain,
% 63.93/64.11 ((~![X: $i, Y: $i, Z: $i] : (~(((~mem(X, Y)) | mem(X, Z)) <=> mem(X, m(Y, Z))))) | (~(((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e)))))) <=> mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(763,plain,
% 63.93/64.11 ($false),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[762, 548, 761])).
% 63.93/64.11 tff(764,plain,(~(((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e)))))) <=> mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.11 tff(765,plain,
% 63.93/64.11 ((((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e)))))) <=> mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e)))))) | mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(766,plain,
% 63.93/64.11 (((~mem(a(e, e), p(u(n(e), n(s(n(e))))))) | mem(a(e, e), p(p(s(n(e)))))) | mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[765, 764])).
% 63.93/64.11 tff(767,plain,
% 63.93/64.11 (mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[766, 760])).
% 63.93/64.11 tff(768,plain,
% 63.93/64.11 (mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> mem(e, a(n(n(e)), n(n(e))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[394])).
% 63.93/64.11 tff(769,plain,
% 63.93/64.11 (mem(e, a(n(n(e)), n(n(e)))) <=> mem(e, u(a(n(e), n(e)), s(n(n(e)))))),
% 63.93/64.11 inference(symmetry,[status(thm)],[768])).
% 63.93/64.11 tff(770,plain,
% 63.93/64.11 ((~mem(e, a(n(n(e)), n(n(e))))) <=> (~mem(e, u(a(n(e), n(e)), s(n(n(e))))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[769])).
% 63.93/64.11 tff(771,assumption,(~mem(e, a(n(n(e)), n(n(e))))), introduced(assumption)).
% 63.93/64.11 tff(772,plain,
% 63.93/64.11 (~mem(e, u(a(n(e), n(e)), s(n(n(e)))))),
% 63.93/64.11 inference(modus_ponens,[status(thm)],[771, 770])).
% 63.93/64.11 tff(773,plain,
% 63.93/64.11 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(774,plain,
% 63.93/64.11 (mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[773, 49])).
% 63.93/64.11 tff(775,plain,
% 63.93/64.11 (mem(e, u(a(e, e), s(n(e)))) <=> mem(e, a(n(e), n(e)))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[124])).
% 63.93/64.11 tff(776,plain,
% 63.93/64.11 (mem(e, a(n(e), n(e))) <=> mem(e, u(a(e, e), s(n(e))))),
% 63.93/64.11 inference(symmetry,[status(thm)],[775])).
% 63.93/64.11 tff(777,plain,
% 63.93/64.11 ((~mem(e, a(n(e), n(e)))) <=> (~mem(e, u(a(e, e), s(n(e)))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[776])).
% 63.93/64.11 tff(778,assumption,(~mem(e, a(n(e), n(e)))), introduced(assumption)).
% 63.93/64.11 tff(779,plain,
% 63.93/64.11 (~mem(e, u(a(e, e), s(n(e))))),
% 63.93/64.11 inference(modus_ponens,[status(thm)],[778, 777])).
% 63.93/64.11 tff(780,plain,
% 63.93/64.11 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, 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(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))))),
% 63.93/64.11 inference(rewrite,[status(thm)],[])).
% 63.93/64.11 tff(781,plain,
% 63.93/64.11 ((mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, s(n(e))) | mem(e, a(e, e)))) <=> (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))),
% 63.93/64.11 inference(rewrite,[status(thm)],[])).
% 63.93/64.11 tff(782,plain,
% 63.93/64.11 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, s(n(e))) | mem(e, a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[781])).
% 63.93/64.11 tff(783,plain,
% 63.93/64.11 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, s(n(e))) | mem(e, a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))))),
% 63.93/64.11 inference(transitivity,[status(thm)],[782, 780])).
% 63.93/64.11 tff(784,plain,
% 63.93/64.11 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, s(n(e))) | mem(e, a(e, e))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(785,plain,
% 63.93/64.11 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))),
% 63.93/64.11 inference(modus_ponens,[status(thm)],[784, 783])).
% 63.93/64.11 tff(786,plain,
% 63.93/64.11 (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[785, 49])).
% 63.93/64.11 tff(787,plain,
% 63.93/64.11 ((mem(e, a(e, e)) | mem(e, s(n(e)))) | (~mem(e, a(e, e)))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(788,plain,
% 63.93/64.11 (mem(e, a(e, e)) | mem(e, s(n(e)))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[787, 202])).
% 63.93/64.11 tff(789,plain,
% 63.93/64.11 ((~(mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))) | mem(e, u(a(e, e), s(n(e)))) | (~(mem(e, a(e, e)) | mem(e, s(n(e)))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(790,plain,
% 63.93/64.11 ((~(mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))) | mem(e, u(a(e, e), s(n(e))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[789, 788])).
% 63.93/64.11 tff(791,plain,
% 63.93/64.11 (mem(e, u(a(e, e), s(n(e))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[790, 786])).
% 63.93/64.11 tff(792,plain,
% 63.93/64.11 ($false),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[791, 779])).
% 63.93/64.11 tff(793,plain,(mem(e, a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.11 tff(794,plain,
% 63.93/64.11 ((mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))) | (~mem(e, a(n(e), n(e))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(795,plain,
% 63.93/64.11 (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[794, 793])).
% 63.93/64.11 tff(796,plain,
% 63.93/64.11 ((~(mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))))) | mem(e, u(a(n(e), n(e)), s(n(n(e))))) | (~(mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(797,plain,
% 63.93/64.11 ((~(mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))))) | mem(e, u(a(n(e), n(e)), s(n(n(e)))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[796, 795])).
% 63.93/64.11 tff(798,plain,
% 63.93/64.11 (mem(e, u(a(n(e), n(e)), s(n(n(e)))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[797, 774])).
% 63.93/64.11 tff(799,plain,
% 63.93/64.11 ($false),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[798, 772])).
% 63.93/64.11 tff(800,plain,(mem(e, a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.11 tff(801,plain,
% 63.93/64.11 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(802,plain,
% 63.93/64.11 (mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[801, 49])).
% 63.93/64.11 tff(803,plain,
% 63.93/64.11 (mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> mem(e, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[487])).
% 63.93/64.11 tff(804,plain,
% 63.93/64.11 (mem(e, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))) <=> mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e))))))),
% 63.93/64.11 inference(symmetry,[status(thm)],[803])).
% 63.93/64.11 tff(805,assumption,(mem(e, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))), introduced(assumption)).
% 63.93/64.11 tff(806,plain,
% 63.93/64.11 (mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e))))))),
% 63.93/64.11 inference(modus_ponens,[status(thm)],[805, 804])).
% 63.93/64.11 tff(807,plain,
% 63.93/64.11 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(808,plain,
% 63.93/64.11 (mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[807, 49])).
% 63.93/64.11 tff(809,plain,
% 63.93/64.11 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e))))))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(810,plain,
% 63.93/64.11 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e)))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[809, 49])).
% 63.93/64.11 tff(811,plain,
% 63.93/64.11 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[276])).
% 63.93/64.11 tff(812,plain,
% 63.93/64.11 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) <=> mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))))),
% 63.93/64.11 inference(symmetry,[status(thm)],[811])).
% 63.93/64.11 tff(813,assumption,(~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))), introduced(assumption)).
% 63.93/64.11 tff(814,plain,
% 63.93/64.11 (((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(815,plain,
% 63.93/64.11 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[814, 813])).
% 63.93/64.11 tff(816,plain,
% 63.93/64.11 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))))),
% 63.93/64.11 inference(modus_ponens,[status(thm)],[815, 812])).
% 63.93/64.11 tff(817,plain,
% 63.93/64.11 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e)) <=> (tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) = e))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(818,plain,
% 63.93/64.11 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e)) <=> (tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) = e)),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[817, 7])).
% 63.93/64.11 tff(819,plain,
% 63.93/64.11 (((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(820,plain,
% 63.93/64.11 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[819, 813])).
% 63.93/64.11 tff(821,plain,
% 63.93/64.11 ((~(mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e)) <=> (tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) = e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) = e)),
% 63.93/64.11 inference(tautology,[status(thm)],[])).
% 63.93/64.11 tff(822,plain,
% 63.93/64.11 ((~(mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e)) <=> (tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) = e))) | (tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) = e)),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[821, 820])).
% 63.93/64.11 tff(823,plain,
% 63.93/64.11 (tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))) = e),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[822, 818])).
% 63.93/64.11 tff(824,plain,
% 63.93/64.11 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))) <=> mem(e, s(u(n(e), n(s(n(e))))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[823])).
% 63.93/64.11 tff(825,plain,
% 63.93/64.11 (mem(e, s(u(n(e), n(s(n(e)))))) <=> mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e))))))),
% 63.93/64.11 inference(symmetry,[status(thm)],[824])).
% 63.93/64.11 tff(826,plain,
% 63.93/64.11 ((~mem(e, s(u(n(e), n(s(n(e))))))) <=> (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[825])).
% 63.93/64.11 tff(827,assumption,(~(mem(e, s(u(n(e), n(s(n(e)))))) <=> (e = u(n(e), n(s(n(e))))))), introduced(assumption)).
% 63.93/64.11 tff(828,plain,
% 63.93/64.11 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(u(n(e), n(s(n(e)))))) <=> (e = u(n(e), n(s(n(e))))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.11 tff(829,plain,
% 63.93/64.11 ($false),
% 63.93/64.11 inference(unit_resolution,[status(thm)],[828, 7, 827])).
% 63.93/64.11 tff(830,plain,(mem(e, s(u(n(e), n(s(n(e)))))) <=> (e = u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.11 tff(831,assumption,(e = u(n(e), n(s(n(e))))), introduced(assumption)).
% 63.93/64.11 tff(832,plain,
% 63.93/64.11 (mem(a(e, e), e) <=> mem(a(e, e), u(n(e), n(s(n(e)))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[831])).
% 63.93/64.11 tff(833,plain,
% 63.93/64.11 (mem(a(e, e), u(n(e), n(s(n(e))))) <=> mem(a(e, e), e)),
% 63.93/64.11 inference(symmetry,[status(thm)],[832])).
% 63.93/64.11 tff(834,plain,
% 63.93/64.11 (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> mem(a(e, e), u(n(e), n(s(n(e)))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[298])).
% 63.93/64.11 tff(835,plain,
% 63.93/64.11 (mem(a(e, e), u(n(e), n(s(n(e))))) <=> mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.11 inference(symmetry,[status(thm)],[834])).
% 63.93/64.11 tff(836,plain,
% 63.93/64.11 ((~mem(a(e, e), u(n(e), n(s(n(e)))))) <=> (~mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[835])).
% 63.93/64.11 tff(837,assumption,(~mem(a(e, e), u(n(e), n(s(n(e)))))), introduced(assumption)).
% 63.93/64.11 tff(838,plain,
% 63.93/64.11 (~mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.11 inference(modus_ponens,[status(thm)],[837, 836])).
% 63.93/64.11 tff(839,plain,
% 63.93/64.11 (((~![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)))))))),
% 63.93/64.11 inference(rewrite,[status(thm)],[])).
% 63.93/64.11 tff(840,plain,
% 63.93/64.11 ((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))))))),
% 63.93/64.11 inference(rewrite,[status(thm)],[])).
% 63.93/64.11 tff(841,plain,
% 63.93/64.11 (((~![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)))))))),
% 63.93/64.11 inference(monotonicity,[status(thm)],[840])).
% 63.93/64.11 tff(842,plain,
% 63.93/64.11 (((~![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)))))))),
% 63.93/64.11 inference(transitivity,[status(thm)],[841, 839])).
% 63.93/64.11 tff(843,plain,
% 63.93/64.11 ((~![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))))),
% 63.93/64.11 inference(quant_inst,[status(thm)],[])).
% 63.93/64.12 tff(844,plain,
% 63.93/64.12 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))),
% 63.93/64.12 inference(modus_ponens,[status(thm)],[843, 842])).
% 63.93/64.12 tff(845,plain,
% 63.93/64.12 (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[844, 49])).
% 63.93/64.12 tff(846,plain,
% 63.93/64.12 ((mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))) | (~mem(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.12 inference(tautology,[status(thm)],[])).
% 63.93/64.12 tff(847,plain,
% 63.93/64.12 (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[846, 730])).
