%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV561+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 1.15s 1.37s
% Output : Proof 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEV561+1 : TPTP v9.1.0. Released v9.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 07:41:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 1.15/1.37 % SZS status Theorem
% 1.15/1.37 % SZS output start Proof
% 1.15/1.37 tff(mem_type, type, (
% 1.15/1.37 mem: ( $i * $i ) > $o)).
% 1.15/1.37 tff(tptp_fun_Z_1_type, type, (
% 1.15/1.37 tptp_fun_Z_1: ( $i * $i ) > $i)).
% 1.15/1.37 tff(p_type, type, (
% 1.15/1.37 p: $i > $i)).
% 1.15/1.37 tff(s_type, type, (
% 1.15/1.37 s: $i > $i)).
% 1.15/1.37 tff(n_type, type, (
% 1.15/1.37 n: $i > $i)).
% 1.15/1.37 tff(e_type, type, (
% 1.15/1.37 e: $i)).
% 1.15/1.37 tff(a_type, type, (
% 1.15/1.37 a: ( $i * $i ) > $i)).
% 1.15/1.37 tff(u_type, type, (
% 1.15/1.37 u: ( $i * $i ) > $i)).
% 1.15/1.37 tff(subq_type, type, (
% 1.15/1.37 subq: ( $i * $i ) > $o)).
% 1.15/1.37 tff(tptp_fun_Z_0_type, type, (
% 1.15/1.37 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 1.15/1.37 tff(disj_type, type, (
% 1.15/1.37 disj: ( $i * $i ) > $o)).
% 1.15/1.37 tff(tptp_fun_Y_2_type, type, (
% 1.15/1.37 tptp_fun_Y_2: $i > $i)).
% 1.15/1.37 tff(atleast2p_type, type, (
% 1.15/1.37 atleast2p: $i > $o)).
% 1.15/1.37 tff(1,assumption,(~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = u(s(s(n(e))), s(n(n(e))))))), introduced(assumption)).
% 1.15/1.37 tff(2,plain,
% 1.15/1.37 (^[X: $i, Y: $i] : refl((mem(X, s(Y)) <=> (X = Y)) <=> (mem(X, s(Y)) <=> (X = Y)))),
% 1.15/1.37 inference(bind,[status(th)],[])).
% 1.15/1.37 tff(3,plain,
% 1.15/1.37 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.15/1.37 inference(quant_intro,[status(thm)],[2])).
% 1.15/1.37 tff(4,plain,
% 1.15/1.37 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5,axiom,(![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','s_ax')).
% 1.15/1.37 tff(6,plain,
% 1.15/1.37 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.15/1.37 tff(7,plain,(
% 1.15/1.37 ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.15/1.37 inference(skolemize,[status(sab)],[6])).
% 1.15/1.37 tff(8,plain,
% 1.15/1.37 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.15/1.37 tff(9,plain,
% 1.15/1.37 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = u(s(s(n(e))), s(n(n(e))))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(10,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.15/1.37 tff(11,plain,(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = u(s(s(n(e))), s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(12,assumption,(~(mem(a(e, e), s(s(n(e)))) <=> (a(e, e) = s(n(e))))), introduced(assumption)).
% 1.15/1.37 tff(13,plain,
% 1.15/1.37 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(s(n(e)))) <=> (a(e, e) = s(n(e))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(14,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 1.15/1.37 tff(15,plain,(mem(a(e, e), s(s(n(e)))) <=> (a(e, e) = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(16,assumption,(a(e, e) = s(n(e))), introduced(assumption)).
% 1.15/1.37 tff(17,plain,
% 1.15/1.37 (s(n(e)) = a(e, e)),
% 1.15/1.37 inference(symmetry,[status(thm)],[16])).
% 1.15/1.37 tff(18,plain,
% 1.15/1.37 (^[X: $i] : refl((n(X) = a(X, X)) <=> (n(X) = a(X, X)))),
% 1.15/1.37 inference(bind,[status(th)],[])).
% 1.15/1.37 tff(19,plain,
% 1.15/1.37 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 1.15/1.37 inference(quant_intro,[status(thm)],[18])).
% 1.15/1.37 tff(20,plain,
% 1.15/1.37 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(21,axiom,(![X: $i] : (n(X) = a(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','n_def')).
% 1.15/1.37 tff(22,plain,
% 1.15/1.37 (![X: $i] : (n(X) = a(X, X))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.15/1.37 tff(23,plain,(
% 1.15/1.37 ![X: $i] : (n(X) = a(X, X))),
% 1.15/1.37 inference(skolemize,[status(sab)],[22])).
% 1.15/1.37 tff(24,plain,
% 1.15/1.37 (![X: $i] : (n(X) = a(X, X))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[23, 19])).
% 1.15/1.37 tff(25,plain,
% 1.15/1.37 ((~![X: $i] : (n(X) = a(X, X))) | (n(e) = a(e, e))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(26,plain,
% 1.15/1.37 (n(e) = a(e, e)),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[25, 24])).
