%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV568+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 27.54s 27.74s
% Output : Proof 27.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEV568+1 : TPTP v9.1.0. Released v9.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 07:43:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 27.54/27.74 % SZS status Theorem
% 27.54/27.74 % SZS output start Proof
% 27.54/27.74 tff(mem_type, type, (
% 27.54/27.74 mem: ( $i * $i ) > $o)).
% 27.54/27.74 tff(e_type, type, (
% 27.54/27.74 e: $i)).
% 27.54/27.74 tff(p_type, type, (
% 27.54/27.74 p: $i > $i)).
% 27.54/27.74 tff(s_type, type, (
% 27.54/27.74 s: $i > $i)).
% 27.54/27.74 tff(n_type, type, (
% 27.54/27.74 n: $i > $i)).
% 27.54/27.74 tff(a_type, type, (
% 27.54/27.74 a: ( $i * $i ) > $i)).
% 27.54/27.74 tff(u_type, type, (
% 27.54/27.74 u: ( $i * $i ) > $i)).
% 27.54/27.74 tff(subq_type, type, (
% 27.54/27.74 subq: ( $i * $i ) > $o)).
% 27.54/27.74 tff(tptp_fun_Z_0_type, type, (
% 27.54/27.74 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 27.54/27.74 tff(1,plain,
% 27.54/27.74 (^[X: $i, Y: $i] : refl((a(X, Y) = u(X, s(Y))) <=> (a(X, Y) = u(X, s(Y))))),
% 27.54/27.74 inference(bind,[status(th)],[])).
% 27.54/27.74 tff(2,plain,
% 27.54/27.74 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 27.54/27.74 inference(quant_intro,[status(thm)],[1])).
% 27.54/27.74 tff(3,plain,
% 27.54/27.74 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 27.54/27.74 inference(rewrite,[status(thm)],[])).
% 27.54/27.74 tff(4,axiom,(![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','a_def')).
% 27.54/27.74 tff(5,plain,
% 27.54/27.74 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 27.54/27.74 inference(modus_ponens,[status(thm)],[4, 3])).
% 27.54/27.74 tff(6,plain,(
% 27.54/27.74 ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 27.54/27.74 inference(skolemize,[status(sab)],[5])).
% 27.54/27.74 tff(7,plain,
% 27.54/27.74 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 27.54/27.74 inference(modus_ponens,[status(thm)],[6, 2])).
% 27.54/27.74 tff(8,plain,
% 27.54/27.74 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(n(n(e))), s(n(n(e)))) = u(s(n(n(e))), s(s(n(n(e))))))),
% 27.54/27.74 inference(quant_inst,[status(thm)],[])).
% 27.54/27.74 tff(9,plain,
% 27.54/27.74 (a(s(n(n(e))), s(n(n(e)))) = u(s(n(n(e))), s(s(n(n(e)))))),
% 27.54/27.74 inference(unit_resolution,[status(thm)],[8, 7])).
% 27.54/27.74 tff(10,plain,
% 27.54/27.74 (mem(e, a(s(n(n(e))), s(n(n(e))))) <=> mem(e, u(s(n(n(e))), s(s(n(n(e))))))),
% 27.54/27.74 inference(monotonicity,[status(thm)],[9])).
% 27.54/27.74 tff(11,plain,
% 27.54/27.74 (mem(e, u(s(n(n(e))), s(s(n(n(e)))))) <=> mem(e, a(s(n(n(e))), s(n(n(e)))))),
% 27.54/27.74 inference(symmetry,[status(thm)],[10])).
% 27.54/27.74 tff(12,plain,
% 27.54/27.74 ((~mem(e, u(s(n(n(e))), s(s(n(n(e))))))) <=> (~mem(e, a(s(n(n(e))), s(n(n(e))))))),
% 27.54/27.74 inference(monotonicity,[status(thm)],[11])).
% 27.54/27.74 tff(13,assumption,(s(n(n(e))) = e), introduced(assumption)).
% 27.54/27.74 tff(14,plain,
% 27.54/27.74 (^[X: $i] : refl((n(X) = a(X, X)) <=> (n(X) = a(X, X)))),
% 27.54/27.74 inference(bind,[status(th)],[])).
% 27.54/27.74 tff(15,plain,
% 27.54/27.74 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 27.54/27.74 inference(quant_intro,[status(thm)],[14])).
% 27.54/27.74 tff(16,plain,
% 27.54/27.74 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 27.54/27.74 inference(rewrite,[status(thm)],[])).
% 27.54/27.74 tff(17,axiom,(![X: $i] : (n(X) = a(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','n_def')).
% 27.54/27.74 tff(18,plain,
% 27.54/27.74 (![X: $i] : (n(X) = a(X, X))),
% 27.54/27.74 inference(modus_ponens,[status(thm)],[17, 16])).
% 27.54/27.74 tff(19,plain,(
% 27.54/27.74 ![X: $i] : (n(X) = a(X, X))),
% 27.54/27.74 inference(skolemize,[status(sab)],[18])).
% 27.54/27.74 tff(20,plain,
% 27.54/27.74 (![X: $i] : (n(X) = a(X, X))),
% 27.54/27.74 inference(modus_ponens,[status(thm)],[19, 15])).
% 27.54/27.74 tff(21,plain,
% 27.54/27.74 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(e)) = a(n(e), n(e)))),
% 27.54/27.74 inference(quant_inst,[status(thm)],[])).
% 27.54/27.74 tff(22,plain,
% 27.54/27.74 (n(n(e)) = a(n(e), n(e))),
% 27.54/27.74 inference(unit_resolution,[status(thm)],[21, 20])).
% 27.54/27.74 tff(23,plain,
% 27.54/27.74 (a(n(e), n(e)) = n(n(e))),
% 27.54/27.74 inference(symmetry,[status(thm)],[22])).
% 27.54/27.74 tff(24,plain,
% 27.54/27.74 (s(a(n(e), n(e))) = s(n(n(e)))),
% 27.54/27.74 inference(monotonicity,[status(thm)],[23])).
% 27.54/27.74 tff(25,plain,
% 27.54/27.74 (s(a(n(e), n(e))) = e),
% 27.54/27.74 inference(transitivity,[status(thm)],[24, 13])).
% 27.54/27.74 tff(26,plain,
% 27.54/27.74 (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> mem(a(n(e), n(e)), e)),
% 27.54/27.74 inference(monotonicity,[status(thm)],[25])).
% 27.54/27.74 tff(27,plain,
% 27.54/27.74 (mem(a(n(e), n(e)), e) <=> mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 27.54/27.74 inference(symmetry,[status(thm)],[26])).
% 27.54/27.74 tff(28,plain,
% 27.54/27.74 ((~mem(a(n(e), n(e)), e)) <=> (~mem(a(n(e), n(e)), s(a(n(e), n(e)))))),
% 27.54/27.74 inference(monotonicity,[status(thm)],[27])).
% 27.54/27.74 tff(29,assumption,(mem(a(n(e), n(e)), e)), introduced(assumption)).
% 27.54/27.74 tff(30,plain,
% 27.54/27.74 (^[X: $i] : refl((~mem(X, e)) <=> (~mem(X, e)))),
% 27.54/27.74 inference(bind,[status(th)],[])).
% 27.54/27.74 tff(31,plain,
% 27.54/27.74 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 27.54/27.74 inference(quant_intro,[status(thm)],[30])).
% 27.54/27.75 tff(32,plain,
% 27.54/27.75 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(33,axiom,(![X: $i] : (~mem(X, e))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','e_ax')).
% 27.54/27.75 tff(34,plain,
% 27.54/27.75 (![X: $i] : (~mem(X, e))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[33, 32])).
% 27.54/27.75 tff(35,plain,(
% 27.54/27.75 ![X: $i] : (~mem(X, e))),
% 27.54/27.75 inference(skolemize,[status(sab)],[34])).
% 27.54/27.75 tff(36,plain,
% 27.54/27.75 (![X: $i] : (~mem(X, e))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[35, 31])).
% 27.54/27.75 tff(37,plain,
% 27.54/27.75 ((~![X: $i] : (~mem(X, e))) | (~mem(a(n(e), n(e)), e))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(38,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[37, 36, 29])).
% 27.54/27.75 tff(39,plain,(~mem(a(n(e), n(e)), e)), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(40,plain,
% 27.54/27.75 (~mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[39, 28])).
% 27.54/27.75 tff(41,plain,
% 27.54/27.75 (^[X: $i, Y: $i] : refl((mem(X, s(Y)) <=> (X = Y)) <=> (mem(X, s(Y)) <=> (X = Y)))),
% 27.54/27.75 inference(bind,[status(th)],[])).
% 27.54/27.75 tff(42,plain,
% 27.54/27.75 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 27.54/27.75 inference(quant_intro,[status(thm)],[41])).
% 27.54/27.75 tff(43,plain,
% 27.54/27.75 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(44,axiom,(![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','s_ax')).
% 27.54/27.75 tff(45,plain,
% 27.54/27.75 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[44, 43])).
% 27.54/27.75 tff(46,plain,(
% 27.54/27.75 ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 27.54/27.75 inference(skolemize,[status(sab)],[45])).
% 27.54/27.75 tff(47,plain,
% 27.54/27.75 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[46, 42])).
% 27.54/27.75 tff(48,plain,
% 27.54/27.75 (((~![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)))))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(49,plain,
% 27.54/27.75 ((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))))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(50,plain,
% 27.54/27.75 ((a(n(e), n(e)) = a(n(e), n(e))) <=> $true),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(51,plain,
% 27.54/27.75 ((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)),
% 27.54/27.75 inference(monotonicity,[status(thm)],[50])).
% 27.54/27.75 tff(52,plain,
% 27.54/27.75 ((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))))),
% 27.54/27.75 inference(transitivity,[status(thm)],[51, 49])).
% 27.54/27.75 tff(53,plain,
% 27.54/27.75 (((~![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)))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[52])).
% 27.54/27.75 tff(54,plain,
% 27.54/27.75 (((~![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)))))),
% 27.54/27.75 inference(transitivity,[status(thm)],[53, 48])).
% 27.54/27.75 tff(55,plain,
% 27.54/27.75 ((~![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))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(56,plain,
% 27.54/27.75 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[55, 54])).
% 27.54/27.75 tff(57,plain,
% 27.54/27.75 (mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[56, 47])).
% 27.54/27.75 tff(58,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[57, 40])).
% 27.54/27.75 tff(59,plain,(~(s(n(n(e))) = e)), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(60,assumption,(e = s(n(n(e)))), introduced(assumption)).
% 27.54/27.75 tff(61,plain,
% 27.54/27.75 (s(n(n(e))) = e),
% 27.54/27.75 inference(symmetry,[status(thm)],[60])).
% 27.54/27.75 tff(62,assumption,(~(s(n(n(e))) = e)), introduced(assumption)).
% 27.54/27.75 tff(63,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[62, 61])).
% 27.54/27.75 tff(64,plain,((~(e = s(n(n(e))))) | (s(n(n(e))) = e)), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(65,plain,
% 27.54/27.75 (~(e = s(n(n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[64, 59])).
% 27.54/27.75 tff(66,assumption,(~(mem(e, s(s(n(n(e))))) <=> (e = s(n(n(e)))))), introduced(assumption)).
% 27.54/27.75 tff(67,plain,
% 27.54/27.75 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(s(n(n(e))))) <=> (e = s(n(n(e)))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(68,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[67, 47, 66])).
% 27.54/27.75 tff(69,plain,(mem(e, s(s(n(n(e))))) <=> (e = s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(70,plain,
% 27.54/27.75 ((~(mem(e, s(s(n(n(e))))) <=> (e = s(n(n(e)))))) | (~mem(e, s(s(n(n(e)))))) | (e = s(n(n(e))))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(71,plain,
% 27.54/27.75 ((~mem(e, s(s(n(n(e)))))) | (e = s(n(n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[70, 69])).
% 27.54/27.75 tff(72,plain,
% 27.54/27.75 (~mem(e, s(s(n(n(e)))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[71, 65])).
% 27.54/27.75 tff(73,plain,
% 27.54/27.75 (mem(e, s(a(n(e), n(e)))) <=> mem(e, s(n(n(e))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[24])).
% 27.54/27.75 tff(74,plain,
% 27.54/27.75 (mem(e, s(n(n(e)))) <=> mem(e, s(a(n(e), n(e))))),
% 27.54/27.75 inference(symmetry,[status(thm)],[73])).
% 27.54/27.75 tff(75,assumption,(mem(e, s(n(n(e))))), introduced(assumption)).
% 27.54/27.75 tff(76,plain,
% 27.54/27.75 (mem(e, s(a(n(e), n(e))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[75, 74])).
% 27.54/27.75 tff(77,assumption,(~(mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e))))), introduced(assumption)).
% 27.54/27.75 tff(78,plain,
% 27.54/27.75 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(79,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[78, 47, 77])).