% 63.93/64.12 tff(848,plain,
% 63.93/64.12 ((~(mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))) | mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) | (~(mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))),
% 63.93/64.12 inference(tautology,[status(thm)],[])).
% 63.93/64.12 tff(849,plain,
% 63.93/64.12 ((~(mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), a(s(n(e)), s(n(e))))))) | mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[848, 847])).
% 63.93/64.12 tff(850,plain,
% 63.93/64.12 (mem(a(e, e), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[849, 845])).
% 63.93/64.12 tff(851,plain,
% 63.93/64.12 ($false),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[850, 838])).
% 63.93/64.12 tff(852,plain,(mem(a(e, e), u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.12 tff(853,plain,
% 63.93/64.12 (mem(a(e, e), e)),
% 63.93/64.12 inference(modus_ponens,[status(thm)],[852, 833])).
% 63.93/64.12 tff(854,plain,
% 63.93/64.12 ((~![X: $i] : (~mem(X, e))) | (~mem(a(e, e), e))),
% 63.93/64.12 inference(quant_inst,[status(thm)],[])).
% 63.93/64.12 tff(855,plain,
% 63.93/64.12 (~mem(a(e, e), e)),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[854, 89])).
% 63.93/64.12 tff(856,plain,
% 63.93/64.12 ($false),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[855, 853])).
% 63.93/64.12 tff(857,plain,(~(e = u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.12 tff(858,plain,
% 63.93/64.12 ((~(mem(e, s(u(n(e), n(s(n(e)))))) <=> (e = u(n(e), n(s(n(e))))))) | (~mem(e, s(u(n(e), n(s(n(e))))))) | (e = u(n(e), n(s(n(e)))))),
% 63.93/64.12 inference(tautology,[status(thm)],[])).
% 63.93/64.12 tff(859,plain,
% 63.93/64.12 ((~(mem(e, s(u(n(e), n(s(n(e)))))) <=> (e = u(n(e), n(s(n(e))))))) | (~mem(e, s(u(n(e), n(s(n(e)))))))),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[858, 857])).
% 63.93/64.12 tff(860,plain,
% 63.93/64.12 (~mem(e, s(u(n(e), n(s(n(e))))))),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[859, 830])).
% 63.93/64.12 tff(861,plain,
% 63.93/64.12 (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e))))))),
% 63.93/64.12 inference(modus_ponens,[status(thm)],[860, 826])).
% 63.93/64.12 tff(862,plain,
% 63.93/64.12 (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e)))))) <=> mem(e, u(s(n(n(e))), s(n(s(n(e))))))),
% 63.93/64.12 inference(monotonicity,[status(thm)],[823])).
% 63.93/64.12 tff(863,plain,
% 63.93/64.12 (mem(e, u(s(n(n(e))), s(n(s(n(e)))))) <=> mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e))))))),
% 63.93/64.12 inference(symmetry,[status(thm)],[862])).
% 63.93/64.12 tff(864,plain,
% 63.93/64.12 ((~mem(e, u(s(n(n(e))), s(n(s(n(e))))))) <=> (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e)))))))),
% 63.93/64.12 inference(monotonicity,[status(thm)],[863])).
% 63.93/64.12 tff(865,assumption,(~(mem(e, u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e))))))), introduced(assumption)).
% 63.93/64.12 tff(866,plain,
% 63.93/64.12 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e))))))),
% 63.93/64.12 inference(quant_inst,[status(thm)],[])).
% 63.93/64.12 tff(867,plain,
% 63.93/64.12 ($false),
% 63.93/64.12 inference(unit_resolution,[status(thm)],[866, 49, 865])).
% 63.93/64.12 tff(868,plain,(mem(e, u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.93/64.12 tff(869,plain,
% 63.93/64.12 (mem(e, s(a(n(e), n(e)))) <=> mem(e, s(n(n(e))))),
% 63.95/64.12 inference(monotonicity,[status(thm)],[31])).
% 63.95/64.12 tff(870,plain,
% 63.95/64.12 (mem(e, s(n(n(e)))) <=> mem(e, s(a(n(e), n(e))))),
% 63.95/64.12 inference(symmetry,[status(thm)],[869])).
% 63.95/64.12 tff(871,assumption,(mem(e, s(n(n(e))))), introduced(assumption)).
% 63.95/64.12 tff(872,plain,
% 63.95/64.12 (mem(e, s(a(n(e), n(e))))),
% 63.95/64.12 inference(modus_ponens,[status(thm)],[871, 870])).
% 63.95/64.12 tff(873,plain,
% 63.95/64.12 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e))))),
% 63.95/64.12 inference(quant_inst,[status(thm)],[])).
% 63.95/64.12 tff(874,plain,
% 63.95/64.12 (mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e)))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[873, 7])).
% 63.95/64.12 tff(875,plain,
% 63.95/64.12 ((~(mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e))))) | (~mem(e, s(a(n(e), n(e))))) | (e = a(n(e), n(e)))),
% 63.95/64.12 inference(tautology,[status(thm)],[])).
% 63.95/64.12 tff(876,plain,
% 63.95/64.12 ((~(mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e))))) | (~mem(e, s(a(n(e), n(e)))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[875, 145])).
% 63.95/64.12 tff(877,plain,
% 63.95/64.12 (~mem(e, s(a(n(e), n(e))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[876, 874])).
% 63.95/64.12 tff(878,plain,
% 63.95/64.12 ($false),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[877, 872])).
% 63.95/64.12 tff(879,plain,((~mem(e, s(n(n(e))))) | (e = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.95/64.12 tff(880,plain,
% 63.95/64.12 (~mem(e, s(n(n(e))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[879, 142])).
% 63.95/64.12 tff(881,assumption,(e = a(s(n(e)), s(n(e)))), introduced(assumption)).
% 63.95/64.12 tff(882,plain,
% 63.95/64.12 (mem(a(e, e), e) <=> mem(a(e, e), a(s(n(e)), s(n(e))))),
% 63.95/64.12 inference(monotonicity,[status(thm)],[881])).
% 63.95/64.12 tff(883,plain,
% 63.95/64.12 (mem(a(e, e), a(s(n(e)), s(n(e)))) <=> mem(a(e, e), e)),
% 63.95/64.12 inference(symmetry,[status(thm)],[882])).
% 63.95/64.12 tff(884,plain,
% 63.95/64.12 (mem(a(e, e), e)),
% 63.95/64.12 inference(modus_ponens,[status(thm)],[730, 883])).
% 63.95/64.12 tff(885,plain,
% 63.95/64.12 ($false),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[855, 884])).
% 63.95/64.12 tff(886,plain,(~(e = a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.95/64.12 tff(887,plain,
% 63.95/64.12 (mem(e, s(a(s(n(e)), s(n(e))))) <=> mem(e, s(n(s(n(e)))))),
% 63.95/64.12 inference(monotonicity,[status(thm)],[20])).
% 63.95/64.12 tff(888,plain,
% 63.95/64.12 (mem(e, s(n(s(n(e))))) <=> mem(e, s(a(s(n(e)), s(n(e)))))),
% 63.95/64.12 inference(symmetry,[status(thm)],[887])).
% 63.95/64.12 tff(889,assumption,(mem(e, s(n(s(n(e)))))), introduced(assumption)).
% 63.95/64.12 tff(890,plain,
% 63.95/64.12 (mem(e, s(a(s(n(e)), s(n(e)))))),
% 63.95/64.12 inference(modus_ponens,[status(thm)],[889, 888])).
% 63.95/64.12 tff(891,plain,
% 63.95/64.12 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(a(s(n(e)), s(n(e))))) <=> (e = a(s(n(e)), s(n(e)))))),
% 63.95/64.12 inference(quant_inst,[status(thm)],[])).
% 63.95/64.12 tff(892,plain,
% 63.95/64.12 (mem(e, s(a(s(n(e)), s(n(e))))) <=> (e = a(s(n(e)), s(n(e))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[891, 7])).
% 63.95/64.12 tff(893,assumption,(~(e = a(s(n(e)), s(n(e))))), introduced(assumption)).
% 63.95/64.12 tff(894,plain,
% 63.95/64.12 ((~(mem(e, s(a(s(n(e)), s(n(e))))) <=> (e = a(s(n(e)), s(n(e)))))) | (~mem(e, s(a(s(n(e)), s(n(e)))))) | (e = a(s(n(e)), s(n(e))))),
% 63.95/64.12 inference(tautology,[status(thm)],[])).
% 63.95/64.12 tff(895,plain,
% 63.95/64.12 ((~(mem(e, s(a(s(n(e)), s(n(e))))) <=> (e = a(s(n(e)), s(n(e)))))) | (~mem(e, s(a(s(n(e)), s(n(e))))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[894, 893])).
% 63.95/64.12 tff(896,plain,
% 63.95/64.12 (~mem(e, s(a(s(n(e)), s(n(e)))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[895, 892])).
% 63.95/64.12 tff(897,plain,
% 63.95/64.12 ($false),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[896, 890])).
% 63.95/64.12 tff(898,plain,((~mem(e, s(n(s(n(e)))))) | (e = a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.95/64.12 tff(899,plain,
% 63.95/64.12 (~mem(e, s(n(s(n(e)))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[898, 886])).
% 63.95/64.12 tff(900,plain,
% 63.95/64.12 ((~(mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e)))))) | mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e))))),
% 63.95/64.12 inference(tautology,[status(thm)],[])).
% 63.95/64.12 tff(901,plain,
% 63.95/64.12 (~(mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e)))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[900, 899, 880])).
% 63.95/64.12 tff(902,plain,
% 63.95/64.12 ((~(mem(e, u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e))))))) | (~mem(e, u(s(n(n(e))), s(n(s(n(e))))))) | (mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e)))))),
% 63.95/64.12 inference(tautology,[status(thm)],[])).
% 63.95/64.12 tff(903,plain,
% 63.95/64.12 ((~(mem(e, u(s(n(n(e))), s(n(s(n(e)))))) <=> (mem(e, s(n(s(n(e))))) | mem(e, s(n(n(e))))))) | (~mem(e, u(s(n(n(e))), s(n(s(n(e)))))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[902, 901])).
% 63.95/64.12 tff(904,plain,
% 63.95/64.12 (~mem(e, u(s(n(n(e))), s(n(s(n(e))))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[903, 868])).
% 63.95/64.12 tff(905,plain,
% 63.95/64.12 (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e))))))),
% 63.95/64.12 inference(modus_ponens,[status(thm)],[904, 864])).
% 63.95/64.12 tff(906,plain,
% 63.95/64.12 ((~(mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e)))))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e))))))),
% 63.95/64.12 inference(tautology,[status(thm)],[])).
% 63.95/64.12 tff(907,plain,
% 63.95/64.12 (~(mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e)))))))),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[906, 905, 861])).
% 63.95/64.12 tff(908,plain,
% 63.95/64.12 ((~(mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e))))))) <=> (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e))))))))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(u(s(n(n(e))), s(n(s(n(e))))), s(u(n(e), n(s(n(e)))))))) | (mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(s(n(n(e))), s(n(s(n(e)))))))),
% 63.95/64.12 inference(tautology,[status(thm)],[])).
% 63.95/64.12 tff(909,plain,
% 63.95/64.12 ($false),
% 63.95/64.12 inference(unit_resolution,[status(thm)],[908, 907, 816, 810])).
% 63.95/64.12 tff(910,plain,((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))), inference(lemma,lemma(discharge,[]))).
% 63.95/64.12 tff(911,plain,
% 63.95/64.12 (^[X: $i, Y: $i] : refl((~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))))),
% 63.95/64.12 inference(bind,[status(th)],[])).
% 63.95/64.12 tff(912,plain,
% 63.95/64.12 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> ![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 63.95/64.12 inference(quant_intro,[status(thm)],[911])).
% 63.95/64.12 tff(913,plain,
% 63.95/64.12 (^[X: $i, Y: $i] : rewrite((~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))))),
% 63.95/64.12 inference(bind,[status(th)],[])).
% 63.95/64.12 tff(914,plain,
% 63.95/64.12 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> ![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 63.95/64.12 inference(quant_intro,[status(thm)],[913])).
% 63.95/64.12 tff(915,plain,
% 63.95/64.12 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> ![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 63.95/64.12 inference(transitivity,[status(thm)],[914, 912])).