% 1.15/1.37 tff(27,plain,
% 1.15/1.37 (a(e, e) = n(e)),
% 1.15/1.37 inference(symmetry,[status(thm)],[26])).
% 1.15/1.37 tff(28,plain,
% 1.15/1.37 (s(n(e)) = n(e)),
% 1.15/1.37 inference(transitivity,[status(thm)],[17, 27])).
% 1.15/1.37 tff(29,plain,
% 1.15/1.37 (s(s(n(e))) = s(n(e))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[28])).
% 1.15/1.37 tff(30,plain,
% 1.15/1.37 (s(s(n(e))) = a(e, e)),
% 1.15/1.37 inference(transitivity,[status(thm)],[29, 17])).
% 1.15/1.37 tff(31,plain,
% 1.15/1.37 (mem(e, s(s(n(e)))) <=> mem(e, a(e, e))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[30])).
% 1.15/1.37 tff(32,plain,
% 1.15/1.37 (mem(e, a(e, e)) <=> mem(e, s(s(n(e))))),
% 1.15/1.37 inference(symmetry,[status(thm)],[31])).
% 1.15/1.37 tff(33,plain,
% 1.15/1.37 (^[X: $i, Y: $i] : refl((a(X, Y) = u(X, s(Y))) <=> (a(X, Y) = u(X, s(Y))))),
% 1.15/1.37 inference(bind,[status(th)],[])).
% 1.15/1.37 tff(34,plain,
% 1.15/1.37 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.15/1.37 inference(quant_intro,[status(thm)],[33])).
% 1.15/1.37 tff(35,plain,
% 1.15/1.37 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(36,axiom,(![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','a_def')).
% 1.15/1.37 tff(37,plain,
% 1.15/1.37 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.15/1.37 tff(38,plain,(
% 1.15/1.37 ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.15/1.37 inference(skolemize,[status(sab)],[37])).
% 1.15/1.37 tff(39,plain,
% 1.15/1.37 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.15/1.37 tff(40,plain,
% 1.15/1.37 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(e, e) = u(e, s(e)))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(41,plain,
% 1.15/1.37 (a(e, e) = u(e, s(e))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[40, 39])).
% 1.15/1.37 tff(42,plain,
% 1.15/1.37 (u(e, s(e)) = a(e, e)),
% 1.15/1.37 inference(symmetry,[status(thm)],[41])).
% 1.15/1.37 tff(43,plain,
% 1.15/1.37 (mem(e, u(e, s(e))) <=> mem(e, a(e, e))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[42])).
% 1.15/1.37 tff(44,plain,
% 1.15/1.37 (mem(e, a(e, e)) <=> mem(e, u(e, s(e)))),
% 1.15/1.37 inference(symmetry,[status(thm)],[43])).
% 1.15/1.37 tff(45,plain,
% 1.15/1.37 ((~mem(e, a(e, e))) <=> (~mem(e, u(e, s(e))))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[44])).
% 1.15/1.37 tff(46,assumption,(~mem(e, a(e, e))), introduced(assumption)).
% 1.15/1.37 tff(47,plain,
% 1.15/1.37 (~mem(e, u(e, s(e)))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.15/1.37 tff(48,plain,
% 1.15/1.37 (^[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))))),
% 1.15/1.37 inference(bind,[status(th)],[])).
% 1.15/1.37 tff(49,plain,
% 1.15/1.37 (![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)))),
% 1.15/1.37 inference(quant_intro,[status(thm)],[48])).
% 1.15/1.37 tff(50,plain,
% 1.15/1.37 (![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)))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(51,plain,
% 1.15/1.37 (^[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))))),
% 1.15/1.37 inference(bind,[status(th)],[])).
% 1.15/1.37 tff(52,plain,
% 1.15/1.37 (![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)))),
% 1.15/1.37 inference(quant_intro,[status(thm)],[51])).
% 1.15/1.37 tff(53,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')).
% 1.15/1.37 tff(54,plain,
% 1.15/1.37 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.15/1.37 tff(55,plain,
% 1.15/1.37 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.15/1.37 tff(56,plain,(
% 1.15/1.37 ![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 1.15/1.37 inference(skolemize,[status(sab)],[55])).
% 1.15/1.37 tff(57,plain,
% 1.15/1.37 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[56, 49])).
% 1.15/1.37 tff(58,plain,
% 1.15/1.37 ((~![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)))),
% 1.22/1.37 inference(quant_inst,[status(thm)],[])).
% 1.22/1.37 tff(59,plain,
% 1.22/1.37 (mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[58, 57])).
% 1.22/1.37 tff(60,plain,
% 1.22/1.37 (((~![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)))),
% 1.22/1.37 inference(rewrite,[status(thm)],[])).
% 1.22/1.37 tff(61,plain,
% 1.22/1.37 ((mem(e, s(e)) <=> $true) <=> mem(e, s(e))),
% 1.22/1.37 inference(rewrite,[status(thm)],[])).