% 27.54/27.75 tff(80,plain,(mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(81,assumption,(e = a(n(e), n(e))), introduced(assumption)).
% 27.54/27.75 tff(82,plain,
% 27.54/27.75 (a(n(e), n(e)) = e),
% 27.54/27.75 inference(symmetry,[status(thm)],[81])).
% 27.54/27.75 tff(83,plain,
% 27.54/27.75 (mem(a(n(e), n(e)), e) <=> mem(e, a(n(e), n(e)))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[82, 81])).
% 27.54/27.75 tff(84,plain,
% 27.54/27.75 (mem(e, a(n(e), n(e))) <=> mem(a(n(e), n(e)), e)),
% 27.54/27.75 inference(symmetry,[status(thm)],[83])).
% 27.54/27.75 tff(85,plain,
% 27.54/27.75 ((~![X: $i] : (n(X) = a(X, X))) | (n(e) = a(e, e))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(86,plain,
% 27.54/27.75 (n(e) = a(e, e)),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[85, 20])).
% 27.54/27.75 tff(87,plain,
% 27.54/27.75 (a(e, e) = n(e)),
% 27.54/27.75 inference(symmetry,[status(thm)],[86])).
% 27.54/27.75 tff(88,plain,
% 27.54/27.75 (a(a(e, e), a(e, e)) = a(n(e), n(e))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[87, 87])).
% 27.54/27.75 tff(89,plain,
% 27.54/27.75 ((~![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))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(90,plain,
% 27.54/27.75 (a(a(e, e), a(e, e)) = u(a(e, e), s(a(e, e)))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[89, 7])).
% 27.54/27.75 tff(91,plain,
% 27.54/27.75 (u(a(e, e), s(a(e, e))) = a(a(e, e), a(e, e))),
% 27.54/27.75 inference(symmetry,[status(thm)],[90])).
% 27.54/27.75 tff(92,plain,
% 27.54/27.75 (s(a(e, e)) = s(n(e))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[87])).
% 27.54/27.75 tff(93,plain,
% 27.54/27.75 (s(n(e)) = s(a(e, e))),
% 27.54/27.75 inference(symmetry,[status(thm)],[92])).
% 27.54/27.75 tff(94,plain,
% 27.54/27.75 (u(a(e, e), s(n(e))) = u(a(e, e), s(a(e, e)))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[93])).
% 27.54/27.75 tff(95,plain,
% 27.54/27.75 (u(a(e, e), s(n(e))) = a(n(e), n(e))),
% 27.54/27.75 inference(transitivity,[status(thm)],[94, 91, 88])).
% 27.54/27.75 tff(96,plain,
% 27.54/27.75 (mem(e, u(a(e, e), s(n(e)))) <=> mem(e, a(n(e), n(e)))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[95])).
% 27.54/27.75 tff(97,plain,
% 27.54/27.75 (mem(e, a(n(e), n(e))) <=> mem(e, u(a(e, e), s(n(e))))),
% 27.54/27.75 inference(symmetry,[status(thm)],[96])).
% 27.54/27.75 tff(98,plain,
% 27.54/27.75 ((~mem(e, a(n(e), n(e)))) <=> (~mem(e, u(a(e, e), s(n(e)))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[97])).
% 27.54/27.75 tff(99,assumption,(~mem(e, a(n(e), n(e)))), introduced(assumption)).
% 27.54/27.75 tff(100,plain,
% 27.54/27.75 (~mem(e, u(a(e, e), s(n(e))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[99, 98])).
% 27.54/27.75 tff(101,plain,
% 27.54/27.75 (^[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))))),
% 27.54/27.75 inference(bind,[status(th)],[])).
% 27.54/27.75 tff(102,plain,
% 27.54/27.75 (![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)))),
% 27.54/27.75 inference(quant_intro,[status(thm)],[101])).
% 27.54/27.75 tff(103,plain,
% 27.54/27.75 (![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)))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(104,plain,
% 27.54/27.75 (^[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))))),
% 27.54/27.75 inference(bind,[status(th)],[])).
% 27.54/27.75 tff(105,plain,
% 27.54/27.75 (![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)))),
% 27.54/27.75 inference(quant_intro,[status(thm)],[104])).
% 27.54/27.75 tff(106,axiom,(![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Y) | mem(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','u_ax')).
% 27.54/27.75 tff(107,plain,
% 27.54/27.75 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[106, 105])).
% 27.54/27.75 tff(108,plain,
% 27.54/27.75 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[107, 103])).
% 27.54/27.75 tff(109,plain,(
% 27.54/27.75 ![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 27.54/27.75 inference(skolemize,[status(sab)],[108])).
% 27.54/27.75 tff(110,plain,
% 27.54/27.75 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[109, 102])).
% 27.54/27.75 tff(111,plain,
% 27.54/27.75 (((~![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))))))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(112,plain,
% 27.54/27.75 ((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)))))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(113,plain,
% 27.54/27.75 (((~![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))))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[112])).
% 27.54/27.75 tff(114,plain,
% 27.54/27.75 (((~![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))))))),
% 27.54/27.75 inference(transitivity,[status(thm)],[113, 111])).
% 27.54/27.75 tff(115,plain,
% 27.54/27.75 ((~![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))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(116,plain,
% 27.54/27.75 ((~![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)))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[115, 114])).
% 27.54/27.75 tff(117,plain,
% 27.54/27.75 (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[116, 110])).
% 27.54/27.75 tff(118,plain,
% 27.54/27.75 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(e, e) = u(e, s(e)))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(119,plain,
% 27.54/27.75 (a(e, e) = u(e, s(e))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[118, 7])).
% 27.54/27.75 tff(120,plain,
% 27.54/27.75 (u(e, s(e)) = a(e, e)),
% 27.54/27.75 inference(symmetry,[status(thm)],[119])).
% 27.54/27.75 tff(121,plain,
% 27.54/27.75 (mem(e, u(e, s(e))) <=> mem(e, a(e, e))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[120])).
% 27.54/27.75 tff(122,plain,
% 27.54/27.75 (mem(e, a(e, e)) <=> mem(e, u(e, s(e)))),
% 27.54/27.75 inference(symmetry,[status(thm)],[121])).
% 27.54/27.75 tff(123,plain,
% 27.54/27.75 ((~mem(e, a(e, e))) <=> (~mem(e, u(e, s(e))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[122])).
% 27.54/27.75 tff(124,assumption,(~mem(e, a(e, e))), introduced(assumption)).
% 27.54/27.75 tff(125,plain,
% 27.54/27.75 (~mem(e, u(e, s(e)))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[124, 123])).
% 27.54/27.75 tff(126,plain,
% 27.54/27.75 ((~![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)))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(127,plain,
% 27.54/27.75 (mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[126, 110])).
% 27.54/27.75 tff(128,plain,
% 27.54/27.75 (((~![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)))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(129,plain,
% 27.54/27.75 ((mem(e, s(e)) <=> $true) <=> mem(e, s(e))),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(130,plain,
% 27.54/27.75 ((e = e) <=> $true),
% 27.54/27.75 inference(rewrite,[status(thm)],[])).
% 27.54/27.75 tff(131,plain,
% 27.54/27.75 ((mem(e, s(e)) <=> (e = e)) <=> (mem(e, s(e)) <=> $true)),
% 27.54/27.75 inference(monotonicity,[status(thm)],[130])).
% 27.54/27.75 tff(132,plain,
% 27.54/27.75 ((mem(e, s(e)) <=> (e = e)) <=> mem(e, s(e))),
% 27.54/27.75 inference(transitivity,[status(thm)],[131, 129])).
% 27.54/27.75 tff(133,plain,
% 27.54/27.75 (((~![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)))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[132])).
% 27.54/27.75 tff(134,plain,
% 27.54/27.75 (((~![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)))),
% 27.54/27.75 inference(transitivity,[status(thm)],[133, 128])).
% 27.54/27.75 tff(135,plain,
% 27.54/27.75 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(e)) <=> (e = e))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(136,plain,
% 27.54/27.75 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(e, s(e))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[135, 134])).
% 27.54/27.75 tff(137,plain,
% 27.54/27.75 (mem(e, s(e))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[136, 47])).
% 27.54/27.75 tff(138,plain,
% 27.54/27.75 ((mem(e, s(e)) | mem(e, e)) | (~mem(e, s(e)))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(139,plain,
% 27.54/27.75 (mem(e, s(e)) | mem(e, e)),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[138, 137])).
% 27.54/27.75 tff(140,plain,
% 27.54/27.75 ((~(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))) | mem(e, u(e, s(e))) | (~(mem(e, s(e)) | mem(e, e)))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(141,plain,
% 27.54/27.75 ((~(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))) | mem(e, u(e, s(e)))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[140, 139])).
% 27.54/27.75 tff(142,plain,
% 27.54/27.75 (mem(e, u(e, s(e)))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[141, 127])).
% 27.54/27.75 tff(143,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[142, 125])).
% 27.54/27.75 tff(144,plain,(mem(e, a(e, e))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(145,plain,
% 27.54/27.75 ((mem(e, a(e, e)) | mem(e, s(n(e)))) | (~mem(e, a(e, e)))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(146,plain,
% 27.54/27.75 (mem(e, a(e, e)) | mem(e, s(n(e)))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[145, 144])).
% 27.54/27.75 tff(147,plain,
% 27.54/27.75 ((~(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)))))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(148,plain,
% 27.54/27.75 ((~(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))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[147, 146])).
% 27.54/27.75 tff(149,plain,
% 27.54/27.75 (mem(e, u(a(e, e), s(n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[148, 117])).
% 27.54/27.75 tff(150,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[149, 100])).
% 27.54/27.75 tff(151,plain,(mem(e, a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(152,plain,
% 27.54/27.75 (mem(a(n(e), n(e)), e)),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[151, 84])).
% 27.54/27.75 tff(153,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[39, 152])).
% 27.54/27.75 tff(154,plain,(~(e = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(155,plain,
% 27.54/27.75 ((~(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)))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(156,plain,
% 27.54/27.75 (~mem(e, s(a(n(e), n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[155, 154, 80])).
% 27.54/27.75 tff(157,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[156, 76])).
% 27.54/27.75 tff(158,plain,(~mem(e, s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(159,plain,
% 27.54/27.75 ((~(mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e)))))) | mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e))))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(160,plain,
% 27.54/27.75 (~(mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e)))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[159, 158, 72])).
% 27.54/27.75 tff(161,assumption,(~(mem(e, u(s(n(n(e))), s(s(n(n(e)))))) <=> (mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e))))))), introduced(assumption)).
% 27.54/27.75 tff(162,plain,
% 27.54/27.75 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(n(e))), s(s(n(n(e)))))) <=> (mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e))))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(163,plain,
% 27.54/27.75 ($false),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[162, 110, 161])).
% 27.54/27.75 tff(164,plain,(mem(e, u(s(n(n(e))), s(s(n(n(e)))))) <=> (mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.75 tff(165,plain,
% 27.54/27.75 ((~(mem(e, u(s(n(n(e))), s(s(n(n(e)))))) <=> (mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e))))))) | (~mem(e, u(s(n(n(e))), s(s(n(n(e))))))) | (mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e)))))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(166,plain,
% 27.54/27.75 ((~mem(e, u(s(n(n(e))), s(s(n(n(e))))))) | (mem(e, s(s(n(n(e))))) | mem(e, s(n(n(e)))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[165, 164])).
% 27.54/27.75 tff(167,plain,
% 27.54/27.75 (~mem(e, u(s(n(n(e))), s(s(n(n(e))))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[166, 160])).
% 27.54/27.75 tff(168,plain,
% 27.54/27.75 (~mem(e, a(s(n(n(e))), s(n(n(e)))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[167, 12])).
% 27.54/27.75 tff(169,plain,
% 27.54/27.75 ((~![X: $i] : (n(X) = a(X, X))) | (n(s(n(n(e)))) = a(s(n(n(e))), s(n(n(e)))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(170,plain,
% 27.54/27.75 (n(s(n(n(e)))) = a(s(n(n(e))), s(n(n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[169, 20])).
% 27.54/27.75 tff(171,plain,
% 27.54/27.75 (a(s(n(n(e))), s(n(n(e)))) = n(s(n(n(e))))),
% 27.54/27.75 inference(symmetry,[status(thm)],[170])).
% 27.54/27.75 tff(172,plain,
% 27.54/27.75 (u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e))))) = u(n(s(n(n(e)))), s(n(n(n(e)))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[171])).
% 27.54/27.75 tff(173,plain,
% 27.54/27.75 (mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e)))))) <=> mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[172])).
% 27.54/27.75 tff(174,plain,
% 27.54/27.75 (mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))) <=> mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e))))))),
% 27.54/27.75 inference(symmetry,[status(thm)],[173])).
% 27.54/27.75 tff(175,assumption,(mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))), introduced(assumption)).