% 63.95/64.12 tff(916,plain,
% 63.95/64.12 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y)) <=> (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))), ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) <=> (disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))))), rewrite((disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))) <=> (disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))), ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) <=> (disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))))), trans(monotonicity(quant_intro(proof_bind(^[Z: $i] : trans(monotonicity(rewrite((mem(Z, X) & mem(Z, Y)) <=> (~((~mem(Z, X)) | (~mem(Z, Y))))), ((~(mem(Z, X) & mem(Z, Y))) <=> (~(~((~mem(Z, X)) | (~mem(Z, Y))))))), rewrite((~(~((~mem(Z, X)) | (~mem(Z, Y))))) <=> ((~mem(Z, X)) | (~mem(Z, Y)))), ((~(mem(Z, X) & mem(Z, Y))) <=> ((~mem(Z, X)) | (~mem(Z, Y)))))), (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) <=> ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))), ((![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))) <=> (![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))) | (~disj(X, Y))))), rewrite((![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))) | (~disj(X, Y))) <=> ((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))), ((![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))) <=> ((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))), (((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> ((disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))) & ((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))), rewrite(((disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))) & ((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))) <=> (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))), (((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))))),
% 63.95/64.12 inference(bind,[status(th)],[])).
% 63.95/64.12 tff(917,plain,
% 63.95/64.12 (![X: $i, Y: $i] : ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> ![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 63.95/64.12 inference(quant_intro,[status(thm)],[916])).
% 63.95/64.12 tff(918,plain,
% 63.95/64.12 (^[X: $i, Y: $i] : rewrite((((mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y)) | disj(X, Y)) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))))),
% 63.95/64.12 inference(bind,[status(th)],[])).
% 63.95/64.12 tff(919,plain,
% 63.95/64.12 (![X: $i, Y: $i] : (((mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y)) | disj(X, Y)) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> ![X: $i, Y: $i] : ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))))),
% 63.95/64.12 inference(quant_intro,[status(thm)],[918])).
% 63.95/64.12 tff(920,plain,
% 63.95/64.12 (![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y))) <=> ![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 63.96/64.12 inference(rewrite,[status(thm)],[])).
% 63.96/64.12 tff(921,plain,
% 63.96/64.12 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite((~?[Z: $i] : (mem(Z, X) & mem(Z, Y))) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))), ((disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> (disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))))), rewrite((disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))), ((disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y))))), rewrite((~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y))) <=> (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))), ((disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))))),
% 63.96/64.12 inference(bind,[status(th)],[])).
% 63.96/64.12 tff(922,plain,
% 63.96/64.12 (![X: $i, Y: $i] : (disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> ![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 63.96/64.12 inference(quant_intro,[status(thm)],[921])).
% 63.96/64.12 tff(923,axiom,(![X: $i, Y: $i] : (disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','disj_def')).
% 63.96/64.12 tff(924,plain,
% 63.96/64.12 (![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 63.96/64.12 inference(modus_ponens,[status(thm)],[923, 922])).
% 63.96/64.12 tff(925,plain,
% 63.96/64.12 (![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 63.96/64.12 inference(modus_ponens,[status(thm)],[924, 920])).
% 63.96/64.12 tff(926,plain,(
% 63.96/64.12 ![X: $i, Y: $i] : (((mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y)) | disj(X, Y)) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))))),
% 63.96/64.12 inference(skolemize,[status(sab)],[925])).
% 63.96/64.12 tff(927,plain,
% 63.96/64.12 (![X: $i, Y: $i] : ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))))),
% 63.96/64.12 inference(modus_ponens,[status(thm)],[926, 919])).
% 63.96/64.12 tff(928,plain,
% 63.96/64.12 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 63.96/64.12 inference(modus_ponens,[status(thm)],[927, 917])).
% 63.96/64.12 tff(929,plain,
% 63.96/64.12 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 63.96/64.12 inference(modus_ponens,[status(thm)],[928, 915])).
% 63.96/64.12 tff(930,plain,
% 63.96/64.12 (((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))))))) <=> ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))))))))),
% 63.96/64.12 inference(rewrite,[status(thm)],[])).
% 63.96/64.12 tff(931,plain,
% 63.96/64.12 ((~((~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))))))) | (~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))))) <=> (~((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))))))),
% 63.96/64.13 inference(rewrite,[status(thm)],[])).
% 63.96/64.13 tff(932,plain,
% 63.96/64.13 (((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))))))) | (~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))))))) <=> ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))))))))),
% 63.96/64.13 inference(monotonicity,[status(thm)],[931])).
% 63.96/64.13 tff(933,plain,
% 63.96/64.13 (((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))))))) | (~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))))))) <=> ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))))))))),
% 63.96/64.13 inference(transitivity,[status(thm)],[932, 930])).
% 63.96/64.13 tff(934,plain,
% 63.96/64.13 ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))))))) | (~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))))))),
% 63.96/64.13 inference(quant_inst,[status(thm)],[])).
% 63.96/64.13 tff(935,plain,
% 63.96/64.13 ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))))))),
% 63.96/64.13 inference(modus_ponens,[status(thm)],[934, 933])).
% 63.96/64.13 tff(936,plain,
% 63.96/64.13 (~((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[935, 929])).
% 63.96/64.13 tff(937,plain,
% 63.96/64.13 (((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))))) | (disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(938,plain,
% 63.96/64.13 (disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[937, 936])).
% 63.96/64.13 tff(939,plain,
% 63.96/64.13 ((~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))))) | disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(940,plain,
% 63.96/64.13 (disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[939, 938])).
% 63.96/64.13 tff(941,plain,
% 63.96/64.13 (disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[940, 910])).
% 63.96/64.13 tff(942,plain,
% 63.96/64.13 (((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~(disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e)) | (~((~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), s(e))) | (~mem(tptp_fun_Z_1(s(e), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))), u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))))) | ((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(943,plain,
% 63.96/64.13 ((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[942, 936])).
% 63.96/64.13 tff(944,plain,
% 63.96/64.13 ((~((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e)))))) | (~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(945,plain,
% 63.96/64.13 ((~disj(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(e))) | ![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[944, 943])).
% 63.96/64.13 tff(946,plain,
% 63.96/64.13 (![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[945, 941])).
% 63.96/64.13 tff(947,plain,
% 63.96/64.13 (((~![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))) | ((~mem(e, s(e))) | (~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))) <=> ((~![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))) | (~mem(e, s(e))) | (~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))),
% 63.96/64.13 inference(rewrite,[status(thm)],[])).
% 63.96/64.13 tff(948,plain,
% 63.96/64.13 (((~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(e, s(e)))) <=> ((~mem(e, s(e))) | (~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))),
% 63.96/64.13 inference(rewrite,[status(thm)],[])).
% 63.96/64.13 tff(949,plain,
% 63.96/64.13 (((~![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))) | ((~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(e, s(e))))) <=> ((~![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))) | ((~mem(e, s(e))) | (~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))))),
% 63.96/64.13 inference(monotonicity,[status(thm)],[948])).
% 63.96/64.13 tff(950,plain,
% 63.96/64.13 (((~![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))) | ((~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(e, s(e))))) <=> ((~![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))) | (~mem(e, s(e))) | (~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))),
% 63.96/64.13 inference(transitivity,[status(thm)],[949, 947])).
% 63.96/64.13 tff(951,plain,
% 63.96/64.13 ((~![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))) | ((~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(e, s(e))))),
% 63.96/64.13 inference(quant_inst,[status(thm)],[])).
% 63.96/64.13 tff(952,plain,
% 63.96/64.13 ((~![Z: $i] : ((~mem(Z, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))) | (~mem(Z, s(e))))) | (~mem(e, s(e))) | (~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))),
% 63.96/64.13 inference(modus_ponens,[status(thm)],[951, 950])).
% 63.96/64.13 tff(953,plain,
% 63.96/64.13 (~mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[952, 946, 185])).
% 63.96/64.13 tff(954,plain,
% 63.96/64.13 (mem(e, s(a(n(n(e)), n(n(e))))) <=> mem(e, s(n(n(n(e)))))),
% 63.96/64.13 inference(monotonicity,[status(thm)],[280])).
% 63.96/64.13 tff(955,plain,
% 63.96/64.13 (mem(e, s(n(n(n(e))))) <=> mem(e, s(a(n(n(e)), n(n(e)))))),
% 63.96/64.13 inference(symmetry,[status(thm)],[954])).
% 63.96/64.13 tff(956,assumption,(mem(e, s(n(n(n(e)))))), introduced(assumption)).
% 63.96/64.13 tff(957,plain,
% 63.96/64.13 (mem(e, s(a(n(n(e)), n(n(e)))))),
% 63.96/64.13 inference(modus_ponens,[status(thm)],[956, 955])).
% 63.96/64.13 tff(958,plain,
% 63.96/64.13 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(a(n(n(e)), n(n(e))))) <=> (e = a(n(n(e)), n(n(e)))))),
% 63.96/64.13 inference(quant_inst,[status(thm)],[])).
% 63.96/64.13 tff(959,plain,
% 63.96/64.13 (mem(e, s(a(n(n(e)), n(n(e))))) <=> (e = a(n(n(e)), n(n(e))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[958, 7])).
% 63.96/64.13 tff(960,assumption,(e = a(n(n(e)), n(n(e)))), introduced(assumption)).
% 63.96/64.13 tff(961,plain,
% 63.96/64.13 (a(n(n(e)), n(n(e))) = e),
% 63.96/64.13 inference(symmetry,[status(thm)],[960])).
% 63.96/64.13 tff(962,plain,
% 63.96/64.13 (mem(a(n(e), n(e)), a(n(n(e)), n(n(e)))) <=> mem(a(n(e), n(e)), e)),
% 63.96/64.13 inference(monotonicity,[status(thm)],[961])).
% 63.96/64.13 tff(963,plain,
% 63.96/64.13 (mem(a(n(e), n(e)), e) <=> mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))),
% 63.96/64.13 inference(symmetry,[status(thm)],[962])).
% 63.96/64.13 tff(964,plain,
% 63.96/64.13 ((~mem(a(n(e), n(e)), e)) <=> (~mem(a(n(e), n(e)), a(n(n(e)), n(n(e)))))),
% 63.96/64.13 inference(monotonicity,[status(thm)],[963])).
% 63.96/64.13 tff(965,plain,
% 63.96/64.13 (~mem(a(n(e), n(e)), a(n(n(e)), n(n(e))))),
% 63.96/64.13 inference(modus_ponens,[status(thm)],[327, 964])).
% 63.96/64.13 tff(966,plain,
% 63.96/64.13 ($false),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[425, 965])).
% 63.96/64.13 tff(967,plain,(~(e = a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.13 tff(968,plain,
% 63.96/64.13 ((~(mem(e, s(a(n(n(e)), n(n(e))))) <=> (e = a(n(n(e)), n(n(e)))))) | (~mem(e, s(a(n(n(e)), n(n(e)))))) | (e = a(n(n(e)), n(n(e))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(969,plain,
% 63.96/64.13 ((~(mem(e, s(a(n(n(e)), n(n(e))))) <=> (e = a(n(n(e)), n(n(e)))))) | (~mem(e, s(a(n(n(e)), n(n(e))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[968, 967])).
% 63.96/64.13 tff(970,plain,
% 63.96/64.13 (~mem(e, s(a(n(n(e)), n(n(e)))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[969, 959])).
% 63.96/64.13 tff(971,plain,
% 63.96/64.13 ($false),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[970, 957])).
% 63.96/64.13 tff(972,plain,(~mem(e, s(n(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.13 tff(973,plain,
% 63.96/64.13 ((~(mem(e, s(n(n(n(e))))) | mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))) | mem(e, s(n(n(n(e))))) | mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(974,plain,
% 63.96/64.13 (~(mem(e, s(n(n(n(e))))) | mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[973, 972, 953])).
% 63.96/64.13 tff(975,plain,
% 63.96/64.13 ((~(mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))) | (~mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e))))))) | (mem(e, s(n(n(n(e))))) | mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e))))))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(976,plain,
% 63.96/64.13 ((~(mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))))))) | (~mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e)))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[975, 974])).