% 1.22/1.37 tff(62,plain,
% 1.22/1.37 ((e = e) <=> $true),
% 1.22/1.37 inference(rewrite,[status(thm)],[])).
% 1.22/1.37 tff(63,plain,
% 1.22/1.37 ((mem(e, s(e)) <=> (e = e)) <=> (mem(e, s(e)) <=> $true)),
% 1.22/1.37 inference(monotonicity,[status(thm)],[62])).
% 1.22/1.37 tff(64,plain,
% 1.22/1.37 ((mem(e, s(e)) <=> (e = e)) <=> mem(e, s(e))),
% 1.22/1.37 inference(transitivity,[status(thm)],[63, 61])).
% 1.22/1.37 tff(65,plain,
% 1.22/1.37 (((~![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)))),
% 1.22/1.37 inference(monotonicity,[status(thm)],[64])).
% 1.22/1.37 tff(66,plain,
% 1.22/1.37 (((~![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)))),
% 1.22/1.37 inference(transitivity,[status(thm)],[65, 60])).
% 1.22/1.37 tff(67,plain,
% 1.22/1.37 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(e)) <=> (e = e))),
% 1.22/1.37 inference(quant_inst,[status(thm)],[])).
% 1.22/1.37 tff(68,plain,
% 1.22/1.37 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(e, s(e))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.22/1.37 tff(69,plain,
% 1.22/1.37 (mem(e, s(e))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[68, 8])).
% 1.22/1.37 tff(70,plain,
% 1.22/1.37 ((mem(e, s(e)) | mem(e, e)) | (~mem(e, s(e)))),
% 1.22/1.37 inference(tautology,[status(thm)],[])).
% 1.22/1.37 tff(71,plain,
% 1.22/1.37 (mem(e, s(e)) | mem(e, e)),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.22/1.37 tff(72,plain,
% 1.22/1.37 ((~(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))) | mem(e, u(e, s(e))) | (~(mem(e, s(e)) | mem(e, e)))),
% 1.22/1.37 inference(tautology,[status(thm)],[])).
% 1.22/1.37 tff(73,plain,
% 1.22/1.37 ((~(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))) | mem(e, u(e, s(e)))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[72, 71])).
% 1.22/1.37 tff(74,plain,
% 1.22/1.37 (mem(e, u(e, s(e)))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[73, 59])).
% 1.22/1.37 tff(75,plain,
% 1.22/1.37 ($false),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[74, 47])).
% 1.22/1.37 tff(76,plain,(mem(e, a(e, e))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.37 tff(77,plain,
% 1.22/1.37 (mem(e, s(s(n(e))))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[76, 32])).
% 1.22/1.37 tff(78,assumption,(~(mem(e, s(s(n(e)))) <=> (e = s(n(e))))), introduced(assumption)).
% 1.22/1.37 tff(79,plain,
% 1.22/1.37 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(s(n(e)))) <=> (e = s(n(e))))),
% 1.22/1.37 inference(quant_inst,[status(thm)],[])).
% 1.22/1.37 tff(80,plain,
% 1.22/1.37 ($false),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[79, 8, 78])).
% 1.22/1.37 tff(81,plain,(mem(e, s(s(n(e)))) <=> (e = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.37 tff(82,plain,
% 1.22/1.37 (s(a(e, e)) = s(n(e))),
% 1.22/1.37 inference(monotonicity,[status(thm)],[27])).
% 1.22/1.37 tff(83,plain,
% 1.22/1.37 (mem(a(e, e), s(a(e, e))) <=> mem(a(e, e), s(n(e)))),
% 1.22/1.37 inference(monotonicity,[status(thm)],[82])).
% 1.22/1.37 tff(84,plain,
% 1.22/1.37 (mem(a(e, e), s(n(e))) <=> mem(a(e, e), s(a(e, e)))),
% 1.22/1.37 inference(symmetry,[status(thm)],[83])).
% 1.22/1.37 tff(85,plain,
% 1.22/1.37 ((~mem(a(e, e), s(n(e)))) <=> (~mem(a(e, e), s(a(e, e))))),
% 1.22/1.37 inference(monotonicity,[status(thm)],[84])).
% 1.22/1.37 tff(86,assumption,(~mem(a(e, e), s(n(e)))), introduced(assumption)).
% 1.22/1.37 tff(87,plain,
% 1.22/1.37 (~mem(a(e, e), s(a(e, e)))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.22/1.37 tff(88,plain,
% 1.22/1.37 (((~![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))))),
% 1.22/1.37 inference(rewrite,[status(thm)],[])).
% 1.22/1.37 tff(89,plain,
% 1.22/1.37 ((mem(a(e, e), s(a(e, e))) <=> $true) <=> mem(a(e, e), s(a(e, e)))),
% 1.22/1.37 inference(rewrite,[status(thm)],[])).
% 1.22/1.37 tff(90,plain,
% 1.22/1.37 ((a(e, e) = a(e, e)) <=> $true),
% 1.22/1.37 inference(rewrite,[status(thm)],[])).