% 27.54/27.75 tff(176,plain,
% 27.54/27.75 (mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e))))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[175, 174])).
% 27.54/27.75 tff(177,plain,
% 27.54/27.75 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, a(s(n(n(e))), s(n(n(e)))))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(178,plain,
% 27.54/27.75 (mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, a(s(n(n(e))), s(n(n(e))))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[177, 110])).
% 27.54/27.75 tff(179,assumption,(~mem(e, a(s(n(n(e))), s(n(n(e)))))), introduced(assumption)).
% 27.54/27.75 tff(180,plain,
% 27.54/27.75 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(n(e))) = a(n(n(e)), n(n(e))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(181,plain,
% 27.54/27.75 (n(n(n(e))) = a(n(n(e)), n(n(e)))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[180, 20])).
% 27.54/27.75 tff(182,plain,
% 27.54/27.75 (a(n(n(e)), n(n(e))) = n(n(n(e)))),
% 27.54/27.75 inference(symmetry,[status(thm)],[181])).
% 27.54/27.75 tff(183,plain,
% 27.54/27.75 (s(a(n(n(e)), n(n(e)))) = s(n(n(n(e))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[182])).
% 27.54/27.75 tff(184,plain,
% 27.54/27.75 (mem(e, s(a(n(n(e)), n(n(e))))) <=> mem(e, s(n(n(n(e)))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[183])).
% 27.54/27.75 tff(185,plain,
% 27.54/27.75 (mem(e, s(n(n(n(e))))) <=> mem(e, s(a(n(n(e)), n(n(e)))))),
% 27.54/27.75 inference(symmetry,[status(thm)],[184])).
% 27.54/27.75 tff(186,assumption,(mem(e, s(n(n(n(e)))))), introduced(assumption)).
% 27.54/27.75 tff(187,plain,
% 27.54/27.75 (mem(e, s(a(n(n(e)), n(n(e)))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[186, 185])).
% 27.54/27.75 tff(188,plain,
% 27.54/27.75 ((~![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)))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(189,plain,
% 27.54/27.75 (mem(e, s(a(n(n(e)), n(n(e))))) <=> (e = a(n(n(e)), n(n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[188, 47])).
% 27.54/27.75 tff(190,assumption,(e = a(n(n(e)), n(n(e)))), introduced(assumption)).
% 27.54/27.75 tff(191,plain,
% 27.54/27.75 (mem(a(n(n(e)), n(n(e))), e) <=> mem(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[190])).
% 27.54/27.75 tff(192,plain,
% 27.54/27.75 (mem(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e)))) <=> mem(a(n(n(e)), n(n(e))), e)),
% 27.54/27.75 inference(symmetry,[status(thm)],[191])).
% 27.54/27.75 tff(193,plain,
% 27.54/27.75 (mem(e, a(n(n(e)), n(n(e)))) <=> mem(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[190])).
% 27.54/27.75 tff(194,plain,
% 27.54/27.75 (mem(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e)))) <=> mem(e, a(n(n(e)), n(n(e))))),
% 27.54/27.75 inference(symmetry,[status(thm)],[193])).
% 27.54/27.75 tff(195,plain,
% 27.54/27.75 ((~mem(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e))))) <=> (~mem(e, a(n(n(e)), n(n(e)))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[194])).
% 27.54/27.75 tff(196,assumption,(~mem(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e))))), introduced(assumption)).
% 27.54/27.75 tff(197,plain,
% 27.54/27.75 (~mem(e, a(n(n(e)), n(n(e))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[196, 195])).
% 27.54/27.75 tff(198,plain,
% 27.54/27.75 (a(a(n(e), n(e)), a(n(e), n(e))) = a(n(n(e)), n(n(e)))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[23, 23])).
% 27.54/27.75 tff(199,plain,
% 27.54/27.75 ((~![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)))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(200,plain,
% 27.54/27.75 (a(a(n(e), n(e)), a(n(e), n(e))) = u(a(n(e), n(e)), s(a(n(e), n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[199, 7])).
% 27.54/27.75 tff(201,plain,
% 27.54/27.75 (u(a(n(e), n(e)), s(a(n(e), n(e)))) = a(a(n(e), n(e)), a(n(e), n(e)))),
% 27.54/27.75 inference(symmetry,[status(thm)],[200])).
% 27.54/27.75 tff(202,plain,
% 27.54/27.75 (s(n(n(e))) = s(a(n(e), n(e)))),
% 27.54/27.75 inference(symmetry,[status(thm)],[24])).
% 27.54/27.75 tff(203,plain,
% 27.54/27.75 (u(a(n(e), n(e)), s(n(n(e)))) = u(a(n(e), n(e)), s(a(n(e), n(e))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[202])).
% 27.54/27.75 tff(204,plain,
% 27.54/27.75 (u(a(n(e), n(e)), s(n(n(e)))) = a(n(n(e)), n(n(e)))),
% 27.54/27.75 inference(transitivity,[status(thm)],[203, 201, 198])).
% 27.54/27.75 tff(205,plain,
% 27.54/27.75 (mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> mem(e, a(n(n(e)), n(n(e))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[204])).
% 27.54/27.75 tff(206,plain,
% 27.54/27.75 (mem(e, a(n(n(e)), n(n(e)))) <=> mem(e, u(a(n(e), n(e)), s(n(n(e)))))),
% 27.54/27.75 inference(symmetry,[status(thm)],[205])).
% 27.54/27.75 tff(207,plain,
% 27.54/27.75 ((~mem(e, a(n(n(e)), n(n(e))))) <=> (~mem(e, u(a(n(e), n(e)), s(n(n(e))))))),
% 27.54/27.75 inference(monotonicity,[status(thm)],[206])).
% 27.54/27.75 tff(208,assumption,(~mem(e, a(n(n(e)), n(n(e))))), introduced(assumption)).
% 27.54/27.75 tff(209,plain,
% 27.54/27.75 (~mem(e, u(a(n(e), n(e)), s(n(n(e)))))),
% 27.54/27.75 inference(modus_ponens,[status(thm)],[208, 207])).
% 27.54/27.75 tff(210,plain,
% 27.54/27.75 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))))),
% 27.54/27.75 inference(quant_inst,[status(thm)],[])).
% 27.54/27.75 tff(211,plain,
% 27.54/27.75 (mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e))))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[210, 110])).
% 27.54/27.75 tff(212,plain,
% 27.54/27.75 ((mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))) | (~mem(e, a(n(e), n(e))))),
% 27.54/27.75 inference(tautology,[status(thm)],[])).
% 27.54/27.75 tff(213,plain,
% 27.54/27.75 (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))),
% 27.54/27.75 inference(unit_resolution,[status(thm)],[212, 151])).
% 27.54/27.75 tff(214,plain,
% 27.54/27.75 ((~(mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))))) | mem(e, u(a(n(e), n(e)), s(n(n(e))))) | (~(mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))))),
% 27.54/27.76 inference(tautology,[status(thm)],[])).
% 27.54/27.76 tff(215,plain,
% 27.54/27.76 ((~(mem(e, u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(e, s(n(n(e)))) | mem(e, a(n(e), n(e)))))) | mem(e, u(a(n(e), n(e)), s(n(n(e)))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[214, 213])).
% 27.54/27.76 tff(216,plain,
% 27.54/27.76 (mem(e, u(a(n(e), n(e)), s(n(n(e)))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[215, 211])).
% 27.54/27.76 tff(217,plain,
% 27.54/27.76 ($false),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[216, 209])).
% 27.54/27.76 tff(218,plain,(mem(e, a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.76 tff(219,plain,
% 27.54/27.76 ($false),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[218, 197])).
% 27.54/27.76 tff(220,plain,(mem(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e)))) | (~(e = a(n(n(e)), n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.76 tff(221,plain,
% 27.54/27.76 (mem(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[220, 190])).
% 27.54/27.76 tff(222,plain,
% 27.54/27.76 (mem(a(n(n(e)), n(n(e))), e)),
% 27.54/27.76 inference(modus_ponens,[status(thm)],[221, 192])).
% 27.54/27.76 tff(223,plain,
% 27.54/27.76 ((~![X: $i] : (~mem(X, e))) | (~mem(a(n(n(e)), n(n(e))), e))),
% 27.54/27.76 inference(quant_inst,[status(thm)],[])).
% 27.54/27.76 tff(224,plain,
% 27.54/27.76 (~mem(a(n(n(e)), n(n(e))), e)),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[223, 36])).
% 27.54/27.76 tff(225,plain,
% 27.54/27.76 ($false),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[224, 222])).
% 27.54/27.76 tff(226,plain,(~(e = a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.76 tff(227,plain,
% 27.54/27.76 ((~(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))))),
% 27.54/27.76 inference(tautology,[status(thm)],[])).
% 27.54/27.76 tff(228,plain,
% 27.54/27.76 ((~(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))))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[227, 226])).
% 27.54/27.76 tff(229,plain,
% 27.54/27.76 (~mem(e, s(a(n(n(e)), n(n(e)))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[228, 189])).
% 27.54/27.76 tff(230,plain,
% 27.54/27.76 ($false),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[229, 187])).
% 27.54/27.76 tff(231,plain,(~mem(e, s(n(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.76 tff(232,plain,
% 27.54/27.76 ((~(mem(e, s(n(n(n(e))))) | mem(e, a(s(n(n(e))), s(n(n(e))))))) | mem(e, s(n(n(n(e))))) | mem(e, a(s(n(n(e))), s(n(n(e)))))),
% 27.54/27.76 inference(tautology,[status(thm)],[])).
% 27.54/27.76 tff(233,plain,
% 27.54/27.76 (~(mem(e, s(n(n(n(e))))) | mem(e, a(s(n(n(e))), s(n(n(e))))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[232, 231, 179])).
% 27.54/27.76 tff(234,plain,
% 27.54/27.76 ((~(mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, a(s(n(n(e))), s(n(n(e)))))))) | (~mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e))))))) | (mem(e, s(n(n(n(e))))) | mem(e, a(s(n(n(e))), s(n(n(e))))))),
% 27.54/27.76 inference(tautology,[status(thm)],[])).
% 27.54/27.76 tff(235,plain,
% 27.54/27.76 ((~(mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, a(s(n(n(e))), s(n(n(e)))))))) | (~mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e)))))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[234, 233])).
% 27.54/27.76 tff(236,plain,
% 27.54/27.76 (~mem(e, u(a(s(n(n(e))), s(n(n(e)))), s(n(n(n(e))))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[235, 178])).
% 27.54/27.76 tff(237,plain,
% 27.54/27.76 ($false),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[236, 176])).
% 27.54/27.76 tff(238,plain,((~mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))) | mem(e, a(s(n(n(e))), s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.76 tff(239,plain,
% 27.54/27.76 (~mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[238, 168])).
% 27.54/27.76 tff(240,assumption,(~(mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))))), introduced(assumption)).
% 27.54/27.76 tff(241,plain,
% 27.54/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))))))),
% 27.54/27.76 inference(rewrite,[status(thm)],[])).
% 27.54/27.76 tff(242,plain,
% 27.54/27.76 ((mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))) | mem(e, u(n(s(n(e))), s(p(s(n(e)))))))) <=> (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))))),
% 27.54/27.76 inference(rewrite,[status(thm)],[])).
% 27.54/27.76 tff(243,plain,
% 27.54/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))) | mem(e, u(n(s(n(e))), s(p(s(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))))))),
% 27.54/27.76 inference(monotonicity,[status(thm)],[242])).
% 27.54/27.76 tff(244,plain,
% 27.54/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))) | mem(e, u(n(s(n(e))), s(p(s(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))))))),
% 27.54/27.76 inference(transitivity,[status(thm)],[243, 241])).
% 27.54/27.76 tff(245,plain,
% 27.54/27.76 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))) | mem(e, u(n(s(n(e))), s(p(s(n(e))))))))),
% 27.54/27.76 inference(quant_inst,[status(thm)],[])).
% 27.54/27.76 tff(246,plain,
% 27.54/27.76 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))))),
% 27.54/27.76 inference(modus_ponens,[status(thm)],[245, 244])).
% 27.54/27.76 tff(247,plain,
% 27.54/27.76 ($false),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[246, 110, 240])).
% 27.54/27.76 tff(248,plain,(mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 27.54/27.76 tff(249,plain,
% 27.54/27.76 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(n(s(n(n(e)))), n(n(n(e)))) = u(n(s(n(n(e)))), s(n(n(n(e))))))),
% 27.54/27.76 inference(quant_inst,[status(thm)],[])).
% 27.54/27.76 tff(250,plain,
% 27.54/27.76 (a(n(s(n(n(e)))), n(n(n(e)))) = u(n(s(n(n(e)))), s(n(n(n(e)))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[249, 7])).