% 63.96/64.13 tff(977,plain,
% 63.96/64.13 (~mem(e, u(u(a(s(n(n(e))), n(s(n(e)))), s(u(n(e), n(s(n(e)))))), s(n(n(n(e))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[976, 808])).
% 63.96/64.13 tff(978,plain,
% 63.96/64.13 ($false),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[977, 806])).
% 63.96/64.13 tff(979,plain,(~mem(e, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.13 tff(980,plain,
% 63.96/64.13 (((~![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) | ((~mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(e, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) <=> ((~![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) | (~mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(e, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))),
% 63.96/64.13 inference(rewrite,[status(thm)],[])).
% 63.96/64.13 tff(981,plain,
% 63.96/64.13 ((~![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) | ((~mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(e, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))),
% 63.96/64.13 inference(quant_inst,[status(thm)],[])).
% 63.96/64.13 tff(982,plain,
% 63.96/64.13 ((~![Z: $i] : ((~mem(Z, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(Z, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e)))))))) | (~mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))) | mem(e, u(a(a(s(n(n(e))), n(s(n(e)))), u(n(e), n(s(n(e))))), s(n(n(n(e))))))),
% 63.96/64.13 inference(modus_ponens,[status(thm)],[981, 980])).
% 63.96/64.13 tff(983,plain,
% 63.96/64.13 (~mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[982, 577, 979])).
% 63.96/64.13 tff(984,plain,
% 63.96/64.13 ((~(mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))) | mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) | (~(mem(e, s(n(n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(985,plain,
% 63.96/64.13 ((~(mem(e, u(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))) | (~(mem(e, s(n(n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[984, 983])).
% 63.96/64.13 tff(986,plain,
% 63.96/64.13 (~(mem(e, s(n(n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[985, 802])).
% 63.96/64.13 tff(987,plain,
% 63.96/64.13 ((mem(e, s(n(n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | (~mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.13 inference(tautology,[status(thm)],[])).
% 63.96/64.13 tff(988,plain,
% 63.96/64.13 (~mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[987, 986])).
% 63.96/64.13 tff(989,assumption,(![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))), introduced(assumption)).
% 63.96/64.13 tff(990,plain,
% 63.96/64.13 (((~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))) | ((~mem(e, a(n(n(e)), n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))) <=> ((~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))) | (~mem(e, a(n(n(e)), n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.13 inference(rewrite,[status(thm)],[])).
% 63.96/64.13 tff(991,plain,
% 63.96/64.13 ((~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))) | ((~mem(e, a(n(n(e)), n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.13 inference(quant_inst,[status(thm)],[])).
% 63.96/64.13 tff(992,plain,
% 63.96/64.13 ((~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))) | (~mem(e, a(n(n(e)), n(n(e))))) | mem(e, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.13 inference(modus_ponens,[status(thm)],[991, 990])).
% 63.96/64.13 tff(993,plain,
% 63.96/64.13 ($false),
% 63.96/64.13 inference(unit_resolution,[status(thm)],[992, 989, 988, 800])).
% 63.96/64.13 tff(994,plain,(~![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.13 tff(995,plain,
% 63.96/64.13 ((~![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(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))) | (~(subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))))))),
% 63.96/64.14 inference(quant_inst,[status(thm)],[])).
% 63.96/64.14 tff(996,plain,
% 63.96/64.14 (~((~((~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))) | (~(subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[995, 229])).
% 63.96/64.14 tff(997,plain,
% 63.96/64.14 (((~((~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))) | (~(subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))))) | ((~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.96/64.14 inference(tautology,[status(thm)],[])).
% 63.96/64.14 tff(998,plain,
% 63.96/64.14 ((~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[997, 996])).
% 63.96/64.14 tff(999,plain,
% 63.96/64.14 ((~((~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))) | (~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.14 inference(tautology,[status(thm)],[])).
% 63.96/64.14 tff(1000,plain,
% 63.96/64.14 ((~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[999, 998])).
% 63.96/64.14 tff(1001,plain,
% 63.96/64.14 (~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1000, 994])).
% 63.96/64.14 tff(1002,plain,
% 63.96/64.14 (((~((~subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ![Z: $i] : ((~mem(Z, a(n(n(e)), n(n(e))))) | mem(Z, m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))) | (~(subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))))) | (subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))))),
% 63.96/64.14 inference(tautology,[status(thm)],[])).
% 63.96/64.14 tff(1003,plain,
% 63.96/64.14 (subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1002, 996])).
% 63.96/64.14 tff(1004,plain,
% 63.96/64.14 ((~(subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))))) | subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.96/64.14 inference(tautology,[status(thm)],[])).
% 63.96/64.14 tff(1005,plain,
% 63.96/64.14 (subq(a(n(n(e)), n(n(e))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1004, 1003])).
% 63.96/64.14 tff(1006,plain,
% 63.96/64.14 (~((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1005, 1001])).
% 63.96/64.14 tff(1007,plain,
% 63.96/64.14 (((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.14 inference(tautology,[status(thm)],[])).
% 63.96/64.14 tff(1008,plain,
% 63.96/64.14 (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1007, 1006])).
% 63.96/64.14 tff(1009,assumption,(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e)), introduced(assumption)).
% 63.96/64.14 tff(1010,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) <=> mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.14 inference(monotonicity,[status(thm)],[1009])).
% 63.96/64.14 tff(1011,plain,
% 63.96/64.14 (mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.14 inference(symmetry,[status(thm)],[1010])).
% 63.96/64.14 tff(1012,assumption,(mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))), introduced(assumption)).
% 63.96/64.14 tff(1013,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.14 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 63.96/64.14 tff(1014,assumption,(~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))), introduced(assumption)).
% 63.96/64.14 tff(1015,plain,
% 63.96/64.14 ($false),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1014, 1013])).
% 63.96/64.14 tff(1016,plain,((~(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.14 tff(1017,plain,
% 63.96/64.14 ((~(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e))) | (~mem(a(e, e), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1016, 1008])).
% 63.96/64.14 tff(1018,plain,
% 63.96/64.14 (~(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1017, 767])).
% 63.96/64.14 tff(1019,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))),
% 63.96/64.14 inference(monotonicity,[status(thm)],[93])).
% 63.96/64.14 tff(1020,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e)))),
% 63.96/64.14 inference(symmetry,[status(thm)],[1019])).
% 63.96/64.14 tff(1021,assumption,(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))), introduced(assumption)).
% 63.96/64.14 tff(1022,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e)))),
% 63.96/64.14 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 63.96/64.14 tff(1023,plain,
% 63.96/64.14 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e))) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e)))),
% 63.96/64.14 inference(quant_inst,[status(thm)],[])).
% 63.96/64.14 tff(1024,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e))) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1023, 7])).
% 63.96/64.14 tff(1025,assumption,(~(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e))), introduced(assumption)).
% 63.96/64.14 tff(1026,plain,
% 63.96/64.14 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e))) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e)))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e)))) | (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e))),
% 63.96/64.14 inference(tautology,[status(thm)],[])).
% 63.96/64.14 tff(1027,plain,
% 63.96/64.14 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e))) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e)))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1026, 1025])).
% 63.96/64.14 tff(1028,plain,
% 63.96/64.14 (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(e, e)))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1027, 1024])).
% 63.96/64.14 tff(1029,plain,
% 63.96/64.14 ($false),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1028, 1022])).
% 63.96/64.14 tff(1030,plain,((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))) | (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(e, e))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.14 tff(1031,plain,
% 63.96/64.14 (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1030, 1018])).
% 63.96/64.14 tff(1032,plain,
% 63.96/64.14 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))))),
% 63.96/64.14 inference(quant_inst,[status(thm)],[])).
% 63.96/64.14 tff(1033,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e)))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1032, 49])).
% 63.96/64.14 tff(1034,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(e, e), s(n(e)))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e)))),
% 63.96/64.14 inference(monotonicity,[status(thm)],[124])).
% 63.96/64.14 tff(1035,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(e, e), s(n(e))))),
% 63.96/64.14 inference(symmetry,[status(thm)],[1034])).
% 63.96/64.14 tff(1036,plain,
% 63.96/64.14 (((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))),
% 63.96/64.14 inference(tautology,[status(thm)],[])).
% 63.96/64.14 tff(1037,plain,
% 63.96/64.14 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1036, 1006])).
% 63.96/64.14 tff(1038,assumption,(((~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e)))))) <=> mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))), introduced(assumption)).
% 63.96/64.14 tff(1039,plain,
% 63.96/64.14 ((~![X: $i, Y: $i, Z: $i] : (~(((~mem(X, Y)) | mem(X, Z)) <=> mem(X, m(Y, Z))))) | (~(((~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e)))))) <=> mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))))),
% 63.96/64.14 inference(quant_inst,[status(thm)],[])).
% 63.96/64.14 tff(1040,plain,
% 63.96/64.14 ($false),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1039, 548, 1038])).
% 63.96/64.14 tff(1041,plain,(~(((~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e)))))) <=> mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.14 tff(1042,assumption,(~(mem(a(n(e), n(e)), p(p(s(n(e))))) <=> subq(a(n(e), n(e)), p(s(n(e)))))), introduced(assumption)).
% 63.96/64.14 tff(1043,plain,
% 63.96/64.14 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(a(n(e), n(e)), p(p(s(n(e))))) <=> subq(a(n(e), n(e)), p(s(n(e)))))),
% 63.96/64.14 inference(quant_inst,[status(thm)],[])).
% 63.96/64.14 tff(1044,plain,
% 63.96/64.14 ($false),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1043, 497, 1042])).
% 63.96/64.14 tff(1045,plain,(mem(a(n(e), n(e)), p(p(s(n(e))))) <=> subq(a(n(e), n(e)), p(s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.14 tff(1046,assumption,((~((~subq(a(n(e), n(e)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e))))))) | (~(subq(a(n(e), n(e)), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), a(n(e), n(e))), p(s(n(e))))))))), introduced(assumption)).
% 63.96/64.14 tff(1047,plain,
% 63.96/64.14 ((~![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)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e))))))) | (~(subq(a(n(e), n(e)), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), a(n(e), n(e))), p(s(n(e))))))))))),
% 63.96/64.14 inference(quant_inst,[status(thm)],[])).
% 63.96/64.14 tff(1048,plain,
% 63.96/64.14 ($false),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1047, 229, 1046])).
% 63.96/64.14 tff(1049,plain,(~((~((~subq(a(n(e), n(e)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e))))))) | (~(subq(a(n(e), n(e)), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), a(n(e), n(e))), p(s(n(e)))))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.14 tff(1050,plain,
% 63.96/64.14 (((~((~subq(a(n(e), n(e)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e))))))) | (~(subq(a(n(e), n(e)), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), a(n(e), n(e))), p(s(n(e))))))))) | ((~subq(a(n(e), n(e)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e))))))),
% 63.96/64.14 inference(tautology,[status(thm)],[])).
% 63.96/64.14 tff(1051,plain,
% 63.96/64.14 ((~subq(a(n(e), n(e)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e)))))),
% 63.96/64.14 inference(unit_resolution,[status(thm)],[1050, 1049])).
% 63.96/64.14 tff(1052,assumption,(![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e)))))), introduced(assumption)).
% 63.96/64.14 tff(1053,assumption,(~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = s(n(e))))), introduced(assumption)).
% 63.96/64.14 tff(1054,plain,
% 63.96/64.14 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = s(n(e))))),
% 63.96/64.15 inference(quant_inst,[status(thm)],[])).
% 63.96/64.15 tff(1055,plain,
% 63.96/64.15 ($false),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1054, 7, 1053])).
% 63.96/64.15 tff(1056,plain,(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.15 tff(1057,assumption,(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = s(n(e))), introduced(assumption)).
% 63.96/64.15 tff(1058,plain,
% 63.96/64.15 (mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))) <=> mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))),
% 63.96/64.15 inference(monotonicity,[status(thm)],[1057])).
% 63.96/64.15 tff(1059,plain,
% 63.96/64.15 (mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e))) <=> mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))),
% 63.96/64.15 inference(symmetry,[status(thm)],[1058])).
% 63.96/64.15 tff(1060,plain,
% 63.96/64.15 ((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))) <=> (~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))))),
% 63.96/64.15 inference(monotonicity,[status(thm)],[1059])).