% 1.22/1.37 tff(91,plain,
% 1.22/1.37 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> (mem(a(e, e), s(a(e, e))) <=> $true)),
% 1.22/1.37 inference(monotonicity,[status(thm)],[90])).
% 1.22/1.37 tff(92,plain,
% 1.22/1.37 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> mem(a(e, e), s(a(e, e)))),
% 1.22/1.37 inference(transitivity,[status(thm)],[91, 89])).
% 1.22/1.37 tff(93,plain,
% 1.22/1.37 (((~![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))))),
% 1.22/1.37 inference(monotonicity,[status(thm)],[92])).
% 1.22/1.37 tff(94,plain,
% 1.22/1.37 (((~![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))))),
% 1.22/1.37 inference(transitivity,[status(thm)],[93, 88])).
% 1.22/1.37 tff(95,plain,
% 1.22/1.37 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e)))),
% 1.22/1.37 inference(quant_inst,[status(thm)],[])).
% 1.22/1.37 tff(96,plain,
% 1.22/1.37 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e)))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.22/1.37 tff(97,plain,
% 1.22/1.37 (mem(a(e, e), s(a(e, e)))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[96, 8])).
% 1.22/1.37 tff(98,plain,
% 1.22/1.37 ($false),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[97, 87])).
% 1.22/1.37 tff(99,plain,(mem(a(e, e), s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.37 tff(100,assumption,(e = s(n(e))), introduced(assumption)).
% 1.22/1.37 tff(101,plain,
% 1.22/1.37 (mem(a(e, e), e) <=> mem(a(e, e), s(n(e)))),
% 1.22/1.37 inference(monotonicity,[status(thm)],[100])).
% 1.22/1.37 tff(102,plain,
% 1.22/1.37 (mem(a(e, e), s(n(e))) <=> mem(a(e, e), e)),
% 1.22/1.37 inference(symmetry,[status(thm)],[101])).
% 1.22/1.37 tff(103,assumption,(mem(a(e, e), s(n(e)))), introduced(assumption)).
% 1.22/1.37 tff(104,plain,
% 1.22/1.37 (mem(a(e, e), e)),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.22/1.37 tff(105,plain,
% 1.22/1.37 (^[X: $i] : refl((~mem(X, e)) <=> (~mem(X, e)))),
% 1.22/1.37 inference(bind,[status(th)],[])).
% 1.22/1.37 tff(106,plain,
% 1.22/1.37 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 1.22/1.37 inference(quant_intro,[status(thm)],[105])).
% 1.22/1.37 tff(107,plain,
% 1.22/1.37 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 1.22/1.37 inference(rewrite,[status(thm)],[])).
% 1.22/1.37 tff(108,axiom,(![X: $i] : (~mem(X, e))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','e_ax')).
% 1.22/1.37 tff(109,plain,
% 1.22/1.37 (![X: $i] : (~mem(X, e))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.22/1.37 tff(110,plain,(
% 1.22/1.37 ![X: $i] : (~mem(X, e))),
% 1.22/1.37 inference(skolemize,[status(sab)],[109])).
% 1.22/1.37 tff(111,plain,
% 1.22/1.37 (![X: $i] : (~mem(X, e))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[110, 106])).
% 1.22/1.37 tff(112,plain,
% 1.22/1.37 ((~![X: $i] : (~mem(X, e))) | (~mem(a(e, e), e))),
% 1.22/1.37 inference(quant_inst,[status(thm)],[])).
% 1.22/1.37 tff(113,plain,
% 1.22/1.37 (~mem(a(e, e), e)),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[112, 111])).
% 1.22/1.37 tff(114,plain,
% 1.22/1.37 ($false),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[113, 104])).
% 1.22/1.37 tff(115,plain,((~(e = s(n(e)))) | (~mem(a(e, e), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.37 tff(116,plain,
% 1.22/1.37 (~(e = s(n(e)))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[115, 99])).
% 1.22/1.37 tff(117,plain,
% 1.22/1.37 ((~(mem(e, s(s(n(e)))) <=> (e = s(n(e))))) | (~mem(e, s(s(n(e))))) | (e = s(n(e)))),
% 1.22/1.37 inference(tautology,[status(thm)],[])).
% 1.22/1.37 tff(118,plain,
% 1.22/1.37 (~mem(e, s(s(n(e))))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[117, 116, 81])).
% 1.22/1.37 tff(119,plain,
% 1.22/1.37 ($false),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[118, 77])).
% 1.22/1.37 tff(120,plain,(~(a(e, e) = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.37 tff(121,plain,
% 1.22/1.37 ((~(mem(a(e, e), s(s(n(e)))) <=> (a(e, e) = s(n(e))))) | (~mem(a(e, e), s(s(n(e))))) | (a(e, e) = s(n(e)))),
% 1.22/1.37 inference(tautology,[status(thm)],[])).