% 27.54/27.76 tff(251,plain,
% 27.54/27.76 (u(n(s(n(n(e)))), s(n(n(n(e))))) = a(n(s(n(n(e)))), n(n(n(e))))),
% 27.54/27.76 inference(symmetry,[status(thm)],[250])).
% 27.54/27.76 tff(252,plain,
% 27.54/27.76 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(n(s(n(e))), p(s(n(e)))) = u(n(s(n(e))), s(p(s(n(e))))))),
% 27.54/27.76 inference(quant_inst,[status(thm)],[])).
% 27.54/27.76 tff(253,plain,
% 27.54/27.76 (a(n(s(n(e))), p(s(n(e)))) = u(n(s(n(e))), s(p(s(n(e)))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[252, 7])).
% 27.54/27.76 tff(254,plain,
% 27.54/27.76 (u(n(s(n(e))), s(p(s(n(e))))) = a(n(s(n(e))), p(s(n(e))))),
% 27.54/27.76 inference(symmetry,[status(thm)],[253])).
% 27.54/27.76 tff(255,plain,
% 27.54/27.76 (u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e)))))) = u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))),
% 27.54/27.76 inference(monotonicity,[status(thm)],[254, 251])).
% 27.54/27.76 tff(256,plain,
% 27.54/27.76 (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> mem(e, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))),
% 27.54/27.76 inference(monotonicity,[status(thm)],[255])).
% 27.54/27.76 tff(257,plain,
% 27.54/27.76 (mem(e, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))) <=> mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e)))))))),
% 27.54/27.76 inference(symmetry,[status(thm)],[256])).
% 27.54/27.76 tff(258,plain,
% 27.54/27.76 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(s(n(e))), p(s(n(e)))) = u(s(s(n(e))), s(p(s(n(e))))))),
% 27.54/27.76 inference(quant_inst,[status(thm)],[])).
% 27.54/27.76 tff(259,plain,
% 27.54/27.76 (a(s(s(n(e))), p(s(n(e)))) = u(s(s(n(e))), s(p(s(n(e)))))),
% 27.54/27.76 inference(unit_resolution,[status(thm)],[258, 7])).
% 27.54/27.76 tff(260,plain,
% 27.54/27.76 (u(s(s(n(e))), s(p(s(n(e))))) = a(s(s(n(e))), p(s(n(e))))),
% 27.54/27.76 inference(symmetry,[status(thm)],[259])).
% 27.54/27.76 tff(261,plain,
% 27.54/27.76 (u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e)))))) = u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e))))))),
% 27.54/27.76 inference(monotonicity,[status(thm)],[260])).
% 27.54/27.76 tff(262,plain,
% 27.54/27.76 (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))),
% 27.54/27.76 inference(monotonicity,[status(thm)],[261])).
% 27.54/27.76 tff(263,plain,
% 27.54/27.76 (mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e)))))))),
% 27.54/27.76 inference(symmetry,[status(thm)],[262])).
% 27.54/27.76 tff(264,plain,
% 27.54/27.76 ((~mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) <=> (~mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))))),
% 27.54/27.76 inference(monotonicity,[status(thm)],[263])).
% 27.54/27.76 tff(265,assumption,(~mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))), introduced(assumption)).
% 27.54/27.76 tff(266,plain,
% 27.54/27.76 (~mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e)))))))),
% 27.54/27.76 inference(modus_ponens,[status(thm)],[265, 264])).
% 27.54/27.76 tff(267,plain,
% 27.54/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))))))),
% 27.54/27.76 inference(rewrite,[status(thm)],[])).
% 27.54/27.76 tff(268,plain,
% 27.54/27.76 ((mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))) | mem(e, u(s(s(n(e))), s(p(s(n(e)))))))) <=> (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))))),
% 27.54/27.76 inference(rewrite,[status(thm)],[])).
% 27.54/27.76 tff(269,plain,
% 27.54/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))) | mem(e, u(s(s(n(e))), s(p(s(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[268])).
% 27.61/27.76 tff(270,plain,
% 27.61/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))) | mem(e, u(s(s(n(e))), s(p(s(n(e))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))))))),
% 27.61/27.76 inference(transitivity,[status(thm)],[269, 267])).
% 27.61/27.76 tff(271,plain,
% 27.61/27.76 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))) | mem(e, u(s(s(n(e))), s(p(s(n(e))))))))),
% 27.61/27.76 inference(quant_inst,[status(thm)],[])).
% 27.61/27.76 tff(272,plain,
% 27.61/27.76 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))))),
% 27.61/27.76 inference(modus_ponens,[status(thm)],[271, 270])).
% 27.61/27.76 tff(273,plain,
% 27.61/27.76 (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))))),
% 27.61/27.76 inference(unit_resolution,[status(thm)],[272, 110])).
% 27.61/27.76 tff(274,plain,
% 27.61/27.76 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(n(n(e)))) = a(n(n(n(e))), n(n(n(e)))))),
% 27.61/27.76 inference(quant_inst,[status(thm)],[])).
% 27.61/27.76 tff(275,plain,
% 27.61/27.76 (n(n(n(n(e)))) = a(n(n(n(e))), n(n(n(e))))),
% 27.61/27.76 inference(unit_resolution,[status(thm)],[274, 20])).
% 27.61/27.76 tff(276,plain,
% 27.61/27.76 (a(n(n(n(e))), n(n(n(e)))) = n(n(n(n(e))))),
% 27.61/27.76 inference(symmetry,[status(thm)],[275])).
% 27.61/27.76 tff(277,plain,
% 27.61/27.76 (u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e))))) = u(s(s(n(n(e)))), n(n(n(n(e)))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[276])).
% 27.61/27.76 tff(278,plain,
% 27.61/27.76 (mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e)))))) <=> mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[277])).
% 27.61/27.76 tff(279,plain,
% 27.61/27.76 (mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))) <=> mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e))))))),
% 27.61/27.76 inference(symmetry,[status(thm)],[278])).
% 27.61/27.76 tff(280,plain,
% 27.61/27.76 ((~mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (~mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e)))))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[279])).
% 27.61/27.76 tff(281,assumption,(~mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))), introduced(assumption)).
% 27.61/27.76 tff(282,plain,
% 27.61/27.76 (~mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e))))))),
% 27.61/27.76 inference(modus_ponens,[status(thm)],[281, 280])).
% 27.61/27.76 tff(283,plain,
% 27.61/27.76 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e)))))) <=> (mem(e, a(n(n(n(e))), n(n(n(e))))) | mem(e, s(s(n(n(e)))))))),
% 27.61/27.76 inference(quant_inst,[status(thm)],[])).
% 27.61/27.76 tff(284,plain,
% 27.61/27.76 (mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e)))))) <=> (mem(e, a(n(n(n(e))), n(n(n(e))))) | mem(e, s(s(n(n(e))))))),
% 27.61/27.76 inference(unit_resolution,[status(thm)],[283, 110])).
% 27.61/27.76 tff(285,plain,
% 27.61/27.76 (a(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e)))) = a(n(n(n(e))), n(n(n(e))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[182, 182])).
% 27.61/27.76 tff(286,plain,
% 27.61/27.76 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e)))) = u(a(n(n(e)), n(n(e))), s(a(n(n(e)), n(n(e))))))),
% 27.61/27.76 inference(quant_inst,[status(thm)],[])).
% 27.61/27.76 tff(287,plain,
% 27.61/27.76 (a(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e)))) = u(a(n(n(e)), n(n(e))), s(a(n(n(e)), n(n(e)))))),
% 27.61/27.76 inference(unit_resolution,[status(thm)],[286, 7])).
% 27.61/27.76 tff(288,plain,
% 27.61/27.76 (u(a(n(n(e)), n(n(e))), s(a(n(n(e)), n(n(e))))) = a(a(n(n(e)), n(n(e))), a(n(n(e)), n(n(e))))),
% 27.61/27.76 inference(symmetry,[status(thm)],[287])).
% 27.61/27.76 tff(289,plain,
% 27.61/27.76 (s(n(n(n(e)))) = s(a(n(n(e)), n(n(e))))),
% 27.61/27.76 inference(symmetry,[status(thm)],[183])).
% 27.61/27.76 tff(290,plain,
% 27.61/27.76 (u(a(n(n(e)), n(n(e))), s(n(n(n(e))))) = u(a(n(n(e)), n(n(e))), s(a(n(n(e)), n(n(e)))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[289])).
% 27.61/27.76 tff(291,plain,
% 27.61/27.76 (u(a(n(n(e)), n(n(e))), s(n(n(n(e))))) = a(n(n(n(e))), n(n(n(e))))),
% 27.61/27.76 inference(transitivity,[status(thm)],[290, 288, 285])).
% 27.61/27.76 tff(292,plain,
% 27.61/27.76 (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> mem(e, a(n(n(n(e))), n(n(n(e)))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[291])).
% 27.61/27.76 tff(293,plain,
% 27.61/27.76 (mem(e, a(n(n(n(e))), n(n(n(e))))) <=> mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e))))))),
% 27.61/27.76 inference(symmetry,[status(thm)],[292])).
% 27.61/27.76 tff(294,plain,
% 27.61/27.76 ((~mem(e, a(n(n(n(e))), n(n(n(e)))))) <=> (~mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[293])).
% 27.61/27.76 tff(295,assumption,(~mem(e, a(n(n(n(e))), n(n(n(e)))))), introduced(assumption)).
% 27.61/27.76 tff(296,plain,
% 27.61/27.76 (~mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e))))))),
% 27.61/27.76 inference(modus_ponens,[status(thm)],[295, 294])).
% 27.61/27.76 tff(297,plain,
% 27.61/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e))))))))),
% 27.61/27.76 inference(rewrite,[status(thm)],[])).
% 27.61/27.76 tff(298,plain,
% 27.61/27.76 ((mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, a(n(n(e)), n(n(e)))))) <=> (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e)))))))),
% 27.61/27.76 inference(rewrite,[status(thm)],[])).
% 27.61/27.76 tff(299,plain,
% 27.61/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, a(n(n(e)), n(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e))))))))),
% 27.61/27.76 inference(monotonicity,[status(thm)],[298])).
% 27.61/27.76 tff(300,plain,
% 27.61/27.76 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, a(n(n(e)), n(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e))))))))),
% 27.61/27.76 inference(transitivity,[status(thm)],[299, 297])).
% 27.61/27.76 tff(301,plain,
% 27.61/27.76 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, a(n(n(e)), n(n(e))))))),
% 27.61/27.76 inference(quant_inst,[status(thm)],[])).
% 27.61/27.76 tff(302,plain,
% 27.61/27.76 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e)))))))),
% 27.61/27.76 inference(modus_ponens,[status(thm)],[301, 300])).
% 27.61/27.76 tff(303,plain,
% 27.61/27.76 (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[302, 110])).
% 27.61/27.77 tff(304,plain,
% 27.61/27.77 ((mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e)))))) | (~mem(e, a(n(n(e)), n(n(e)))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(305,plain,
% 27.61/27.77 (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e)))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[304, 218])).
% 27.61/27.77 tff(306,plain,
% 27.61/27.77 ((~(mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e)))))))) | mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) | (~(mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e)))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(307,plain,
% 27.61/27.77 ((~(mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e)))))) <=> (mem(e, a(n(n(e)), n(n(e)))) | mem(e, s(n(n(n(e)))))))) | mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[306, 305])).
% 27.61/27.77 tff(308,plain,
% 27.61/27.77 (mem(e, u(a(n(n(e)), n(n(e))), s(n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[307, 303])).
% 27.61/27.77 tff(309,plain,
% 27.61/27.77 ($false),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[308, 296])).
% 27.61/27.77 tff(310,plain,(mem(e, a(n(n(n(e))), n(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.77 tff(311,plain,
% 27.61/27.77 ((mem(e, a(n(n(n(e))), n(n(n(e))))) | mem(e, s(s(n(n(e)))))) | (~mem(e, a(n(n(n(e))), n(n(n(e))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(312,plain,
% 27.61/27.77 (mem(e, a(n(n(n(e))), n(n(n(e))))) | mem(e, s(s(n(n(e)))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[311, 310])).
% 27.61/27.77 tff(313,plain,
% 27.61/27.77 ((~(mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e)))))) <=> (mem(e, a(n(n(n(e))), n(n(n(e))))) | mem(e, s(s(n(n(e)))))))) | mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e)))))) | (~(mem(e, a(n(n(n(e))), n(n(n(e))))) | mem(e, s(s(n(n(e)))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(314,plain,
% 27.61/27.77 ((~(mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e)))))) <=> (mem(e, a(n(n(n(e))), n(n(n(e))))) | mem(e, s(s(n(n(e)))))))) | mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[313, 312])).
% 27.61/27.77 tff(315,plain,
% 27.61/27.77 (mem(e, u(s(s(n(n(e)))), a(n(n(n(e))), n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[314, 284])).
% 27.61/27.77 tff(316,plain,
% 27.61/27.77 ($false),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[315, 282])).