% 63.96/64.15 tff(1061,plain,
% 63.96/64.15 ((~![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(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(Z, s(n(e)))))) | (~(subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))))))))),
% 63.96/64.15 inference(quant_inst,[status(thm)],[])).
% 63.96/64.15 tff(1062,plain,
% 63.96/64.15 (~((~((~subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(Z, s(n(e)))))) | (~(subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e))))))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1061, 229])).
% 63.96/64.15 tff(1063,plain,
% 63.96/64.15 (((~((~subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(Z, s(n(e)))))) | (~(subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))))))) | (subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e))))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1064,plain,
% 63.96/64.15 (subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1063, 1062])).
% 63.96/64.15 tff(1065,plain,
% 63.96/64.15 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))) <=> subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))))),
% 63.96/64.15 inference(quant_inst,[status(thm)],[])).
% 63.96/64.15 tff(1066,plain,
% 63.96/64.15 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))) <=> subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1065, 497])).
% 63.96/64.15 tff(1067,assumption,(![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))), introduced(assumption)).
% 63.96/64.15 tff(1068,plain,
% 63.96/64.15 (((~![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))) | ((~mem(a(e, e), u(n(e), n(s(n(e)))))) | mem(a(e, e), p(s(n(e)))))) <=> ((~![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))) | (~mem(a(e, e), u(n(e), n(s(n(e)))))) | mem(a(e, e), p(s(n(e)))))),
% 63.96/64.15 inference(rewrite,[status(thm)],[])).
% 63.96/64.15 tff(1069,plain,
% 63.96/64.15 ((~![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))) | ((~mem(a(e, e), u(n(e), n(s(n(e)))))) | mem(a(e, e), p(s(n(e)))))),
% 63.96/64.15 inference(quant_inst,[status(thm)],[])).
% 63.96/64.15 tff(1070,plain,
% 63.96/64.15 ((~![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))) | (~mem(a(e, e), u(n(e), n(s(n(e)))))) | mem(a(e, e), p(s(n(e))))),
% 63.96/64.15 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 63.96/64.15 tff(1071,plain,
% 63.96/64.15 ($false),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1070, 852, 1067, 505])).
% 63.96/64.15 tff(1072,plain,((~![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))) | mem(a(e, e), p(s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.15 tff(1073,plain,
% 63.96/64.15 (~![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1072, 503])).
% 63.96/64.15 tff(1074,assumption,((~((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))))), introduced(assumption)).
% 63.96/64.15 tff(1075,plain,
% 63.96/64.15 (((~![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(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))))))) <=> ((~![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(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e)))))))))),
% 63.96/64.15 inference(rewrite,[status(thm)],[])).
% 63.96/64.15 tff(1076,plain,
% 63.96/64.15 ((~((~((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~(subq(u(n(e), n(s(n(e)))), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))))))) <=> (~((~((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))))))),
% 63.96/64.15 inference(rewrite,[status(thm)],[])).
% 63.96/64.15 tff(1077,plain,
% 63.96/64.15 (((~![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(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~(subq(u(n(e), n(s(n(e)))), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e))))))))))) <=> ((~![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(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e)))))))))),
% 63.96/64.15 inference(monotonicity,[status(thm)],[1076])).
% 63.96/64.15 tff(1078,plain,
% 63.96/64.15 (((~![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(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~(subq(u(n(e), n(s(n(e)))), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e))))))))))) <=> ((~![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(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e)))))))))),
% 63.96/64.15 inference(transitivity,[status(thm)],[1077, 1075])).
% 63.96/64.15 tff(1079,plain,
% 63.96/64.15 ((~![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(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~(subq(u(n(e), n(s(n(e)))), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e))))))))))),
% 63.96/64.15 inference(quant_inst,[status(thm)],[])).
% 63.96/64.15 tff(1080,plain,
% 63.96/64.15 ((~![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(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))))))),
% 63.96/64.15 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 63.96/64.15 tff(1081,plain,
% 63.96/64.15 ($false),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1080, 229, 1074])).
% 63.96/64.15 tff(1082,plain,(~((~((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.15 tff(1083,plain,
% 63.96/64.15 (((~((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))))) | ((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1084,plain,
% 63.96/64.15 ((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1083, 1082])).
% 63.96/64.15 tff(1085,plain,
% 63.96/64.15 ((~((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1086,plain,
% 63.96/64.15 ((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e)))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1085, 1084])).
% 63.96/64.15 tff(1087,plain,
% 63.96/64.15 (~subq(u(n(e), n(s(n(e)))), p(s(n(e))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1086, 1073])).
% 63.96/64.15 tff(1088,plain,
% 63.96/64.15 (((~((~subq(u(n(e), n(s(n(e)))), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, u(n(e), n(s(n(e)))))) | mem(Z, p(s(n(e))))))) | (~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))))) | ((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e)))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1089,plain,
% 63.96/64.15 ((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1088, 1082])).
% 63.96/64.15 tff(1090,plain,
% 63.96/64.15 ((~((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e)))))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1091,plain,
% 63.96/64.15 ((~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) | subq(u(n(e), n(s(n(e)))), p(s(n(e))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1090, 1089])).
% 63.96/64.15 tff(1092,plain,
% 63.96/64.15 (~((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1091, 1087])).
% 63.96/64.15 tff(1093,plain,
% 63.96/64.15 (((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1094,plain,
% 63.96/64.15 (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1093, 1092])).
% 63.96/64.15 tff(1095,plain,
% 63.96/64.15 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))) <=> subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))) | (~subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1096,plain,
% 63.96/64.15 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))) <=> subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))))) | (~subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1095, 1094])).
% 63.96/64.15 tff(1097,plain,
% 63.96/64.15 (~subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1096, 1066])).
% 63.96/64.15 tff(1098,plain,
% 63.96/64.15 ((~(subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e))))))) | subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1099,plain,
% 63.96/64.15 ((~(subq(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e))))))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1098, 1097])).
% 63.96/64.15 tff(1100,plain,
% 63.96/64.15 (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1099, 1064])).
% 63.96/64.15 tff(1101,plain,
% 63.96/64.15 (((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))) | (~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1102,plain,
% 63.96/64.15 (~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1101, 1100])).
% 63.96/64.15 tff(1103,plain,
% 63.96/64.15 (~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))),
% 63.96/64.15 inference(modus_ponens,[status(thm)],[1102, 1060])).
% 63.96/64.15 tff(1104,plain,
% 63.96/64.15 (((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), s(n(e)))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1105,plain,
% 63.96/64.15 (mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1104, 1100])).
% 63.96/64.15 tff(1106,plain,
% 63.96/64.15 ($false),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1105, 1103])).
% 63.96/64.15 tff(1107,plain,(~(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.15 tff(1108,plain,
% 63.96/64.15 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = s(n(e))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))) | (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = s(n(e)))),
% 63.96/64.15 inference(tautology,[status(thm)],[])).
% 63.96/64.15 tff(1109,plain,
% 63.96/64.15 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = s(n(e))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1108, 1107])).
% 63.96/64.15 tff(1110,plain,
% 63.96/64.15 (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))),
% 63.96/64.15 inference(unit_resolution,[status(thm)],[1109, 1056])).
% 63.96/64.15 tff(1111,plain,
% 63.96/64.15 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))),
% 63.96/64.15 inference(monotonicity,[status(thm)],[193])).
% 63.96/64.15 tff(1112,plain,
% 63.96/64.15 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e)) <=> mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e)))),
% 63.96/64.15 inference(symmetry,[status(thm)],[1111])).
% 63.96/64.15 tff(1113,assumption,(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))), introduced(assumption)).
% 63.96/64.15 tff(1114,plain,
% 63.96/64.15 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e)))),
% 63.96/64.15 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 63.96/64.15 tff(1115,plain,
% 63.96/64.15 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), 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(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)))))),
% 63.96/64.16 inference(rewrite,[status(thm)],[])).
% 63.96/64.16 tff(1116,plain,
% 63.96/64.16 ((mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e))))),
% 63.96/64.16 inference(rewrite,[status(thm)],[])).
% 63.96/64.16 tff(1117,plain,
% 63.96/64.16 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) | mem(tptp_fun_Z_0(p(s(n(e))), 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(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)))))),
% 63.96/64.16 inference(monotonicity,[status(thm)],[1116])).
% 63.96/64.16 tff(1118,plain,
% 63.96/64.16 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) | mem(tptp_fun_Z_0(p(s(n(e))), 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(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)))))),
% 63.96/64.16 inference(transitivity,[status(thm)],[1117, 1115])).
% 63.96/64.16 tff(1119,plain,
% 63.96/64.16 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e)))),
% 63.96/64.16 inference(quant_inst,[status(thm)],[])).
% 63.96/64.16 tff(1120,plain,
% 63.96/64.16 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e))))),
% 63.96/64.16 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 63.96/64.16 tff(1121,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1120, 49])).
% 63.96/64.16 tff(1122,assumption,(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e)), introduced(assumption)).
% 63.96/64.16 tff(1123,plain,
% 63.96/64.16 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e))),
% 63.96/64.16 inference(quant_inst,[status(thm)],[])).
% 63.96/64.16 tff(1124,plain,
% 63.96/64.16 ($false),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1123, 89, 1122])).
% 63.96/64.16 tff(1125,plain,(~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e)), inference(lemma,lemma(discharge,[]))).
% 63.96/64.16 tff(1126,assumption,(~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = e))), introduced(assumption)).
% 63.96/64.16 tff(1127,plain,
% 63.96/64.16 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = e))),
% 63.96/64.16 inference(quant_inst,[status(thm)],[])).
% 63.96/64.16 tff(1128,plain,
% 63.96/64.16 ($false),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1127, 7, 1126])).
% 63.96/64.16 tff(1129,plain,(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = e)), inference(lemma,lemma(discharge,[]))).
% 63.96/64.16 tff(1130,assumption,(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = e), introduced(assumption)).
% 63.96/64.16 tff(1131,plain,
% 63.96/64.16 (e = tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))),
% 63.96/64.16 inference(symmetry,[status(thm)],[1130])).
% 63.96/64.16 tff(1132,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), e) <=> mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))))),
% 63.96/64.16 inference(monotonicity,[status(thm)],[1131])).
% 63.96/64.16 tff(1133,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))) <=> mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), e)),
% 63.96/64.16 inference(symmetry,[status(thm)],[1132])).
% 63.96/64.16 tff(1134,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), e)),
% 63.96/64.16 inference(modus_ponens,[status(thm)],[1105, 1133])).
% 63.96/64.16 tff(1135,plain,
% 63.96/64.16 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), e))),
% 63.96/64.16 inference(quant_inst,[status(thm)],[])).
% 63.96/64.16 tff(1136,plain,
% 63.96/64.16 (~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e)))))), e)),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1135, 89])).
% 63.96/64.16 tff(1137,plain,
% 63.96/64.16 ($false),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1136, 1134])).
% 63.96/64.16 tff(1138,plain,(~(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = e)), inference(lemma,lemma(discharge,[]))).
% 63.96/64.16 tff(1139,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = e))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e))) | (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = e)),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1140,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))) = e))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1139, 1138])).
% 63.96/64.16 tff(1141,plain,
% 63.96/64.16 (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1140, 1129])).
% 63.96/64.16 tff(1142,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1143,plain,
% 63.96/64.16 (~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1142, 1141, 1125])).
% 63.96/64.16 tff(1144,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e)))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1145,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), e) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(e))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1144, 1143])).
% 63.96/64.16 tff(1146,plain,
% 63.96/64.16 (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(e, s(e)))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1145, 1121])).
% 63.96/64.16 tff(1147,plain,
% 63.96/64.16 ($false),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1146, 1114])).
% 63.96/64.16 tff(1148,plain,(~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.16 tff(1149,plain,
% 63.96/64.16 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))))),
% 63.96/64.16 inference(quant_inst,[status(thm)],[])).
% 63.96/64.16 tff(1150,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e)))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1149, 49])).
% 63.96/64.16 tff(1151,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))),
% 63.96/64.16 inference(monotonicity,[status(thm)],[298])).
% 63.96/64.16 tff(1152,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e))))) <=> mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.96/64.16 inference(symmetry,[status(thm)],[1151])).
% 63.96/64.16 tff(1153,plain,
% 63.96/64.16 (((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1154,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(n(e), n(s(n(e)))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1153, 1092])).