% 1.22/1.37 tff(122,plain,
% 1.22/1.37 ((~(mem(a(e, e), s(s(n(e)))) <=> (a(e, e) = s(n(e))))) | (~mem(a(e, e), s(s(n(e)))))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[121, 120])).
% 1.22/1.37 tff(123,plain,
% 1.22/1.37 (~mem(a(e, e), s(s(n(e))))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[122, 15])).
% 1.22/1.37 tff(124,assumption,(~mem(a(e, e), s(s(n(e))))), introduced(assumption)).
% 1.22/1.37 tff(125,assumption,(mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))), introduced(assumption)).
% 1.22/1.37 tff(126,plain,
% 1.22/1.37 (^[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))))))))),
% 1.22/1.37 inference(bind,[status(th)],[])).
% 1.22/1.37 tff(127,plain,
% 1.22/1.37 (![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)))))))),
% 1.22/1.37 inference(quant_intro,[status(thm)],[126])).
% 1.22/1.37 tff(128,plain,
% 1.22/1.37 (^[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))))))))),
% 1.22/1.37 inference(bind,[status(th)],[])).
% 1.22/1.37 tff(129,plain,
% 1.22/1.37 (![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)))))))),
% 1.22/1.37 inference(quant_intro,[status(thm)],[128])).
% 1.22/1.37 tff(130,plain,
% 1.22/1.37 (![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)))))))),
% 1.22/1.37 inference(transitivity,[status(thm)],[129, 127])).
% 1.22/1.37 tff(131,plain,
% 1.22/1.37 (^[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)))))))))),
% 1.22/1.37 inference(bind,[status(th)],[])).
% 1.22/1.37 tff(132,plain,
% 1.22/1.37 (![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)))))))),
% 1.22/1.37 inference(quant_intro,[status(thm)],[131])).
% 1.22/1.37 tff(133,plain,
% 1.22/1.37 (![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)))),
% 1.22/1.37 inference(rewrite,[status(thm)],[])).
% 1.22/1.37 tff(134,plain,
% 1.22/1.37 (^[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))))),
% 1.22/1.37 inference(bind,[status(th)],[])).
% 1.22/1.37 tff(135,plain,
% 1.22/1.37 (![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)))),
% 1.22/1.37 inference(quant_intro,[status(thm)],[134])).
% 1.22/1.37 tff(136,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')).
% 1.22/1.37 tff(137,plain,
% 1.22/1.37 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.22/1.37 tff(138,plain,
% 1.22/1.37 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[137, 133])).
% 1.22/1.37 tff(139,plain,(
% 1.22/1.37 ![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)))))),
% 1.22/1.37 inference(skolemize,[status(sab)],[138])).
% 1.22/1.37 tff(140,plain,
% 1.22/1.37 (![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)))))))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[139, 132])).
% 1.22/1.37 tff(141,plain,
% 1.22/1.37 (![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)))))))),
% 1.22/1.37 inference(modus_ponens,[status(thm)],[140, 130])).
% 1.22/1.37 tff(142,plain,
% 1.22/1.37 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e))))))) | (~(subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))) | (~((~mem(tptp_fun_Z_0(s(s(n(e))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(tptp_fun_Z_0(s(s(n(e))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))), s(s(n(e))))))))))),
% 1.22/1.37 inference(quant_inst,[status(thm)],[])).
% 1.22/1.37 tff(143,plain,
% 1.22/1.37 (~((~((~subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e))))))) | (~(subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))) | (~((~mem(tptp_fun_Z_0(s(s(n(e))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(tptp_fun_Z_0(s(s(n(e))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))), s(s(n(e)))))))))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[142, 141])).
% 1.22/1.37 tff(144,plain,
% 1.22/1.37 (((~((~subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e))))))) | (~(subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))) | (~((~mem(tptp_fun_Z_0(s(s(n(e))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(tptp_fun_Z_0(s(s(n(e))), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))), s(s(n(e))))))))) | ((~subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e))))))),
% 1.22/1.37 inference(tautology,[status(thm)],[])).
% 1.22/1.37 tff(145,plain,
% 1.22/1.37 ((~subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))),
% 1.22/1.37 inference(unit_resolution,[status(thm)],[144, 143])).
% 1.22/1.37 tff(146,plain,
% 1.22/1.37 (^[X: $i, Y: $i] : refl((mem(X, p(Y)) <=> subq(X, Y)) <=> (mem(X, p(Y)) <=> subq(X, Y)))),
% 1.22/1.37 inference(bind,[status(th)],[])).
% 1.22/1.37 tff(147,plain,
% 1.22/1.37 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y)) <=> ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.22/1.37 inference(quant_intro,[status(thm)],[146])).
% 1.22/1.37 tff(148,plain,
% 1.22/1.37 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y)) <=> ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(149,axiom,(![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','p_ax')).
% 1.22/1.38 tff(150,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.22/1.38 tff(151,plain,(
% 1.22/1.38 ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.22/1.38 inference(skolemize,[status(sab)],[150])).
% 1.22/1.38 tff(152,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[151, 147])).