% 27.61/27.77 tff(317,plain,(mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.77 tff(318,plain,
% 27.61/27.77 ((mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))) | (~mem(e, u(s(s(n(n(e)))), n(n(n(n(e)))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(319,plain,
% 27.61/27.77 (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[318, 317])).
% 27.61/27.77 tff(320,plain,
% 27.61/27.77 ((~(mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))))) | mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) | (~(mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(321,plain,
% 27.61/27.77 ((~(mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e))))))) <=> (mem(e, u(s(s(n(e))), s(p(s(n(e)))))) | mem(e, u(s(s(n(n(e)))), n(n(n(n(e))))))))) | mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e)))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[320, 319])).
% 27.61/27.77 tff(322,plain,
% 27.61/27.77 (mem(e, u(u(s(s(n(e))), s(p(s(n(e))))), u(s(s(n(n(e)))), n(n(n(n(e)))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[321, 273])).
% 27.61/27.77 tff(323,plain,
% 27.61/27.77 ($false),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[322, 266])).
% 27.61/27.77 tff(324,plain,(mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.77 tff(325,plain,
% 27.61/27.77 (^[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))))))))),
% 27.61/27.77 inference(bind,[status(th)],[])).
% 27.61/27.77 tff(326,plain,
% 27.61/27.77 (![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)))))))),
% 27.61/27.77 inference(quant_intro,[status(thm)],[325])).
% 27.61/27.77 tff(327,plain,
% 27.61/27.77 (^[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))))))))),
% 27.61/27.77 inference(bind,[status(th)],[])).
% 27.61/27.77 tff(328,plain,
% 27.61/27.77 (![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)))))))),
% 27.61/27.77 inference(quant_intro,[status(thm)],[327])).
% 27.61/27.77 tff(329,plain,
% 27.61/27.77 (![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)))))))),
% 27.61/27.77 inference(transitivity,[status(thm)],[328, 326])).
% 27.61/27.77 tff(330,plain,
% 27.61/27.77 (^[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)))))))))),
% 27.61/27.77 inference(bind,[status(th)],[])).
% 27.61/27.77 tff(331,plain,
% 27.61/27.77 (![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)))))))),
% 27.61/27.77 inference(quant_intro,[status(thm)],[330])).
% 27.61/27.77 tff(332,plain,
% 27.61/27.77 (![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)))),
% 27.61/27.77 inference(rewrite,[status(thm)],[])).
% 27.61/27.77 tff(333,plain,
% 27.61/27.77 (^[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))))),
% 27.61/27.77 inference(bind,[status(th)],[])).
% 27.61/27.77 tff(334,plain,
% 27.61/27.77 (![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)))),
% 27.61/27.77 inference(quant_intro,[status(thm)],[333])).
% 27.61/27.77 tff(335,axiom,(![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : (mem(Z, X) => mem(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','subq_def')).
% 27.61/27.77 tff(336,plain,
% 27.61/27.77 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[335, 334])).
% 27.61/27.77 tff(337,plain,
% 27.61/27.77 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[336, 332])).
% 27.61/27.77 tff(338,plain,(
% 27.61/27.77 ![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)))))),
% 27.61/27.77 inference(skolemize,[status(sab)],[337])).
% 27.61/27.77 tff(339,plain,
% 27.61/27.77 (![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)))))))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[338, 331])).
% 27.61/27.77 tff(340,plain,
% 27.61/27.77 (![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)))))))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[339, 329])).
% 27.61/27.77 tff(341,plain,
% 27.61/27.77 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))))) | (~(subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e))))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(tptp_fun_Z_0(u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e))))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))))))))),
% 27.61/27.77 inference(quant_inst,[status(thm)],[])).
% 27.61/27.77 tff(342,plain,
% 27.61/27.77 (~((~((~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))))) | (~(subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e))))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(tptp_fun_Z_0(u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e))))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[341, 340])).
% 27.61/27.77 tff(343,plain,
% 27.61/27.77 (((~((~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))))) | (~(subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e))))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(tptp_fun_Z_0(u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))), u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e))))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))))))) | ((~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(344,plain,
% 27.61/27.77 ((~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[343, 342])).
% 27.61/27.77 tff(345,plain,
% 27.61/27.77 (subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))) <=> subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))),
% 27.61/27.77 inference(rewrite,[status(thm)],[])).
% 27.61/27.77 tff(346,plain,
% 27.61/27.77 ((~(~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))) <=> subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))),
% 27.61/27.77 inference(rewrite,[status(thm)],[])).
% 27.61/27.77 tff(347,axiom,(~(~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nsubq_2351_2350')).
% 27.61/27.77 tff(348,plain,
% 27.61/27.77 (subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[347, 346])).
% 27.61/27.77 tff(349,plain,
% 27.61/27.77 (subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[348, 345])).
% 27.61/27.77 tff(350,plain,
% 27.61/27.77 ((~((~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))))) | (~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(351,plain,
% 27.61/27.77 ((~((~subq(u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))), u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))))) | ![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[350, 349])).
% 27.61/27.77 tff(352,plain,
% 27.61/27.77 (![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[351, 344])).
% 27.61/27.77 tff(353,plain,
% 27.61/27.77 (((~![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))) | ((~mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(e, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))) <=> ((~![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))) | (~mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(e, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))),
% 27.61/27.77 inference(rewrite,[status(thm)],[])).
% 27.61/27.77 tff(354,plain,
% 27.61/27.77 ((~![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))) | ((~mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(e, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))),
% 27.61/27.77 inference(quant_inst,[status(thm)],[])).
% 27.61/27.77 tff(355,plain,
% 27.61/27.77 ((~![Z: $i] : ((~mem(Z, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(Z, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e)))))))) | (~mem(e, u(a(s(s(n(e))), p(s(n(e)))), u(s(s(n(n(e)))), n(n(n(n(e)))))))) | mem(e, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[354, 353])).
% 27.61/27.77 tff(356,plain,
% 27.61/27.77 (mem(e, u(a(n(s(n(e))), p(s(n(e)))), a(n(s(n(n(e)))), n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[355, 352, 324])).
% 27.61/27.77 tff(357,plain,
% 27.61/27.77 (mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e)))))))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[356, 257])).
% 27.61/27.77 tff(358,assumption,(~mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e)))))))), introduced(assumption)).
% 27.61/27.77 tff(359,plain,
% 27.61/27.77 ($false),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[358, 357])).
% 27.61/27.77 tff(360,plain,(mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.77 tff(361,plain,
% 27.61/27.77 ((~(mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))))) | (~mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e)))))))) | (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(362,plain,
% 27.61/27.77 ((~(mem(e, u(u(n(s(n(e))), s(p(s(n(e))))), u(n(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))))) | (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[361, 360])).
% 27.61/27.77 tff(363,plain,
% 27.61/27.77 (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[362, 248])).
% 27.61/27.77 tff(364,plain,
% 27.61/27.77 ((~(mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e)))))))) | mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(365,plain,
% 27.61/27.77 (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) | mem(e, u(n(s(n(n(e)))), s(n(n(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[364, 363])).
% 27.61/27.77 tff(366,plain,
% 27.61/27.77 (mem(e, u(n(s(n(e))), s(p(s(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[365, 239])).
% 27.61/27.77 tff(367,plain,
% 27.61/27.77 ((~![X: $i] : (n(X) = a(X, X))) | (n(s(n(e))) = a(s(n(e)), s(n(e))))),
% 27.61/27.77 inference(quant_inst,[status(thm)],[])).
% 27.61/27.77 tff(368,plain,
% 27.61/27.77 (n(s(n(e))) = a(s(n(e)), s(n(e)))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[367, 20])).
% 27.61/27.77 tff(369,plain,
% 27.61/27.77 (a(s(n(e)), s(n(e))) = n(s(n(e)))),
% 27.61/27.77 inference(symmetry,[status(thm)],[368])).
% 27.61/27.77 tff(370,plain,
% 27.61/27.77 (u(a(s(n(e)), s(n(e))), s(p(s(n(e))))) = u(n(s(n(e))), s(p(s(n(e)))))),
% 27.61/27.77 inference(monotonicity,[status(thm)],[369])).
% 27.61/27.77 tff(371,plain,
% 27.61/27.77 (mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e)))))) <=> mem(e, u(n(s(n(e))), s(p(s(n(e))))))),
% 27.61/27.77 inference(monotonicity,[status(thm)],[370])).
% 27.61/27.77 tff(372,plain,
% 27.61/27.77 (mem(e, u(n(s(n(e))), s(p(s(n(e)))))) <=> mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e))))))),
% 27.61/27.77 inference(symmetry,[status(thm)],[371])).
% 27.61/27.77 tff(373,assumption,(mem(e, u(n(s(n(e))), s(p(s(n(e))))))), introduced(assumption)).
% 27.61/27.77 tff(374,plain,
% 27.61/27.77 (mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e))))))),
% 27.61/27.77 inference(modus_ponens,[status(thm)],[373, 372])).
% 27.61/27.77 tff(375,assumption,(~mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e))))))), introduced(assumption)).
% 27.61/27.77 tff(376,plain,
% 27.61/27.77 ($false),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[375, 374])).
% 27.61/27.77 tff(377,plain,(mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e)))))) | (~mem(e, u(n(s(n(e))), s(p(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.77 tff(378,plain,
% 27.61/27.77 (mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e))))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[377, 366])).
% 27.61/27.77 tff(379,assumption,(~(mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e)))))) <=> (mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e))))))), introduced(assumption)).
% 27.61/27.77 tff(380,plain,
% 27.61/27.77 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e)))))) <=> (mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e))))))),
% 27.61/27.77 inference(quant_inst,[status(thm)],[])).
% 27.61/27.77 tff(381,plain,
% 27.61/27.77 ($false),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[380, 110, 379])).
% 27.61/27.77 tff(382,plain,(mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e)))))) <=> (mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.77 tff(383,plain,
% 27.61/27.77 ((~(mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e)))))) <=> (mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e))))))) | (~mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e))))))) | (mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e)))))),
% 27.61/27.77 inference(tautology,[status(thm)],[])).
% 27.61/27.77 tff(384,plain,
% 27.61/27.77 ((~mem(e, u(a(s(n(e)), s(n(e))), s(p(s(n(e))))))) | (mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e)))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[383, 382])).
% 27.61/27.77 tff(385,plain,
% 27.61/27.77 (mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e))))),
% 27.61/27.77 inference(unit_resolution,[status(thm)],[384, 378])).
% 27.61/27.77 tff(386,assumption,(e = a(e, e)), introduced(assumption)).
% 27.61/27.77 tff(387,plain,
% 27.61/27.77 (a(e, e) = e),
% 27.61/27.77 inference(symmetry,[status(thm)],[386])).
% 27.61/27.77 tff(388,plain,
% 27.61/27.77 (n(e) = e),
% 27.61/27.77 inference(transitivity,[status(thm)],[86, 387])).
% 27.61/27.77 tff(389,plain,
% 27.61/27.77 (n(n(e)) = n(e)),
% 27.61/27.77 inference(monotonicity,[status(thm)],[388])).
% 27.61/27.77 tff(390,plain,
% 27.61/27.77 (n(e) = n(n(e))),
% 27.61/27.77 inference(symmetry,[status(thm)],[389])).
% 27.61/27.77 tff(391,plain,
% 27.61/27.77 (a(e, e) = a(n(e), n(e))),
% 27.61/27.77 inference(transitivity,[status(thm)],[87, 390, 22])).
% 27.61/27.77 tff(392,assumption,(a(e, e) = a(n(e), n(e))), introduced(assumption)).
% 27.61/27.77 tff(393,plain,
% 27.61/27.77 (a(n(e), n(e)) = a(e, e)),
% 27.61/27.77 inference(symmetry,[status(thm)],[392])).
% 27.61/27.77 tff(394,plain,
% 27.61/27.77 (n(n(e)) = n(e)),
% 27.61/27.77 inference(transitivity,[status(thm)],[22, 393, 87])).
% 27.61/27.77 tff(395,plain,
% 27.61/27.77 (n(n(n(e))) = n(n(e))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[394])).
% 27.61/27.78 tff(396,plain,
% 27.61/27.78 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(397,plain,
% 27.61/27.78 (mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e)),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[396, 47])).
% 27.61/27.78 tff(398,plain,
% 27.61/27.78 ((~![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)))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(399,plain,
% 27.61/27.78 (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))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[398, 110])).
% 27.61/27.78 tff(400,plain,
% 27.61/27.78 (u(e, s(e)) = a(n(e), n(e))),
% 27.61/27.78 inference(transitivity,[status(thm)],[120, 392])).
% 27.61/27.78 tff(401,plain,
% 27.61/27.78 (mem(a(n(e), n(e)), u(e, s(e))) <=> mem(a(e, e), a(n(e), n(e)))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[393, 400])).