% 63.96/64.16 tff(1155,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.96/64.16 inference(modus_ponens,[status(thm)],[1154, 1152])).
% 63.96/64.16 tff(1156,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), a(s(n(e)), s(n(e)))))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e)))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1157,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1156, 1155, 1150])).
% 63.96/64.16 tff(1158,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1159,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1158, 1157])).
% 63.96/64.16 tff(1160,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1159, 1148])).
% 63.96/64.16 tff(1161,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e))))),
% 63.96/64.16 inference(monotonicity,[status(thm)],[338])).
% 63.96/64.16 tff(1162,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e)))) <=> mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e)))))),
% 63.96/64.16 inference(symmetry,[status(thm)],[1161])).
% 63.96/64.16 tff(1163,assumption,(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e))))), introduced(assumption)).
% 63.96/64.16 tff(1164,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e)))))),
% 63.96/64.16 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 63.96/64.16 tff(1165,plain,
% 63.96/64.16 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))))))),
% 63.96/64.16 inference(rewrite,[status(thm)],[])).
% 63.96/64.16 tff(1166,plain,
% 63.96/64.16 ((mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))))),
% 63.96/64.16 inference(rewrite,[status(thm)],[])).
% 63.96/64.16 tff(1167,plain,
% 63.96/64.16 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))))))),
% 63.96/64.16 inference(monotonicity,[status(thm)],[1166])).
% 63.96/64.16 tff(1168,plain,
% 63.96/64.16 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))))))),
% 63.96/64.16 inference(transitivity,[status(thm)],[1167, 1165])).
% 63.96/64.16 tff(1169,plain,
% 63.96/64.16 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))))),
% 63.96/64.16 inference(quant_inst,[status(thm)],[])).
% 63.96/64.16 tff(1170,plain,
% 63.96/64.16 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))))),
% 63.96/64.16 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 63.96/64.16 tff(1171,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1170, 49])).
% 63.96/64.16 tff(1172,assumption,(~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))), introduced(assumption)).
% 63.96/64.16 tff(1173,assumption,(~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))), introduced(assumption)).
% 63.96/64.16 tff(1174,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1175,plain,
% 63.96/64.16 (~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1174, 1173, 1172])).
% 63.96/64.16 tff(1176,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e)))))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1177,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e))))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e))))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1176, 1175])).
% 63.96/64.16 tff(1178,plain,
% 63.96/64.16 (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(s(n(e)), s(s(n(e)))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1177, 1171])).
% 63.96/64.16 tff(1179,plain,
% 63.96/64.16 ($false),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1178, 1164])).
% 63.96/64.16 tff(1180,plain,((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(s(n(e)), s(n(e))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.16 tff(1181,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(s(n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1180, 1160])).
% 63.96/64.16 tff(1182,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1181, 1110])).
% 63.96/64.16 tff(1183,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e)))) <=> mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e)))),
% 63.96/64.16 inference(monotonicity,[status(thm)],[124])).
% 63.96/64.16 tff(1184,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e))) <=> mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e))))),
% 63.96/64.16 inference(symmetry,[status(thm)],[1183])).
% 63.96/64.16 tff(1185,plain,
% 63.96/64.16 ((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e)))) <=> (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e)))))),
% 63.96/64.16 inference(monotonicity,[status(thm)],[1184])).
% 63.96/64.16 tff(1186,assumption,(~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e)))), introduced(assumption)).
% 63.96/64.16 tff(1187,plain,
% 63.96/64.16 (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e))))),
% 63.96/64.16 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 63.96/64.16 tff(1188,plain,
% 63.96/64.16 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))))),
% 63.96/64.16 inference(quant_inst,[status(thm)],[])).
% 63.96/64.16 tff(1189,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e)))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1188, 49])).
% 63.96/64.16 tff(1190,assumption,(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e)))), introduced(assumption)).
% 63.96/64.16 tff(1191,plain,
% 63.96/64.16 ((mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1192,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1191, 1190])).
% 63.96/64.16 tff(1193,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e)))) | (~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))))),
% 63.96/64.16 inference(tautology,[status(thm)],[])).
% 63.96/64.16 tff(1194,plain,
% 63.96/64.16 ((~(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(e, e))))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1193, 1192])).
% 63.96/64.16 tff(1195,plain,
% 63.96/64.16 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), u(a(e, e), s(n(e))))),
% 63.96/64.16 inference(unit_resolution,[status(thm)],[1194, 1189])).
% 63.96/64.17 tff(1196,plain,
% 63.96/64.17 ($false),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1195, 1187])).
% 63.96/64.17 tff(1197,plain,(mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.17 tff(1198,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e)))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1197, 1182])).
% 63.96/64.17 tff(1199,plain,
% 63.96/64.17 (((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e)))))) | ((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))) <=> ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e)))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))),
% 63.96/64.17 inference(rewrite,[status(thm)],[])).
% 63.96/64.17 tff(1200,plain,
% 63.96/64.17 ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e)))))) | ((~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e)))))),
% 63.96/64.17 inference(quant_inst,[status(thm)],[])).
% 63.96/64.17 tff(1201,plain,
% 63.96/64.17 ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e)))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), u(n(e), n(s(n(e))))), p(s(n(e))))),
% 63.96/64.17 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 63.96/64.17 tff(1202,plain,
% 63.96/64.17 ($false),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1201, 1094, 1198, 1052])).
% 63.96/64.17 tff(1203,plain,(~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.17 tff(1204,plain,
% 63.96/64.17 ((~((~subq(a(n(e), n(e)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e))))))) | (~subq(a(n(e), n(e)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e)))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1205,plain,
% 63.96/64.17 ((~((~subq(a(n(e), n(e)), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(s(n(e))))))) | (~subq(a(n(e), n(e)), p(s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1204, 1203])).
% 63.96/64.17 tff(1206,plain,
% 63.96/64.17 (~subq(a(n(e), n(e)), p(s(n(e))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1205, 1051])).
% 63.96/64.17 tff(1207,plain,
% 63.96/64.17 ((~(mem(a(n(e), n(e)), p(p(s(n(e))))) <=> subq(a(n(e), n(e)), p(s(n(e)))))) | (~mem(a(n(e), n(e)), p(p(s(n(e)))))) | subq(a(n(e), n(e)), p(s(n(e))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1208,plain,
% 63.96/64.17 ((~(mem(a(n(e), n(e)), p(p(s(n(e))))) <=> subq(a(n(e), n(e)), p(s(n(e)))))) | (~mem(a(n(e), n(e)), p(p(s(n(e))))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1207, 1206])).
% 63.96/64.17 tff(1209,plain,
% 63.96/64.17 (~mem(a(n(e), n(e)), p(p(s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1208, 1045])).
% 63.96/64.17 tff(1210,assumption,(~(mem(a(n(e), n(e)), p(u(n(e), n(s(n(e)))))) <=> subq(a(n(e), n(e)), u(n(e), n(s(n(e))))))), introduced(assumption)).
% 63.96/64.17 tff(1211,plain,
% 63.96/64.17 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(a(n(e), n(e)), p(u(n(e), n(s(n(e)))))) <=> subq(a(n(e), n(e)), u(n(e), n(s(n(e))))))),
% 63.96/64.17 inference(quant_inst,[status(thm)],[])).
% 63.96/64.17 tff(1212,plain,
% 63.96/64.17 ($false),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1211, 497, 1210])).
% 63.96/64.17 tff(1213,plain,(mem(a(n(e), n(e)), p(u(n(e), n(s(n(e)))))) <=> subq(a(n(e), n(e)), u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.17 tff(1214,assumption,((~((~subq(a(n(e), n(e)), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))))))), introduced(assumption)).
% 63.96/64.17 tff(1215,plain,
% 63.96/64.17 ((~![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)), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))))))))),
% 63.96/64.17 inference(quant_inst,[status(thm)],[])).
% 63.96/64.17 tff(1216,plain,
% 63.96/64.17 ($false),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1215, 229, 1214])).
% 63.96/64.17 tff(1217,plain,(~((~((~subq(a(n(e), n(e)), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e))))))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.17 tff(1218,plain,
% 63.96/64.17 (((~((~subq(a(n(e), n(e)), u(n(e), n(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, u(n(e), n(s(n(e)))))))) | (~(subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))))))) | (subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e))))))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1219,plain,
% 63.96/64.17 (subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1218, 1217])).
% 63.96/64.17 tff(1220,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e))))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))),
% 63.96/64.17 inference(monotonicity,[status(thm)],[338])).
% 63.96/64.17 tff(1221,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e)))))),
% 63.96/64.17 inference(symmetry,[status(thm)],[1220])).
% 63.96/64.17 tff(1222,plain,
% 63.96/64.17 ((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))) <=> (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e))))))),
% 63.96/64.17 inference(monotonicity,[status(thm)],[1221])).
% 63.96/64.17 tff(1223,plain,
% 63.96/64.17 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(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(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))))))),
% 63.96/64.17 inference(rewrite,[status(thm)],[])).
% 63.96/64.17 tff(1224,plain,
% 63.96/64.17 ((mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))))),
% 63.96/64.17 inference(rewrite,[status(thm)],[])).
% 63.96/64.17 tff(1225,plain,
% 63.96/64.17 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))))))),
% 63.96/64.17 inference(monotonicity,[status(thm)],[1224])).
% 63.96/64.17 tff(1226,plain,
% 63.96/64.17 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))))))),
% 63.96/64.17 inference(transitivity,[status(thm)],[1225, 1223])).
% 63.96/64.17 tff(1227,plain,
% 63.96/64.17 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e))))),
% 63.96/64.17 inference(quant_inst,[status(thm)],[])).
% 63.96/64.17 tff(1228,plain,
% 63.96/64.17 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))))),
% 63.96/64.17 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 63.96/64.17 tff(1229,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1228, 49])).
% 63.96/64.17 tff(1230,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))),
% 63.96/64.17 inference(monotonicity,[status(thm)],[298])).
% 63.96/64.17 tff(1231,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e))))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.96/64.17 inference(symmetry,[status(thm)],[1230])).
% 63.96/64.17 tff(1232,plain,
% 63.96/64.17 ((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))) <=> (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))))),
% 63.96/64.17 inference(monotonicity,[status(thm)],[1231])).
% 63.96/64.17 tff(1233,assumption,(~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e))))))), introduced(assumption)).
% 63.96/64.17 tff(1234,plain,
% 63.96/64.17 (((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e))))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1235,plain,
% 63.96/64.17 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1234, 1233])).
% 63.96/64.17 tff(1236,plain,
% 63.96/64.17 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e)))))),
% 63.96/64.17 inference(modus_ponens,[status(thm)],[1235, 1232])).
% 63.96/64.17 tff(1237,plain,
% 63.96/64.17 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), a(s(n(e)), s(n(e))))) | (~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1238,plain,
% 63.96/64.17 (~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1237, 1236, 1229])).
% 63.96/64.17 tff(1239,plain,
% 63.96/64.17 ((mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e)))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1240,plain,
% 63.96/64.17 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1239, 1238])).
% 63.96/64.17 tff(1241,plain,
% 63.96/64.17 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e)))))),
% 63.96/64.17 inference(modus_ponens,[status(thm)],[1240, 1222])).
% 63.96/64.17 tff(1242,plain,
% 63.96/64.17 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e)))))),
% 63.96/64.17 inference(quant_inst,[status(thm)],[])).
% 63.96/64.17 tff(1243,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1242, 49])).
% 63.96/64.17 tff(1244,plain,
% 63.96/64.17 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e))))),
% 63.96/64.17 inference(quant_inst,[status(thm)],[])).
% 63.96/64.17 tff(1245,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1244, 49])).
% 63.96/64.17 tff(1246,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), s(n(e)))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))),
% 63.96/64.17 inference(monotonicity,[status(thm)],[124])).
% 63.96/64.17 tff(1247,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e))) <=> mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), s(n(e))))),
% 63.96/64.17 inference(symmetry,[status(thm)],[1246])).
% 63.96/64.17 tff(1248,plain,
% 63.96/64.17 (((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1249,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1248, 1233])).
% 63.96/64.17 tff(1250,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), s(n(e))))),
% 63.96/64.17 inference(modus_ponens,[status(thm)],[1249, 1247])).