% 1.22/1.38 tff(153,plain,
% 1.22/1.38 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e))))) <=> subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))))),
% 1.22/1.38 inference(quant_inst,[status(thm)],[])).
% 1.22/1.38 tff(154,plain,
% 1.22/1.38 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e))))) <=> subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[153, 152])).
% 1.22/1.38 tff(155,plain,
% 1.22/1.38 (^[X: $i, Y: $i] : refl((~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(156,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> ![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[155])).
% 1.22/1.38 tff(157,plain,
% 1.22/1.38 (^[X: $i, Y: $i] : rewrite((~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(158,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> ![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[157])).
% 1.22/1.38 tff(159,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))) <=> ![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 1.22/1.38 inference(transitivity,[status(thm)],[158, 156])).
% 1.22/1.38 tff(160,plain,
% 1.22/1.38 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y)) <=> (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))), ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) <=> (disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))))), rewrite((disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))) <=> (disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))), ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) <=> (disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))))), trans(monotonicity(quant_intro(proof_bind(^[Z: $i] : trans(monotonicity(rewrite((mem(Z, X) & mem(Z, Y)) <=> (~((~mem(Z, X)) | (~mem(Z, Y))))), ((~(mem(Z, X) & mem(Z, Y))) <=> (~(~((~mem(Z, X)) | (~mem(Z, Y))))))), rewrite((~(~((~mem(Z, X)) | (~mem(Z, Y))))) <=> ((~mem(Z, X)) | (~mem(Z, Y)))), ((~(mem(Z, X) & mem(Z, Y))) <=> ((~mem(Z, X)) | (~mem(Z, Y)))))), (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) <=> ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))), ((![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))) <=> (![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))) | (~disj(X, Y))))), rewrite((![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))) | (~disj(X, Y))) <=> ((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))), ((![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))) <=> ((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))), (((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> ((disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))) & ((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))))), rewrite(((disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y))))) & ((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y))))) <=> (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))), (((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(161,plain,
% 1.22/1.38 (![X: $i, Y: $i] : ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> ![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[160])).
% 1.22/1.38 tff(162,plain,
% 1.22/1.38 (^[X: $i, Y: $i] : rewrite((((mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y)) | disj(X, Y)) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(163,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (((mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y)) | disj(X, Y)) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y)))) <=> ![X: $i, Y: $i] : ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[162])).
% 1.22/1.38 tff(164,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y))) <=> ![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(165,plain,
% 1.22/1.38 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite((~?[Z: $i] : (mem(Z, X) & mem(Z, Y))) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))), ((disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> (disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))))), rewrite((disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))), ((disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y))))), rewrite((~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y))) <=> (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))), ((disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(166,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y)))) <=> ![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[165])).
% 1.22/1.38 tff(167,axiom,(![X: $i, Y: $i] : (disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','disj_def')).
% 1.22/1.38 tff(168,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.22/1.38 tff(169,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[168, 164])).
% 1.22/1.38 tff(170,plain,(
% 1.22/1.38 ![X: $i, Y: $i] : (((mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y)) | disj(X, Y)) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))))),
% 1.22/1.38 inference(skolemize,[status(sab)],[169])).
% 1.22/1.38 tff(171,plain,
% 1.22/1.38 (![X: $i, Y: $i] : ((disj(X, Y) | (mem(tptp_fun_Z_1(Y, X), X) & mem(tptp_fun_Z_1(Y, X), Y))) & (![Z: $i] : (~(mem(Z, X) & mem(Z, Y))) | (~disj(X, Y))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[170, 163])).
% 1.22/1.38 tff(172,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[171, 161])).
% 1.22/1.38 tff(173,plain,
% 1.22/1.38 (![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[172, 159])).
% 1.22/1.38 tff(174,plain,
% 1.22/1.38 (((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))) | (~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))))))))) <=> ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))) | (~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(175,plain,
% 1.22/1.38 ((~((~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))) | (~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))))) <=> (~((~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))) | (~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))))))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(176,plain,
% 1.22/1.38 (((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))) | (~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e)))))))))))) <=> ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))) | (~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))))))),
% 1.22/1.38 inference(monotonicity,[status(thm)],[175])).
% 1.22/1.38 tff(177,plain,
% 1.22/1.38 (((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))) | (~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e)))))))))))) <=> ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))) | (~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))))))),
% 1.22/1.38 inference(transitivity,[status(thm)],[176, 174])).
% 1.22/1.38 tff(178,plain,
% 1.22/1.38 ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))) | (~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e)))))))))))),
% 1.22/1.38 inference(quant_inst,[status(thm)],[])).
% 1.22/1.38 tff(179,plain,
% 1.22/1.38 ((~![X: $i, Y: $i] : (~((~(disj(X, Y) | (~((~mem(tptp_fun_Z_1(Y, X), X)) | (~mem(tptp_fun_Z_1(Y, X), Y)))))) | (~((~disj(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | (~mem(Z, Y)))))))) | (~((~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))) | (~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))))))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.22/1.38 tff(180,plain,
% 1.22/1.38 (~((~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))) | (~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[179, 173])).