% 27.61/27.78 tff(402,plain,
% 27.61/27.78 (mem(a(e, e), a(n(e), n(e))) <=> mem(a(n(e), n(e)), u(e, s(e)))),
% 27.61/27.78 inference(symmetry,[status(thm)],[401])).
% 27.61/27.78 tff(403,plain,
% 27.61/27.78 (mem(a(e, e), s(a(e, e))) <=> mem(a(e, e), s(n(e)))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[92])).
% 27.61/27.78 tff(404,plain,
% 27.61/27.78 (mem(a(e, e), s(n(e))) <=> mem(a(e, e), s(a(e, e)))),
% 27.61/27.78 inference(symmetry,[status(thm)],[403])).
% 27.61/27.78 tff(405,plain,
% 27.61/27.78 ((~mem(a(e, e), s(n(e)))) <=> (~mem(a(e, e), s(a(e, e))))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[404])).
% 27.61/27.78 tff(406,assumption,(~mem(a(e, e), s(n(e)))), introduced(assumption)).
% 27.61/27.78 tff(407,plain,
% 27.61/27.78 (~mem(a(e, e), s(a(e, e)))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[406, 405])).
% 27.61/27.78 tff(408,plain,
% 27.61/27.78 (((~![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))))),
% 27.61/27.78 inference(rewrite,[status(thm)],[])).
% 27.61/27.78 tff(409,plain,
% 27.61/27.78 ((mem(a(e, e), s(a(e, e))) <=> $true) <=> mem(a(e, e), s(a(e, e)))),
% 27.61/27.78 inference(rewrite,[status(thm)],[])).
% 27.61/27.78 tff(410,plain,
% 27.61/27.78 ((a(e, e) = a(e, e)) <=> $true),
% 27.61/27.78 inference(rewrite,[status(thm)],[])).
% 27.61/27.78 tff(411,plain,
% 27.61/27.78 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> (mem(a(e, e), s(a(e, e))) <=> $true)),
% 27.61/27.78 inference(monotonicity,[status(thm)],[410])).
% 27.61/27.78 tff(412,plain,
% 27.61/27.78 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> mem(a(e, e), s(a(e, e)))),
% 27.61/27.78 inference(transitivity,[status(thm)],[411, 409])).
% 27.61/27.78 tff(413,plain,
% 27.61/27.78 (((~![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))))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[412])).
% 27.61/27.78 tff(414,plain,
% 27.61/27.78 (((~![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))))),
% 27.61/27.78 inference(transitivity,[status(thm)],[413, 408])).
% 27.61/27.78 tff(415,plain,
% 27.61/27.78 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e)))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(416,plain,
% 27.61/27.78 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e)))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[415, 414])).
% 27.61/27.78 tff(417,plain,
% 27.61/27.78 (mem(a(e, e), s(a(e, e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[416, 47])).
% 27.61/27.78 tff(418,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[417, 407])).
% 27.61/27.78 tff(419,plain,(mem(a(e, e), s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(420,plain,
% 27.61/27.78 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> mem(a(e, e), a(n(e), n(e)))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[95])).
% 27.61/27.78 tff(421,plain,
% 27.61/27.78 (mem(a(e, e), a(n(e), n(e))) <=> mem(a(e, e), u(a(e, e), s(n(e))))),
% 27.61/27.78 inference(symmetry,[status(thm)],[420])).
% 27.61/27.78 tff(422,plain,
% 27.61/27.78 ((~mem(a(e, e), a(n(e), n(e)))) <=> (~mem(a(e, e), u(a(e, e), s(n(e)))))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[421])).
% 27.61/27.78 tff(423,assumption,(~mem(a(e, e), a(n(e), n(e)))), introduced(assumption)).
% 27.61/27.78 tff(424,plain,
% 27.61/27.78 (~mem(a(e, e), u(a(e, e), s(n(e))))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[423, 422])).
% 27.61/27.78 tff(425,plain,
% 27.61/27.78 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e))))))),
% 27.61/27.78 inference(rewrite,[status(thm)],[])).
% 27.61/27.78 tff(426,plain,
% 27.61/27.78 ((mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e)))) <=> (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))),
% 27.61/27.78 inference(rewrite,[status(thm)],[])).
% 27.61/27.78 tff(427,plain,
% 27.61/27.78 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e))))))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[426])).
% 27.61/27.78 tff(428,plain,
% 27.61/27.78 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e))))))),
% 27.61/27.78 inference(transitivity,[status(thm)],[427, 425])).
% 27.61/27.78 tff(429,plain,
% 27.61/27.78 ((~![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))))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(430,plain,
% 27.61/27.78 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[429, 428])).
% 27.61/27.78 tff(431,plain,
% 27.61/27.78 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e))))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[430, 110])).
% 27.61/27.78 tff(432,assumption,(mem(a(e, e), s(n(e)))), introduced(assumption)).
% 27.61/27.78 tff(433,plain,
% 27.61/27.78 ((mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))) | (~mem(a(e, e), s(n(e))))),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(434,plain,
% 27.61/27.78 (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[433, 432])).
% 27.61/27.78 tff(435,plain,
% 27.61/27.78 ((~(mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))) | mem(a(e, e), u(a(e, e), s(n(e)))) | (~(mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(436,plain,
% 27.61/27.78 ((~(mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), a(e, e)) | mem(a(e, e), s(n(e)))))) | mem(a(e, e), u(a(e, e), s(n(e))))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[435, 434])).
% 27.61/27.78 tff(437,plain,
% 27.61/27.78 (mem(a(e, e), u(a(e, e), s(n(e))))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[436, 431])).
% 27.61/27.78 tff(438,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[437, 424])).
% 27.61/27.78 tff(439,plain,(mem(a(e, e), a(n(e), n(e))) | (~mem(a(e, e), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(440,plain,
% 27.61/27.78 (mem(a(e, e), a(n(e), n(e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[439, 419])).
% 27.61/27.78 tff(441,plain,
% 27.61/27.78 (mem(a(n(e), n(e)), u(e, s(e)))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[440, 402])).
% 27.61/27.78 tff(442,plain,
% 27.61/27.78 ((~(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)), s(e)) | mem(a(n(e), n(e)), e))),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(443,plain,
% 27.61/27.78 (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e)),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[442, 441, 399])).
% 27.61/27.78 tff(444,plain,
% 27.61/27.78 ((~(mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e))) | mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e)),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(445,plain,
% 27.61/27.78 ((~(mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e))) | mem(a(n(e), n(e)), s(e))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[444, 39])).
% 27.61/27.78 tff(446,plain,
% 27.61/27.78 (mem(a(n(e), n(e)), s(e))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[445, 443])).
% 27.61/27.78 tff(447,plain,
% 27.61/27.78 ((~(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)),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(448,plain,
% 27.61/27.78 ((~(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))) | (a(n(e), n(e)) = e)),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[447, 446])).
% 27.61/27.78 tff(449,plain,
% 27.61/27.78 (a(n(e), n(e)) = e),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[448, 397])).
% 27.61/27.78 tff(450,plain,
% 27.61/27.78 (e = a(n(e), n(e))),
% 27.61/27.78 inference(symmetry,[status(thm)],[449])).
% 27.61/27.78 tff(451,plain,
% 27.61/27.78 (e = a(e, e)),
% 27.61/27.78 inference(transitivity,[status(thm)],[450, 393])).
% 27.61/27.78 tff(452,plain,
% 27.61/27.78 (a(n(n(e)), n(n(e))) = a(e, e)),
% 27.61/27.78 inference(transitivity,[status(thm)],[182, 395, 22, 393])).
% 27.61/27.78 tff(453,plain,
% 27.61/27.78 ((e = a(n(n(e)), n(n(e)))) <=> (e = a(e, e))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[452])).
% 27.61/27.78 tff(454,plain,
% 27.61/27.78 ((~(e = a(n(n(e)), n(n(e))))) <=> (~(e = a(e, e)))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[453])).
% 27.61/27.78 tff(455,assumption,(~(e = a(n(n(e)), n(n(e))))), introduced(assumption)).
% 27.61/27.78 tff(456,plain,
% 27.61/27.78 (~(e = a(e, e))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[455, 454])).
% 27.61/27.78 tff(457,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[456, 451])).
% 27.61/27.78 tff(458,plain,((~(a(e, e) = a(n(e), n(e)))) | (e = a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(459,plain,
% 27.61/27.78 (e = a(n(n(e)), n(n(e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[458, 392])).
% 27.61/27.78 tff(460,plain,
% 27.61/27.78 (e = a(n(e), n(e))),
% 27.61/27.78 inference(transitivity,[status(thm)],[459, 182, 395, 22])).
% 27.61/27.78 tff(461,plain,
% 27.61/27.78 (mem(a(n(e), n(e)), e) <=> mem(a(e, e), a(n(e), n(e)))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[393, 460])).
% 27.61/27.78 tff(462,plain,
% 27.61/27.78 (mem(a(e, e), a(n(e), n(e))) <=> mem(a(n(e), n(e)), e)),
% 27.61/27.78 inference(symmetry,[status(thm)],[461])).
% 27.61/27.78 tff(463,plain,
% 27.61/27.78 (mem(a(n(e), n(e)), e)),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[440, 462])).
% 27.61/27.78 tff(464,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[39, 463])).
% 27.61/27.78 tff(465,plain,(~(a(e, e) = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(466,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[465, 391])).
% 27.61/27.78 tff(467,plain,(~(e = a(e, e))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(468,assumption,(~(mem(e, s(a(e, e))) <=> (e = a(e, e)))), introduced(assumption)).
% 27.61/27.78 tff(469,plain,
% 27.61/27.78 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(a(e, e))) <=> (e = a(e, e)))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(470,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[469, 47, 468])).
% 27.61/27.78 tff(471,plain,(mem(e, s(a(e, e))) <=> (e = a(e, e))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(472,plain,
% 27.61/27.78 ((~(mem(e, s(a(e, e))) <=> (e = a(e, e)))) | (~mem(e, s(a(e, e)))) | (e = a(e, e))),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(473,plain,
% 27.61/27.78 ((~mem(e, s(a(e, e)))) | (e = a(e, e))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[472, 471])).
% 27.61/27.78 tff(474,plain,
% 27.61/27.78 (~mem(e, s(a(e, e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[473, 467])).
% 27.61/27.78 tff(475,assumption,(~(mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e)))))), introduced(assumption)).
% 27.61/27.78 tff(476,plain,
% 27.61/27.78 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e)))))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(477,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[476, 110, 475])).
% 27.61/27.78 tff(478,plain,(mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(479,plain,
% 27.61/27.78 (mem(e, s(n(e))) <=> mem(e, s(a(e, e)))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[93])).
% 27.61/27.78 tff(480,plain,
% 27.61/27.78 (mem(e, s(a(e, e))) <=> mem(e, s(n(e)))),
% 27.61/27.78 inference(symmetry,[status(thm)],[479])).
% 27.61/27.78 tff(481,plain,
% 27.61/27.78 ((~mem(e, s(a(e, e)))) <=> (~mem(e, s(n(e))))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[480])).
% 27.61/27.78 tff(482,assumption,(~mem(e, s(a(e, e)))), introduced(assumption)).
% 27.61/27.78 tff(483,plain,
% 27.61/27.78 (~mem(e, s(n(e)))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[482, 481])).
% 27.61/27.78 tff(484,assumption,(mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e))))), introduced(assumption)).
% 27.61/27.78 tff(485,plain,
% 27.61/27.78 ((~![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)))))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(486,plain,
% 27.61/27.78 (a(s(n(e)), s(n(e))) = u(s(n(e)), s(s(n(e))))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[485, 7])).
% 27.61/27.78 tff(487,plain,
% 27.61/27.78 (u(s(n(e)), s(s(n(e)))) = a(s(n(e)), s(n(e)))),
% 27.61/27.78 inference(symmetry,[status(thm)],[486])).
% 27.61/27.78 tff(488,plain,
% 27.61/27.78 (mem(e, u(s(n(e)), s(s(n(e))))) <=> mem(e, a(s(n(e)), s(n(e))))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[487])).
% 27.61/27.78 tff(489,plain,
% 27.61/27.78 (mem(e, a(s(n(e)), s(n(e)))) <=> mem(e, u(s(n(e)), s(s(n(e)))))),
% 27.61/27.78 inference(symmetry,[status(thm)],[488])).
% 27.61/27.78 tff(490,assumption,(mem(e, a(s(n(e)), s(n(e))))), introduced(assumption)).
% 27.61/27.78 tff(491,plain,
% 27.61/27.78 (mem(e, u(s(n(e)), s(s(n(e)))))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[490, 489])).
% 27.61/27.78 tff(492,plain,
% 27.61/27.78 ((~(mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e)))))) | (~mem(e, u(s(n(e)), s(s(n(e)))))) | (mem(e, s(s(n(e)))) | mem(e, s(n(e))))),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(493,plain,
% 27.61/27.78 (mem(e, s(s(n(e)))) | mem(e, s(n(e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[492, 491, 484])).