% 63.96/64.17 tff(1251,plain,
% 63.96/64.17 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e))))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(a(e, e), s(n(e))))) | (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1252,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1251, 1250, 1245])).
% 63.96/64.17 tff(1253,plain,
% 63.96/64.17 ((mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(s(n(e)), s(n(e))))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1254,plain,
% 63.96/64.17 (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1253, 1238])).
% 63.96/64.17 tff(1255,plain,
% 63.96/64.17 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(e, e))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1256,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e)))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1255, 1254, 1252])).
% 63.96/64.17 tff(1257,plain,
% 63.96/64.17 ((mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e)))) | (~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1258,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e)))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1257, 1256])).
% 63.96/64.17 tff(1259,plain,
% 63.96/64.17 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e)))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e))))) | (~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e)))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1260,plain,
% 63.96/64.17 ((~(mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e))))) <=> (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(s(n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), s(n(e)))))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1259, 1258])).
% 63.96/64.17 tff(1261,plain,
% 63.96/64.17 (mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(s(n(e)), s(s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1260, 1243])).
% 63.96/64.17 tff(1262,plain,
% 63.96/64.17 ($false),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1261, 1241])).
% 63.96/64.17 tff(1263,plain,((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.17 tff(1264,plain,
% 63.96/64.17 ((~(subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e))))))))) | subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e)))))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1265,plain,
% 63.96/64.17 ((~(subq(a(n(e), n(e)), u(n(e), n(s(n(e))))) | (~((~mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(u(n(e), n(s(n(e)))), a(n(e), n(e))), u(n(e), n(s(n(e))))))))) | subq(a(n(e), n(e)), u(n(e), n(s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1264, 1263])).
% 63.96/64.17 tff(1266,plain,
% 63.96/64.17 (subq(a(n(e), n(e)), u(n(e), n(s(n(e)))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1265, 1219])).
% 63.96/64.17 tff(1267,plain,
% 63.96/64.17 ((~(mem(a(n(e), n(e)), p(u(n(e), n(s(n(e)))))) <=> subq(a(n(e), n(e)), u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(u(n(e), n(s(n(e)))))) | (~subq(a(n(e), n(e)), u(n(e), n(s(n(e))))))),
% 63.96/64.17 inference(tautology,[status(thm)],[])).
% 63.96/64.17 tff(1268,plain,
% 63.96/64.17 ((~(mem(a(n(e), n(e)), p(u(n(e), n(s(n(e)))))) <=> subq(a(n(e), n(e)), u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1267, 1266])).
% 63.96/64.17 tff(1269,plain,
% 63.96/64.17 (mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))),
% 63.96/64.17 inference(unit_resolution,[status(thm)],[1268, 1213])).
% 63.96/64.17 tff(1270,plain,
% 63.96/64.17 ((~((~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e))))))) | (~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e)))))),
% 63.96/64.18 inference(tautology,[status(thm)],[])).
% 63.96/64.18 tff(1271,plain,
% 63.96/64.18 (~((~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e))))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1270, 1269, 1209])).
% 63.96/64.18 tff(1272,plain,
% 63.96/64.18 ((((~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e)))))) <=> mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | ((~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e)))))) | mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.18 inference(tautology,[status(thm)],[])).
% 63.96/64.18 tff(1273,plain,
% 63.96/64.18 ((((~mem(a(n(e), n(e)), p(u(n(e), n(s(n(e))))))) | mem(a(n(e), n(e)), p(p(s(n(e)))))) <=> mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))) | mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1272, 1271])).
% 63.96/64.18 tff(1274,plain,
% 63.96/64.18 (mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1273, 1041])).
% 63.96/64.18 tff(1275,assumption,(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e))), introduced(assumption)).
% 63.96/64.18 tff(1276,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) <=> mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.18 inference(monotonicity,[status(thm)],[1275])).
% 63.96/64.18 tff(1277,plain,
% 63.96/64.18 (mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.18 inference(symmetry,[status(thm)],[1276])).
% 63.96/64.18 tff(1278,assumption,(mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))), introduced(assumption)).
% 63.96/64.18 tff(1279,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.18 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 63.96/64.18 tff(1280,plain,
% 63.96/64.18 ($false),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1014, 1279])).
% 63.96/64.18 tff(1281,plain,((~(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))) | (~mem(a(n(e), n(e)), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.18 tff(1282,plain,
% 63.96/64.18 ((~(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1281, 1274])).
% 63.96/64.18 tff(1283,plain,
% 63.96/64.18 (~(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e)))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1282, 1008])).
% 63.96/64.18 tff(1284,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e)))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e))))),
% 63.96/64.18 inference(monotonicity,[status(thm)],[31])).
% 63.96/64.18 tff(1285,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e))))),
% 63.96/64.18 inference(symmetry,[status(thm)],[1284])).
% 63.96/64.18 tff(1286,assumption,(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e))))), introduced(assumption)).
% 63.96/64.18 tff(1287,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e))))),
% 63.96/64.18 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 63.96/64.18 tff(1288,plain,
% 63.96/64.18 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e)))) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e))))),
% 63.96/64.18 inference(quant_inst,[status(thm)],[])).
% 63.96/64.18 tff(1289,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e)))) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e)))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1288, 7])).
% 63.96/64.18 tff(1290,assumption,(~(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e)))), introduced(assumption)).
% 63.96/64.18 tff(1291,plain,
% 63.96/64.18 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e)))) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e))))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e))))) | (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e)))),
% 63.96/64.18 inference(tautology,[status(thm)],[])).
% 63.96/64.18 tff(1292,plain,
% 63.96/64.18 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e)))) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e))))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e)))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1291, 1290])).
% 63.96/64.18 tff(1293,plain,
% 63.96/64.18 (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(a(n(e), n(e))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1292, 1289])).
% 63.96/64.18 tff(1294,plain,
% 63.96/64.18 ($false),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1293, 1287])).
% 63.96/64.18 tff(1295,plain,((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e))))) | (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.18 tff(1296,plain,
% 63.96/64.18 (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1295, 1283])).
% 63.96/64.18 tff(1297,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e))))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))),
% 63.96/64.18 inference(monotonicity,[status(thm)],[394])).
% 63.96/64.18 tff(1298,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e)))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e)))))),
% 63.96/64.18 inference(symmetry,[status(thm)],[1297])).
% 63.96/64.18 tff(1299,assumption,(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))), introduced(assumption)).
% 63.96/64.18 tff(1300,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e)))))),
% 63.96/64.18 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 63.96/64.18 tff(1301,plain,
% 63.96/64.18 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e)))))),
% 63.96/64.18 inference(quant_inst,[status(thm)],[])).
% 63.96/64.18 tff(1302,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1301, 49])).
% 63.96/64.18 tff(1303,assumption,(~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e)))), introduced(assumption)).
% 63.96/64.18 tff(1304,assumption,(~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e))))), introduced(assumption)).
% 63.96/64.18 tff(1305,plain,
% 63.96/64.18 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e)))),
% 63.96/64.18 inference(tautology,[status(thm)],[])).
% 63.96/64.18 tff(1306,plain,
% 63.96/64.18 (~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1305, 1304, 1303])).
% 63.96/64.18 tff(1307,plain,
% 63.96/64.18 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e)))))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e)))))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e))))),
% 63.96/64.18 inference(tautology,[status(thm)],[])).
% 63.96/64.18 tff(1308,plain,
% 63.96/64.18 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e)))))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e))))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1307, 1306])).
% 63.96/64.18 tff(1309,plain,
% 63.96/64.18 (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(n(e), n(e)), s(n(n(e)))))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1308, 1302])).
% 63.96/64.18 tff(1310,plain,
% 63.96/64.18 ($false),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1309, 1300])).
% 63.96/64.18 tff(1311,plain,((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(n(e)), n(n(e))))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(n(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.18 tff(1312,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(n(e), n(e)))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1311, 1296, 1037])).
% 63.96/64.18 tff(1313,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(e, e), s(n(e))))),
% 63.96/64.18 inference(modus_ponens,[status(thm)],[1312, 1035])).
% 63.96/64.18 tff(1314,plain,
% 63.96/64.18 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(e, e), s(n(e)))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(a(e, e), s(n(e))))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e)))),
% 63.96/64.18 inference(tautology,[status(thm)],[])).
% 63.96/64.18 tff(1315,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1314, 1313, 1033])).
% 63.96/64.18 tff(1316,plain,
% 63.96/64.18 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))),
% 63.96/64.18 inference(tautology,[status(thm)],[])).
% 63.96/64.18 tff(1317,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1316, 1315])).
% 63.96/64.18 tff(1318,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))),
% 63.96/64.18 inference(unit_resolution,[status(thm)],[1317, 1031])).
% 63.96/64.18 tff(1319,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))),
% 63.96/64.18 inference(monotonicity,[status(thm)],[193])).
% 63.96/64.18 tff(1320,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e)) <=> mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e)))),
% 63.96/64.18 inference(symmetry,[status(thm)],[1319])).
% 63.96/64.18 tff(1321,assumption,(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))), introduced(assumption)).
% 63.96/64.18 tff(1322,plain,
% 63.96/64.18 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e)))),
% 63.96/64.18 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 63.96/64.18 tff(1323,plain,
% 63.96/64.18 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)))))),
% 63.96/64.18 inference(rewrite,[status(thm)],[])).
% 63.96/64.18 tff(1324,plain,
% 63.96/64.18 ((mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))))),
% 63.96/64.18 inference(rewrite,[status(thm)],[])).
% 63.96/64.18 tff(1325,plain,
% 63.96/64.18 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)))))),
% 63.96/64.18 inference(monotonicity,[status(thm)],[1324])).
% 63.96/64.18 tff(1326,plain,
% 63.96/64.18 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)))))),
% 63.96/64.19 inference(transitivity,[status(thm)],[1325, 1323])).
% 63.96/64.19 tff(1327,plain,
% 63.96/64.19 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e)))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1328,plain,
% 63.96/64.19 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))))),
% 63.96/64.19 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 63.96/64.19 tff(1329,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1328, 49])).
% 63.96/64.19 tff(1330,assumption,(~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))), introduced(assumption)).
% 63.96/64.19 tff(1331,assumption,(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e)), introduced(assumption)).
% 63.96/64.19 tff(1332,plain,
% 63.96/64.19 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1333,plain,
% 63.96/64.19 ($false),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1332, 89, 1331])).
% 63.96/64.19 tff(1334,plain,(~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e)), inference(lemma,lemma(discharge,[]))).
% 63.96/64.19 tff(1335,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1336,plain,
% 63.96/64.19 (~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1335, 1334, 1330])).
% 63.96/64.19 tff(1337,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e)))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)))),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1338,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))) <=> (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), e) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e))))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1337, 1336])).
% 63.96/64.19 tff(1339,plain,
% 63.96/64.19 (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), u(e, s(e)))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1338, 1329])).
% 63.96/64.19 tff(1340,plain,
% 63.96/64.19 ($false),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1339, 1322])).
% 63.96/64.19 tff(1341,plain,((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), a(e, e))) | mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.19 tff(1342,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1341, 1318])).
% 63.96/64.19 tff(1343,assumption,(~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = e))), introduced(assumption)).
% 63.96/64.19 tff(1344,plain,
% 63.96/64.19 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = e))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1345,plain,
% 63.96/64.19 ($false),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1344, 7, 1343])).
% 63.96/64.19 tff(1346,plain,(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = e)), inference(lemma,lemma(discharge,[]))).
% 63.96/64.19 tff(1347,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e)) <=> (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = e))) | (~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))) | (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = e)),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1348,plain,
% 63.96/64.19 ((~mem(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(e))) | (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = e)),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1347, 1346])).
% 63.96/64.19 tff(1349,plain,
% 63.96/64.19 (tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))) = e),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1348, 1342])).
% 63.96/64.19 tff(1350,plain,
% 63.96/64.19 (e = tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))),
% 63.96/64.19 inference(symmetry,[status(thm)],[1349])).
% 63.96/64.19 tff(1351,plain,
% 63.96/64.19 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), a(e, e)) = e))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1352,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), a(e, e)) = e)),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1351, 7])).
% 63.96/64.19 tff(1353,plain,
% 63.96/64.19 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)))))),
% 63.96/64.19 inference(rewrite,[status(thm)],[])).