% 1.22/1.38 tff(181,plain,
% 1.22/1.38 (((~((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) | ![Z: $i] : ((~mem(Z, p(s(s(n(e)))))) | (~mem(Z, n(a(s(s(n(e))), n(n(e))))))))) | (~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))))))) | (disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))),
% 1.22/1.38 inference(tautology,[status(thm)],[])).
% 1.22/1.38 tff(182,plain,
% 1.22/1.38 (disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[181, 180])).
% 1.22/1.38 tff(183,plain,
% 1.22/1.38 ((~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))) <=> (~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(184,axiom,(~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','disj_17_4108')).
% 1.22/1.38 tff(185,plain,
% 1.22/1.38 (~disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e)))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.22/1.38 tff(186,plain,
% 1.22/1.38 ((~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))) | disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))))),
% 1.22/1.38 inference(tautology,[status(thm)],[])).
% 1.22/1.38 tff(187,plain,
% 1.22/1.38 ((~(disj(p(s(s(n(e)))), n(a(s(s(n(e))), n(n(e))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))))) | (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[186, 185])).
% 1.22/1.38 tff(188,plain,
% 1.22/1.38 (~((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[187, 182])).
% 1.22/1.38 tff(189,plain,
% 1.22/1.38 (((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))),
% 1.22/1.38 inference(tautology,[status(thm)],[])).
% 1.22/1.38 tff(190,plain,
% 1.22/1.38 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[189, 188])).
% 1.22/1.38 tff(191,plain,
% 1.22/1.38 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e))))) <=> subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))),
% 1.22/1.38 inference(tautology,[status(thm)],[])).
% 1.22/1.38 tff(192,plain,
% 1.22/1.38 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e))))) <=> subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))))) | subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[191, 190])).
% 1.22/1.38 tff(193,plain,
% 1.22/1.38 (subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[192, 154])).
% 1.22/1.38 tff(194,plain,
% 1.22/1.38 ((~((~subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e))))))) | (~subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))),
% 1.22/1.38 inference(tautology,[status(thm)],[])).
% 1.22/1.38 tff(195,plain,
% 1.22/1.38 ((~((~subq(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e))))))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[194, 193])).
% 1.22/1.38 tff(196,plain,
% 1.22/1.38 (![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[195, 145])).
% 1.22/1.38 tff(197,plain,
% 1.22/1.38 (((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | ((~mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(a(e, e), s(s(n(e)))))) <=> ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | (~mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(a(e, e), s(s(n(e)))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(198,plain,
% 1.22/1.38 ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | ((~mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(a(e, e), s(s(n(e)))))),
% 1.22/1.38 inference(quant_inst,[status(thm)],[])).
% 1.22/1.38 tff(199,plain,
% 1.22/1.38 ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | (~mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(a(e, e), s(s(n(e))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.22/1.38 tff(200,plain,
% 1.22/1.38 ($false),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[199, 196, 125, 124])).
% 1.22/1.38 tff(201,plain,(mem(a(e, e), s(s(n(e)))) | (~mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.38 tff(202,plain,
% 1.22/1.38 (~mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[201, 123])).
% 1.22/1.38 tff(203,plain,
% 1.22/1.38 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = s(n(e))))),
% 1.22/1.38 inference(quant_inst,[status(thm)],[])).
% 1.22/1.38 tff(204,plain,
% 1.22/1.38 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = s(n(e)))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[203, 8])).
% 1.22/1.38 tff(205,assumption,(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))), introduced(assumption)).
% 1.22/1.38 tff(206,assumption,(~mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))), introduced(assumption)).
% 1.22/1.38 tff(207,assumption,(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e))), introduced(assumption)).
% 1.22/1.38 tff(208,plain,
% 1.22/1.38 (a(n(e), n(e)) = tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))),
% 1.22/1.38 inference(symmetry,[status(thm)],[207])).
% 1.22/1.38 tff(209,plain,
% 1.22/1.38 (a(a(e, e), a(e, e)) = a(n(e), n(e))),
% 1.22/1.38 inference(monotonicity,[status(thm)],[27, 27])).
% 1.22/1.38 tff(210,plain,
% 1.22/1.38 ((~![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))))),
% 1.22/1.38 inference(quant_inst,[status(thm)],[])).
% 1.22/1.38 tff(211,plain,
% 1.22/1.38 (a(a(e, e), a(e, e)) = u(a(e, e), s(a(e, e)))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[210, 39])).
% 1.22/1.38 tff(212,plain,
% 1.22/1.38 (u(a(e, e), s(a(e, e))) = a(a(e, e), a(e, e))),
% 1.22/1.38 inference(symmetry,[status(thm)],[211])).
% 1.22/1.38 tff(213,plain,
% 1.22/1.38 (s(n(e)) = s(a(e, e))),
% 1.22/1.38 inference(symmetry,[status(thm)],[82])).