% 27.61/27.78 tff(494,assumption,(~(mem(e, s(s(n(e)))) <=> (e = s(n(e))))), introduced(assumption)).
% 27.61/27.78 tff(495,plain,
% 27.61/27.78 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(s(n(e)))) <=> (e = s(n(e))))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(496,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[495, 47, 494])).
% 27.61/27.78 tff(497,plain,(mem(e, s(s(n(e)))) <=> (e = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(498,assumption,(e = s(n(e))), introduced(assumption)).
% 27.61/27.78 tff(499,plain,
% 27.61/27.78 (s(n(e)) = e),
% 27.61/27.78 inference(symmetry,[status(thm)],[498])).
% 27.61/27.78 tff(500,plain,
% 27.61/27.78 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e)))))),
% 27.61/27.78 inference(rewrite,[status(thm)],[])).
% 27.61/27.78 tff(501,plain,
% 27.61/27.78 ((mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), s(e)) | mem(s(n(e)), e))) <=> (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e))))),
% 27.61/27.78 inference(rewrite,[status(thm)],[])).
% 27.61/27.78 tff(502,plain,
% 27.61/27.78 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), s(e)) | mem(s(n(e)), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e)))))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[501])).
% 27.61/27.78 tff(503,plain,
% 27.61/27.78 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), s(e)) | mem(s(n(e)), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e)))))),
% 27.61/27.78 inference(transitivity,[status(thm)],[502, 500])).
% 27.61/27.78 tff(504,plain,
% 27.61/27.78 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), s(e)) | mem(s(n(e)), e)))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(505,plain,
% 27.61/27.78 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e))))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[504, 503])).
% 27.61/27.78 tff(506,plain,
% 27.61/27.78 (mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[505, 110])).
% 27.61/27.78 tff(507,plain,
% 27.61/27.78 (mem(s(n(e)), u(e, s(e))) <=> mem(s(n(e)), a(e, e))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[120])).
% 27.61/27.78 tff(508,plain,
% 27.61/27.78 (mem(s(n(e)), a(e, e)) <=> mem(s(n(e)), u(e, s(e)))),
% 27.61/27.78 inference(symmetry,[status(thm)],[507])).
% 27.61/27.78 tff(509,plain,
% 27.61/27.78 ((~mem(s(n(e)), a(e, e))) <=> (~mem(s(n(e)), u(e, s(e))))),
% 27.61/27.78 inference(monotonicity,[status(thm)],[508])).
% 27.61/27.78 tff(510,assumption,(mem(s(n(e)), a(e, e))), introduced(assumption)).
% 27.61/27.78 tff(511,plain,
% 27.61/27.78 (mem(s(n(e)), u(e, s(e)))),
% 27.61/27.78 inference(modus_ponens,[status(thm)],[510, 508])).
% 27.61/27.78 tff(512,assumption,(~mem(s(n(e)), s(e))), introduced(assumption)).
% 27.61/27.78 tff(513,assumption,(mem(s(n(e)), e)), introduced(assumption)).
% 27.61/27.78 tff(514,plain,
% 27.61/27.78 ((~![X: $i] : (~mem(X, e))) | (~mem(s(n(e)), e))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(515,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[514, 36, 513])).
% 27.61/27.78 tff(516,plain,(~mem(s(n(e)), e)), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(517,plain,
% 27.61/27.78 ((~(mem(s(n(e)), e) | mem(s(n(e)), s(e)))) | mem(s(n(e)), e) | mem(s(n(e)), s(e))),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(518,plain,
% 27.61/27.78 (~(mem(s(n(e)), e) | mem(s(n(e)), s(e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[517, 516, 512])).
% 27.61/27.78 tff(519,plain,
% 27.61/27.78 ((~(mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e))))) | (~mem(s(n(e)), u(e, s(e)))) | (mem(s(n(e)), e) | mem(s(n(e)), s(e)))),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(520,plain,
% 27.61/27.78 ((~(mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e))))) | (~mem(s(n(e)), u(e, s(e))))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[519, 518])).
% 27.61/27.78 tff(521,plain,
% 27.61/27.78 (~mem(s(n(e)), u(e, s(e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[520, 506])).
% 27.61/27.78 tff(522,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[521, 511])).
% 27.61/27.78 tff(523,plain,((~mem(s(n(e)), a(e, e))) | mem(s(n(e)), s(e))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(524,plain,
% 27.61/27.78 (mem(s(n(e)), s(e))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[523, 510])).
% 27.61/27.78 tff(525,assumption,(~(mem(s(n(e)), s(e)) <=> (s(n(e)) = e))), introduced(assumption)).
% 27.61/27.78 tff(526,plain,
% 27.61/27.78 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(s(n(e)), s(e)) <=> (s(n(e)) = e))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(527,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[526, 47, 525])).
% 27.61/27.78 tff(528,plain,(mem(s(n(e)), s(e)) <=> (s(n(e)) = e)), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(529,plain,
% 27.61/27.78 ((~(mem(s(n(e)), s(e)) <=> (s(n(e)) = e))) | (~mem(s(n(e)), s(e))) | (s(n(e)) = e)),
% 27.61/27.78 inference(tautology,[status(thm)],[])).
% 27.61/27.78 tff(530,plain,
% 27.61/27.78 ((~mem(s(n(e)), s(e))) | (s(n(e)) = e)),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[529, 528])).
% 27.61/27.78 tff(531,plain,
% 27.61/27.78 (s(n(e)) = e),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[530, 524])).
% 27.61/27.78 tff(532,assumption,(s(n(e)) = e), introduced(assumption)).
% 27.61/27.78 tff(533,plain,
% 27.61/27.78 (n(s(n(e))) = n(e)),
% 27.61/27.78 inference(monotonicity,[status(thm)],[532])).
% 27.61/27.78 tff(534,plain,
% 27.61/27.78 (n(e) = n(s(n(e)))),
% 27.61/27.78 inference(symmetry,[status(thm)],[533])).
% 27.61/27.78 tff(535,plain,
% 27.61/27.78 (a(e, e) = a(s(n(e)), s(n(e)))),
% 27.61/27.78 inference(transitivity,[status(thm)],[87, 534, 368])).
% 27.61/27.78 tff(536,assumption,(~(a(e, e) = a(s(n(e)), s(n(e))))), introduced(assumption)).
% 27.61/27.78 tff(537,plain,
% 27.61/27.78 ($false),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[536, 535])).
% 27.61/27.78 tff(538,plain,((~(s(n(e)) = e)) | (a(e, e) = a(s(n(e)), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.78 tff(539,plain,
% 27.61/27.78 (a(e, e) = a(s(n(e)), s(n(e)))),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[538, 531])).
% 27.61/27.78 tff(540,plain,
% 27.61/27.78 (a(s(n(e)), s(n(e))) = a(e, e)),
% 27.61/27.78 inference(symmetry,[status(thm)],[539])).
% 27.61/27.78 tff(541,plain,
% 27.61/27.78 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(s(n(e)), s(n(e))), s(e)) <=> (a(s(n(e)), s(n(e))) = e))),
% 27.61/27.78 inference(quant_inst,[status(thm)],[])).
% 27.61/27.78 tff(542,plain,
% 27.61/27.78 (mem(a(s(n(e)), s(n(e))), s(e)) <=> (a(s(n(e)), s(n(e))) = e)),
% 27.61/27.78 inference(unit_resolution,[status(thm)],[541, 47])).
% 27.61/27.78 tff(543,plain,
% 27.61/27.78 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e)))))),
% 27.61/27.79 inference(rewrite,[status(thm)],[])).
% 27.61/27.79 tff(544,plain,
% 27.61/27.79 ((mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), s(e)) | mem(a(s(n(e)), s(n(e))), e))) <=> (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e))))),
% 27.61/27.79 inference(rewrite,[status(thm)],[])).
% 27.61/27.79 tff(545,plain,
% 27.61/27.79 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), s(e)) | mem(a(s(n(e)), s(n(e))), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e)))))),
% 27.61/27.79 inference(monotonicity,[status(thm)],[544])).
% 27.61/27.79 tff(546,plain,
% 27.61/27.79 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), s(e)) | mem(a(s(n(e)), s(n(e))), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e)))))),
% 27.61/27.79 inference(transitivity,[status(thm)],[545, 543])).
% 27.61/27.79 tff(547,plain,
% 27.61/27.79 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), s(e)) | mem(a(s(n(e)), s(n(e))), e)))),
% 27.61/27.79 inference(quant_inst,[status(thm)],[])).
% 27.61/27.79 tff(548,plain,
% 27.61/27.79 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e))))),
% 27.61/27.79 inference(modus_ponens,[status(thm)],[547, 546])).
% 27.61/27.79 tff(549,plain,
% 27.61/27.79 (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e)))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[548, 110])).
% 27.61/27.79 tff(550,plain,
% 27.61/27.79 (u(e, s(e)) = u(s(n(e)), s(s(n(e))))),
% 27.61/27.79 inference(transitivity,[status(thm)],[120, 539, 486])).
% 27.61/27.79 tff(551,plain,
% 27.61/27.79 (mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> mem(a(e, e), u(s(n(e)), s(s(n(e)))))),
% 27.61/27.79 inference(monotonicity,[status(thm)],[540, 550])).
% 27.61/27.79 tff(552,plain,
% 27.61/27.79 (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> mem(a(s(n(e)), s(n(e))), u(e, s(e)))),
% 27.61/27.79 inference(symmetry,[status(thm)],[551])).
% 27.61/27.79 tff(553,plain,
% 27.61/27.79 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(n(e))))) <=> (mem(a(e, e), s(s(n(e)))) | mem(a(e, e), s(n(e)))))),
% 27.61/27.79 inference(quant_inst,[status(thm)],[])).
% 27.61/27.79 tff(554,plain,
% 27.61/27.79 (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))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[553, 110])).
% 27.61/27.79 tff(555,plain,
% 27.61/27.79 ((mem(a(e, e), s(s(n(e)))) | mem(a(e, e), s(n(e)))) | (~mem(a(e, e), s(n(e))))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(556,plain,
% 27.61/27.79 (mem(a(e, e), s(s(n(e)))) | mem(a(e, e), s(n(e)))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[555, 419])).
% 27.61/27.79 tff(557,plain,
% 27.61/27.79 ((~(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)))))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(558,plain,
% 27.61/27.79 ((~(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)))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[557, 556])).
% 27.61/27.79 tff(559,plain,
% 27.61/27.79 (mem(a(e, e), u(s(n(e)), s(s(n(e)))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[558, 554])).
% 27.61/27.79 tff(560,plain,
% 27.61/27.79 (mem(a(s(n(e)), s(n(e))), u(e, s(e)))),
% 27.61/27.79 inference(modus_ponens,[status(thm)],[559, 552])).
% 27.61/27.79 tff(561,plain,
% 27.61/27.79 ((~(mem(a(s(n(e)), s(n(e))), u(e, s(e))) <=> (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e))))) | (~mem(a(s(n(e)), s(n(e))), u(e, s(e)))) | (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e)))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(562,plain,
% 27.61/27.79 (mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[561, 560, 549])).
% 27.61/27.79 tff(563,assumption,(mem(a(s(n(e)), s(n(e))), e)), introduced(assumption)).
% 27.61/27.79 tff(564,plain,
% 27.61/27.79 ((~![X: $i] : (~mem(X, e))) | (~mem(a(s(n(e)), s(n(e))), e))),
% 27.61/27.79 inference(quant_inst,[status(thm)],[])).
% 27.61/27.79 tff(565,plain,
% 27.61/27.79 ($false),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[564, 36, 563])).
% 27.61/27.79 tff(566,plain,(~mem(a(s(n(e)), s(n(e))), e)), inference(lemma,lemma(discharge,[]))).
% 27.61/27.79 tff(567,plain,
% 27.61/27.79 ((~(mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e)))) | mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(568,plain,
% 27.61/27.79 ((~(mem(a(s(n(e)), s(n(e))), e) | mem(a(s(n(e)), s(n(e))), s(e)))) | mem(a(s(n(e)), s(n(e))), s(e))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[567, 566])).
% 27.61/27.79 tff(569,plain,
% 27.61/27.79 (mem(a(s(n(e)), s(n(e))), s(e))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[568, 562])).
% 27.61/27.79 tff(570,plain,
% 27.61/27.79 ((~(mem(a(s(n(e)), s(n(e))), s(e)) <=> (a(s(n(e)), s(n(e))) = e))) | (~mem(a(s(n(e)), s(n(e))), s(e))) | (a(s(n(e)), s(n(e))) = e)),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(571,plain,
% 27.61/27.79 ((~(mem(a(s(n(e)), s(n(e))), s(e)) <=> (a(s(n(e)), s(n(e))) = e))) | (a(s(n(e)), s(n(e))) = e)),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[570, 569])).