% 63.96/64.19 tff(1354,plain,
% 63.96/64.19 ((mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))))),
% 63.96/64.19 inference(rewrite,[status(thm)],[])).
% 63.96/64.19 tff(1355,plain,
% 63.96/64.19 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)))))),
% 63.96/64.19 inference(monotonicity,[status(thm)],[1354])).
% 63.96/64.19 tff(1356,plain,
% 63.96/64.19 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)))))),
% 63.96/64.19 inference(transitivity,[status(thm)],[1355, 1353])).
% 63.96/64.19 tff(1357,plain,
% 63.96/64.19 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e)))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1358,plain,
% 63.96/64.19 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))))),
% 63.96/64.19 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 63.96/64.19 tff(1359,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1358, 49])).
% 63.96/64.19 tff(1360,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))),
% 63.96/64.19 inference(monotonicity,[status(thm)],[193])).
% 63.96/64.19 tff(1361,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e)) <=> mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e)))),
% 63.96/64.19 inference(symmetry,[status(thm)],[1360])).
% 63.96/64.19 tff(1362,assumption,((~((~subq(a(e, e), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, p(s(n(e))))))) | (~(subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))))))), introduced(assumption)).
% 63.96/64.19 tff(1363,plain,
% 63.96/64.19 ((~![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(e, e), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, p(s(n(e))))))) | (~(subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))))))))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1364,plain,
% 63.96/64.19 ($false),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1363, 229, 1362])).
% 63.96/64.19 tff(1365,plain,(~((~((~subq(a(e, e), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, p(s(n(e))))))) | (~(subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.19 tff(1366,plain,
% 63.96/64.19 (((~((~subq(a(e, e), p(s(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, p(s(n(e))))))) | (~(subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))))))) | (subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))))))),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1367,plain,
% 63.96/64.19 (subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1366, 1365])).
% 63.96/64.19 tff(1368,plain,
% 63.96/64.19 ((~(subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))))))) | subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))))),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1369,plain,
% 63.96/64.19 (subq(a(e, e), p(s(n(e)))) | (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1368, 1367])).
% 63.96/64.19 tff(1370,plain,
% 63.96/64.19 (~((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1369, 743])).
% 63.96/64.19 tff(1371,plain,
% 63.96/64.19 (((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1372,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1371, 1370])).
% 63.96/64.19 tff(1373,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e)))),
% 63.96/64.19 inference(modus_ponens,[status(thm)],[1372, 1361])).
% 63.96/64.19 tff(1374,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e))) <=> (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), u(e, s(e)))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)))),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1375,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1374, 1373, 1359])).
% 63.96/64.19 tff(1376,assumption,(mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e)), introduced(assumption)).
% 63.96/64.19 tff(1377,plain,
% 63.96/64.19 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1378,plain,
% 63.96/64.19 ($false),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1377, 89, 1376])).
% 63.96/64.19 tff(1379,plain,(~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e)), inference(lemma,lemma(discharge,[]))).
% 63.96/64.19 tff(1380,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1381,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), e) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1380, 1379])).
% 63.96/64.19 tff(1382,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1381, 1375])).
% 63.96/64.19 tff(1383,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), a(e, e)) = e))) | (~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e))) | (tptp_fun_Z_0(p(s(n(e))), a(e, e)) = e)),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1384,plain,
% 63.96/64.19 ((~(mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(e)) <=> (tptp_fun_Z_0(p(s(n(e))), a(e, e)) = e))) | (tptp_fun_Z_0(p(s(n(e))), a(e, e)) = e)),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1383, 1382])).
% 63.96/64.19 tff(1385,plain,
% 63.96/64.19 (tptp_fun_Z_0(p(s(n(e))), a(e, e)) = e),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1384, 1352])).
% 63.96/64.19 tff(1386,plain,
% 63.96/64.19 (tptp_fun_Z_0(p(s(n(e))), a(e, e)) = tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))),
% 63.96/64.19 inference(transitivity,[status(thm)],[1385, 1350])).
% 63.96/64.19 tff(1387,plain,
% 63.96/64.19 (subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e))) <=> subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))),
% 63.96/64.19 inference(monotonicity,[status(thm)],[1386])).
% 63.96/64.19 tff(1388,plain,
% 63.96/64.19 (subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) <=> subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e)))),
% 63.96/64.19 inference(symmetry,[status(thm)],[1387])).
% 63.96/64.19 tff(1389,plain,
% 63.96/64.19 (tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))) = tptp_fun_Z_0(s(n(e)), e)),
% 63.96/64.19 inference(monotonicity,[status(thm)],[1349])).
% 63.96/64.19 tff(1390,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))) <=> mem(tptp_fun_Z_0(s(n(e)), e), e)),
% 63.96/64.19 inference(monotonicity,[status(thm)],[1389, 1349])).
% 63.96/64.19 tff(1391,plain,
% 63.96/64.19 (mem(tptp_fun_Z_0(s(n(e)), e), e) <=> mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))),
% 63.96/64.19 inference(symmetry,[status(thm)],[1390])).
% 63.96/64.19 tff(1392,plain,
% 63.96/64.19 ((~mem(tptp_fun_Z_0(s(n(e)), e), e)) <=> (~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))))),
% 63.96/64.19 inference(monotonicity,[status(thm)],[1391])).
% 63.96/64.19 tff(1393,assumption,(mem(tptp_fun_Z_0(s(n(e)), e), e)), introduced(assumption)).
% 63.96/64.19 tff(1394,plain,
% 63.96/64.19 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(s(n(e)), e), e))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1395,plain,
% 63.96/64.19 ($false),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1394, 89, 1393])).
% 63.96/64.19 tff(1396,plain,(~mem(tptp_fun_Z_0(s(n(e)), e), e)), inference(lemma,lemma(discharge,[]))).
% 63.96/64.19 tff(1397,plain,
% 63.96/64.19 (~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))),
% 63.96/64.19 inference(modus_ponens,[status(thm)],[1396, 1392])).
% 63.96/64.19 tff(1398,plain,
% 63.96/64.19 (((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e)))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))),
% 63.96/64.19 inference(tautology,[status(thm)],[])).
% 63.96/64.19 tff(1399,plain,
% 63.96/64.19 ((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e)))),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1398, 1397])).
% 63.96/64.19 tff(1400,assumption,((~((~subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(Z, s(n(e)))))) | (~(subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e)))))))), introduced(assumption)).
% 63.96/64.19 tff(1401,plain,
% 63.96/64.19 ((~![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(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(Z, s(n(e)))))) | (~(subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e)))))))))),
% 63.96/64.19 inference(quant_inst,[status(thm)],[])).
% 63.96/64.19 tff(1402,plain,
% 63.96/64.19 ($false),
% 63.96/64.19 inference(unit_resolution,[status(thm)],[1401, 229, 1400])).
% 63.96/64.19 tff(1403,plain,(~((~((~subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(Z, s(n(e)))))) | (~(subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e))))))))), inference(lemma,lemma(discharge,[]))).
% 63.96/64.20 tff(1404,plain,
% 63.96/64.20 (((~((~subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(Z, s(n(e)))))) | (~(subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e)))))))) | (subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e))))))),
% 63.96/64.20 inference(tautology,[status(thm)],[])).
% 63.96/64.20 tff(1405,plain,
% 63.96/64.20 (subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e)))))),
% 63.96/64.20 inference(unit_resolution,[status(thm)],[1404, 1403])).
% 63.96/64.20 tff(1406,plain,
% 63.96/64.20 ((~(subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e))))))) | subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e)))))),
% 63.96/64.20 inference(tautology,[status(thm)],[])).
% 63.96/64.20 tff(1407,plain,
% 63.96/64.20 (subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))))) | mem(tptp_fun_Z_0(s(n(e)), tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e))))), s(n(e)))))),
% 63.96/64.20 inference(unit_resolution,[status(thm)],[1406, 1405])).
% 63.96/64.20 tff(1408,plain,
% 63.96/64.20 (subq(tptp_fun_Z_0(m(p(u(n(e), n(s(n(e))))), p(p(s(n(e))))), a(n(n(e)), n(n(e)))), s(n(e)))),
% 63.96/64.20 inference(unit_resolution,[status(thm)],[1407, 1399])).
% 63.96/64.20 tff(1409,plain,
% 63.96/64.20 (subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e)))),
% 63.96/64.20 inference(modus_ponens,[status(thm)],[1408, 1388])).
% 63.96/64.20 tff(1410,plain,
% 63.96/64.20 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))) <=> subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e))))),
% 63.96/64.20 inference(quant_inst,[status(thm)],[])).
% 63.96/64.20 tff(1411,plain,
% 63.96/64.20 (mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))) <=> subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e)))),
% 63.96/64.20 inference(unit_resolution,[status(thm)],[1410, 497])).
% 63.96/64.20 tff(1412,plain,
% 63.96/64.20 (((~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))) | (~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))))),
% 64.03/64.21 inference(tautology,[status(thm)],[])).
% 64.03/64.21 tff(1413,plain,
% 64.03/64.21 (~mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e))))),
% 64.03/64.21 inference(unit_resolution,[status(thm)],[1412, 1370])).
% 64.03/64.21 tff(1414,plain,
% 64.03/64.21 ((~(mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))) <=> subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e))))) | mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))) | (~subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e))))),
% 64.03/64.21 inference(tautology,[status(thm)],[])).
% 64.03/64.21 tff(1415,plain,
% 64.03/64.21 ((~(mem(tptp_fun_Z_0(p(s(n(e))), a(e, e)), p(s(n(e)))) <=> subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e))))) | (~subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e))))),
% 64.03/64.21 inference(unit_resolution,[status(thm)],[1414, 1413])).
% 64.03/64.21 tff(1416,plain,
% 64.03/64.21 (~subq(tptp_fun_Z_0(p(s(n(e))), a(e, e)), s(n(e)))),
% 64.03/64.21 inference(unit_resolution,[status(thm)],[1415, 1411])).
% 64.03/64.21 tff(1417,plain,
% 64.03/64.21 ($false),
% 64.03/64.21 inference(unit_resolution,[status(thm)],[1416, 1409])).
% 64.03/64.21 tff(1418,plain,(subq(a(e, e), p(s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 64.03/64.21 tff(1419,plain,
% 64.03/64.21 ((~(mem(a(e, e), p(p(s(n(e))))) <=> subq(a(e, e), p(s(n(e)))))) | mem(a(e, e), p(p(s(n(e))))) | (~subq(a(e, e), p(s(n(e)))))),
% 64.03/64.21 inference(tautology,[status(thm)],[])).
% 64.03/64.21 tff(1420,plain,
% 64.03/64.21 (mem(a(e, e), p(p(s(n(e))))) | (~subq(a(e, e), p(s(n(e)))))),
% 64.03/64.21 inference(unit_resolution,[status(thm)],[1419, 747])).
% 64.03/64.21 tff(1421,plain,
% 64.03/64.21 (mem(a(e, e), p(p(s(n(e)))))),
% 64.03/64.21 inference(unit_resolution,[status(thm)],[1420, 1418])).
% 64.03/64.21 tff(1422,plain,
% 64.03/64.21 ($false),
% 64.03/64.21 inference(unit_resolution,[status(thm)],[1421, 742])).
% 64.03/64.21 tff(1423,plain,(~(a(e, e) = a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 64.03/64.21 tff(1424,plain,
% 64.03/64.21 (~(a(s(n(e)), s(n(e))) = a(e, e))),
% 64.03/64.21 inference(modus_ponens,[status(thm)],[1423, 701])).
% 64.03/64.21 tff(1425,plain,
% 64.03/64.21 ((~(mem(a(s(n(e)), s(n(e))), s(a(e, e))) <=> (a(s(n(e)), s(n(e))) = a(e, e)))) | (~mem(a(s(n(e)), s(n(e))), s(a(e, e)))) | (a(s(n(e)), s(n(e))) = a(e, e))),
% 64.03/64.21 inference(tautology,[status(thm)],[])).
% 64.03/64.21 tff(1426,plain,
% 64.03/64.21 ($false),
% 64.03/64.21 inference(unit_resolution,[status(thm)],[1425, 1424, 698, 9])).
% 64.03/64.21 % SZS output end Proof
% 64.03/64.21 % E exiting
%------------------------------------------------------------------------------