% 27.61/27.79 tff(572,plain,
% 27.61/27.79 (a(s(n(e)), s(n(e))) = e),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[571, 542])).
% 27.61/27.79 tff(573,plain,
% 27.61/27.79 (e = a(s(n(e)), s(n(e)))),
% 27.61/27.79 inference(symmetry,[status(thm)],[572])).
% 27.61/27.79 tff(574,plain,
% 27.61/27.79 (e = a(e, e)),
% 27.61/27.79 inference(transitivity,[status(thm)],[573, 540])).
% 27.61/27.79 tff(575,plain,
% 27.61/27.79 (mem(s(n(e)), e) <=> mem(s(n(e)), a(e, e))),
% 27.61/27.79 inference(monotonicity,[status(thm)],[574])).
% 27.61/27.79 tff(576,plain,
% 27.61/27.79 (mem(s(n(e)), a(e, e)) <=> mem(s(n(e)), e)),
% 27.61/27.79 inference(symmetry,[status(thm)],[575])).
% 27.61/27.79 tff(577,plain,
% 27.61/27.79 (mem(s(n(e)), e)),
% 27.61/27.79 inference(modus_ponens,[status(thm)],[510, 576])).
% 27.61/27.79 tff(578,plain,
% 27.61/27.79 ($false),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[516, 577])).
% 27.61/27.79 tff(579,plain,(~mem(s(n(e)), a(e, e))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.79 tff(580,plain,
% 27.61/27.79 (~mem(s(n(e)), u(e, s(e)))),
% 27.61/27.79 inference(modus_ponens,[status(thm)],[579, 509])).
% 27.61/27.79 tff(581,plain,
% 27.61/27.79 ((~(mem(s(n(e)), u(e, s(e))) <=> (mem(s(n(e)), e) | mem(s(n(e)), s(e))))) | mem(s(n(e)), u(e, s(e))) | (~(mem(s(n(e)), e) | mem(s(n(e)), s(e))))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(582,plain,
% 27.61/27.79 (~(mem(s(n(e)), e) | mem(s(n(e)), s(e)))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[581, 580, 506])).
% 27.61/27.79 tff(583,plain,
% 27.61/27.79 ((mem(s(n(e)), e) | mem(s(n(e)), s(e))) | (~mem(s(n(e)), s(e)))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(584,plain,
% 27.61/27.79 (~mem(s(n(e)), s(e))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[583, 582])).
% 27.61/27.79 tff(585,plain,
% 27.61/27.79 ((~(mem(s(n(e)), s(e)) <=> (s(n(e)) = e))) | mem(s(n(e)), s(e)) | (~(s(n(e)) = e))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(586,plain,
% 27.61/27.79 (mem(s(n(e)), s(e)) | (~(s(n(e)) = e))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[585, 528])).
% 27.61/27.79 tff(587,plain,
% 27.61/27.79 (~(s(n(e)) = e)),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[586, 584])).
% 27.61/27.79 tff(588,plain,
% 27.61/27.79 ($false),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[587, 499])).
% 27.61/27.79 tff(589,plain,(~(e = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.79 tff(590,plain,
% 27.61/27.79 ((~(mem(e, s(s(n(e)))) <=> (e = s(n(e))))) | (~mem(e, s(s(n(e))))) | (e = s(n(e)))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(591,plain,
% 27.61/27.79 ((~(mem(e, s(s(n(e)))) <=> (e = s(n(e))))) | (~mem(e, s(s(n(e)))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[590, 589])).
% 27.61/27.79 tff(592,plain,
% 27.61/27.79 (~mem(e, s(s(n(e))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[591, 497])).
% 27.61/27.79 tff(593,plain,
% 27.61/27.79 ((~(mem(e, s(s(n(e)))) | mem(e, s(n(e))))) | mem(e, s(s(n(e)))) | mem(e, s(n(e)))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(594,plain,
% 27.61/27.79 ((~(mem(e, s(s(n(e)))) | mem(e, s(n(e))))) | mem(e, s(n(e)))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[593, 592])).
% 27.61/27.79 tff(595,plain,
% 27.61/27.79 ($false),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[594, 493, 483])).
% 27.61/27.79 tff(596,plain,((~(mem(e, u(s(n(e)), s(s(n(e))))) <=> (mem(e, s(s(n(e)))) | mem(e, s(n(e)))))) | mem(e, s(a(e, e))) | (~mem(e, a(s(n(e)), s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.79 tff(597,plain,
% 27.61/27.79 (mem(e, s(a(e, e))) | (~mem(e, a(s(n(e)), s(n(e)))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[596, 478])).
% 27.61/27.79 tff(598,plain,
% 27.61/27.79 (~mem(e, a(s(n(e)), s(n(e))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[597, 474])).
% 27.61/27.79 tff(599,plain,
% 27.61/27.79 ((~(mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e)))))) | mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e))))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(600,plain,
% 27.61/27.79 ((~(mem(e, s(p(s(n(e))))) | mem(e, a(s(n(e)), s(n(e)))))) | mem(e, s(p(s(n(e)))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[599, 598])).
% 27.61/27.79 tff(601,plain,
% 27.61/27.79 (mem(e, s(p(s(n(e)))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[600, 385])).
% 27.61/27.79 tff(602,assumption,(~(mem(e, s(p(s(n(e))))) <=> (e = p(s(n(e)))))), introduced(assumption)).
% 27.61/27.79 tff(603,plain,
% 27.61/27.79 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(p(s(n(e))))) <=> (e = p(s(n(e)))))),
% 27.61/27.79 inference(quant_inst,[status(thm)],[])).
% 27.61/27.79 tff(604,plain,
% 27.61/27.79 ($false),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[603, 47, 602])).
% 27.61/27.79 tff(605,plain,(mem(e, s(p(s(n(e))))) <=> (e = p(s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.79 tff(606,plain,
% 27.61/27.79 ((~(mem(e, s(p(s(n(e))))) <=> (e = p(s(n(e)))))) | (~mem(e, s(p(s(n(e)))))) | (e = p(s(n(e))))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(607,plain,
% 27.61/27.79 ((~mem(e, s(p(s(n(e)))))) | (e = p(s(n(e))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[606, 605])).
% 27.61/27.79 tff(608,plain,
% 27.61/27.79 (e = p(s(n(e)))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[607, 601])).
% 27.61/27.79 tff(609,plain,
% 27.61/27.79 (mem(e, e) <=> mem(e, p(s(n(e))))),
% 27.61/27.79 inference(monotonicity,[status(thm)],[608])).
% 27.61/27.79 tff(610,plain,
% 27.61/27.79 (mem(e, p(s(n(e)))) <=> mem(e, e)),
% 27.61/27.79 inference(symmetry,[status(thm)],[609])).
% 27.61/27.79 tff(611,assumption,(mem(tptp_fun_Z_0(s(n(e)), e), e)), introduced(assumption)).
% 27.61/27.79 tff(612,plain,
% 27.61/27.79 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(s(n(e)), e), e))),
% 27.61/27.79 inference(quant_inst,[status(thm)],[])).
% 27.61/27.79 tff(613,plain,
% 27.61/27.79 ($false),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[612, 36, 611])).
% 27.61/27.79 tff(614,plain,(~mem(tptp_fun_Z_0(s(n(e)), e), e)), inference(lemma,lemma(discharge,[]))).
% 27.61/27.79 tff(615,plain,
% 27.61/27.79 (((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e)))) | mem(tptp_fun_Z_0(s(n(e)), e), e)),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(616,plain,
% 27.61/27.79 ((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e)))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[615, 614])).
% 27.61/27.79 tff(617,plain,
% 27.61/27.79 ((~![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(e, s(n(e)))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, s(n(e)))))) | (~(subq(e, s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e)))))))))),
% 27.61/27.79 inference(quant_inst,[status(thm)],[])).
% 27.61/27.79 tff(618,plain,
% 27.61/27.79 (~((~((~subq(e, s(n(e)))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, s(n(e)))))) | (~(subq(e, s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e))))))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[617, 340])).
% 27.61/27.79 tff(619,plain,
% 27.61/27.79 (((~((~subq(e, s(n(e)))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, s(n(e)))))) | (~(subq(e, s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e)))))))) | (subq(e, s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e))))))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.79 tff(620,plain,
% 27.61/27.79 (subq(e, s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e)))))),
% 27.61/27.79 inference(unit_resolution,[status(thm)],[619, 618])).
% 27.61/27.79 tff(621,plain,
% 27.61/27.79 ((~(subq(e, s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e))))))) | subq(e, s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e)))))),
% 27.61/27.79 inference(tautology,[status(thm)],[])).
% 27.61/27.80 tff(622,plain,
% 27.61/27.80 (subq(e, s(n(e))) | (~((~mem(tptp_fun_Z_0(s(n(e)), e), e)) | mem(tptp_fun_Z_0(s(n(e)), e), s(n(e)))))),
% 27.61/27.80 inference(unit_resolution,[status(thm)],[621, 620])).
% 27.61/27.80 tff(623,plain,
% 27.61/27.80 (subq(e, s(n(e)))),
% 27.61/27.80 inference(unit_resolution,[status(thm)],[622, 616])).
% 27.61/27.80 tff(624,assumption,(~(mem(e, p(s(n(e)))) <=> subq(e, s(n(e))))), introduced(assumption)).
% 27.61/27.80 tff(625,plain,
% 27.61/27.80 (^[X: $i, Y: $i] : refl((mem(X, p(Y)) <=> subq(X, Y)) <=> (mem(X, p(Y)) <=> subq(X, Y)))),
% 27.61/27.80 inference(bind,[status(th)],[])).
% 27.61/27.80 tff(626,plain,
% 27.61/27.80 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y)) <=> ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 27.61/27.80 inference(quant_intro,[status(thm)],[625])).
% 27.61/27.80 tff(627,plain,
% 27.61/27.80 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y)) <=> ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 27.61/27.80 inference(rewrite,[status(thm)],[])).
% 27.61/27.80 tff(628,axiom,(![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','p_ax')).
% 27.61/27.80 tff(629,plain,
% 27.61/27.80 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 27.61/27.80 inference(modus_ponens,[status(thm)],[628, 627])).
% 27.61/27.80 tff(630,plain,(
% 27.61/27.80 ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 27.61/27.80 inference(skolemize,[status(sab)],[629])).
% 27.61/27.80 tff(631,plain,
% 27.61/27.80 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 27.61/27.80 inference(modus_ponens,[status(thm)],[630, 626])).
% 27.61/27.80 tff(632,plain,
% 27.61/27.80 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(e, p(s(n(e)))) <=> subq(e, s(n(e))))),
% 27.61/27.80 inference(quant_inst,[status(thm)],[])).
% 27.61/27.80 tff(633,plain,
% 27.61/27.80 ($false),
% 27.61/27.80 inference(unit_resolution,[status(thm)],[632, 631, 624])).
% 27.61/27.80 tff(634,plain,(mem(e, p(s(n(e)))) <=> subq(e, s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 27.61/27.80 tff(635,plain,
% 27.61/27.80 ((~(mem(e, p(s(n(e)))) <=> subq(e, s(n(e))))) | mem(e, p(s(n(e)))) | (~subq(e, s(n(e))))),
% 27.61/27.80 inference(tautology,[status(thm)],[])).
% 27.61/27.80 tff(636,plain,
% 27.61/27.80 (mem(e, p(s(n(e)))) | (~subq(e, s(n(e))))),
% 27.61/27.80 inference(unit_resolution,[status(thm)],[635, 634])).
% 27.61/27.80 tff(637,plain,
% 27.61/27.80 (mem(e, p(s(n(e))))),
% 27.61/27.80 inference(unit_resolution,[status(thm)],[636, 623])).
% 27.61/27.80 tff(638,plain,
% 27.61/27.80 (mem(e, e)),
% 27.61/27.80 inference(modus_ponens,[status(thm)],[637, 610])).
% 27.61/27.80 tff(639,assumption,(~mem(e, e)), introduced(assumption)).
% 27.61/27.80 tff(640,plain,
% 27.61/27.80 ($false),
% 27.61/27.80 inference(unit_resolution,[status(thm)],[639, 638])).
% 27.61/27.80 tff(641,plain,(mem(e, e)), inference(lemma,lemma(discharge,[]))).
% 27.61/27.80 tff(642,plain,
% 27.61/27.80 ((~![X: $i] : (~mem(X, e))) | (~mem(e, e))),
% 27.61/27.80 inference(quant_inst,[status(thm)],[])).
% 27.61/27.80 tff(643,plain,
% 27.61/27.80 ($false),
% 27.61/27.80 inference(unit_resolution,[status(thm)],[642, 36, 641])).
% 27.61/27.80 % SZS output end Proof
% 27.64/27.81 % E exiting
%------------------------------------------------------------------------------