% 1.22/1.38 tff(214,plain,
% 1.22/1.38 (u(a(e, e), s(n(e))) = u(a(e, e), s(a(e, e)))),
% 1.22/1.38 inference(monotonicity,[status(thm)],[213])).
% 1.22/1.38 tff(215,plain,
% 1.22/1.38 (u(a(e, e), s(n(e))) = tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))),
% 1.22/1.38 inference(transitivity,[status(thm)],[214, 212, 209, 208])).
% 1.22/1.38 tff(216,plain,
% 1.22/1.38 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))),
% 1.22/1.38 inference(monotonicity,[status(thm)],[215])).
% 1.22/1.38 tff(217,plain,
% 1.22/1.38 (mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))) <=> mem(a(e, e), u(a(e, e), s(n(e))))),
% 1.22/1.38 inference(symmetry,[status(thm)],[216])).
% 1.22/1.38 tff(218,plain,
% 1.22/1.38 ((~mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) <=> (~mem(a(e, e), u(a(e, e), s(n(e)))))),
% 1.22/1.38 inference(monotonicity,[status(thm)],[217])).
% 1.22/1.38 tff(219,plain,
% 1.22/1.38 (~mem(a(e, e), u(a(e, e), s(n(e))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[206, 218])).
% 1.22/1.38 tff(220,plain,
% 1.22/1.38 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(221,plain,
% 1.22/1.39 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e)))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[220, 57])).
% 1.22/1.39 tff(222,plain,
% 1.22/1.39 ((mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))) | (~mem(a(e, e), s(n(e))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(223,plain,
% 1.22/1.39 (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[222, 99])).
% 1.22/1.39 tff(224,plain,
% 1.22/1.39 ((~(mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))) | mem(a(e, e), u(a(e, e), s(n(e)))) | (~(mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(225,plain,
% 1.22/1.39 ((~(mem(a(e, e), u(a(e, e), s(n(e)))) <=> (mem(a(e, e), s(n(e))) | mem(a(e, e), a(e, e))))) | mem(a(e, e), u(a(e, e), s(n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[224, 223])).
% 1.22/1.39 tff(226,plain,
% 1.22/1.39 (mem(a(e, e), u(a(e, e), s(n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[225, 221])).
% 1.22/1.39 tff(227,plain,
% 1.22/1.39 ($false),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[226, 219])).
% 1.22/1.39 tff(228,plain,((~(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e)))) | mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.39 tff(229,plain,
% 1.22/1.39 (~(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e)))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[228, 206])).
% 1.22/1.39 tff(230,plain,
% 1.22/1.39 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(e)) = a(n(e), n(e)))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(231,plain,
% 1.22/1.39 (n(n(e)) = a(n(e), n(e))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[230, 24])).
% 1.22/1.39 tff(232,plain,
% 1.22/1.39 (a(n(e), n(e)) = n(n(e))),
% 1.22/1.39 inference(symmetry,[status(thm)],[231])).
% 1.22/1.39 tff(233,plain,
% 1.22/1.39 (s(a(n(e), n(e))) = s(n(n(e)))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[232])).
% 1.22/1.39 tff(234,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e)))) <=> mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[233])).
% 1.22/1.39 tff(235,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) <=> mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e))))),
% 1.22/1.39 inference(symmetry,[status(thm)],[234])).
% 1.22/1.39 tff(236,assumption,(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e))))), introduced(assumption)).
% 1.22/1.39 tff(237,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.22/1.39 tff(238,plain,
% 1.22/1.39 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e)))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(239,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e)))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e)))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[238, 8])).
% 1.22/1.39 tff(240,assumption,(~(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e)))), introduced(assumption)).
% 1.22/1.39 tff(241,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e)))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e))))) | (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e)))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(242,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e)))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[241, 240])).
% 1.22/1.39 tff(243,plain,
% 1.22/1.39 (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(a(n(e), n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[242, 239])).
% 1.22/1.39 tff(244,plain,
% 1.22/1.39 ($false),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[243, 237])).
% 1.22/1.39 tff(245,plain,((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e))))) | (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.39 tff(246,plain,
% 1.22/1.39 (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[245, 229])).
% 1.22/1.39 tff(247,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(248,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[247, 246, 205])).
% 1.22/1.39 tff(249,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = s(n(e))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))) | (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = s(n(e)))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(250,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = s(n(e))))) | (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = s(n(e)))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[249, 248])).
% 1.22/1.39 tff(251,plain,
% 1.22/1.39 (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = s(n(e))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[250, 204])).
% 1.22/1.39 tff(252,plain,
% 1.22/1.39 (mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))) <=> mem(a(e, e), s(n(e)))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[251])).
% 1.22/1.39 tff(253,plain,
% 1.22/1.39 (mem(a(e, e), s(n(e))) <=> mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))),
% 1.22/1.39 inference(symmetry,[status(thm)],[252])).
% 1.22/1.39 tff(254,plain,
% 1.22/1.39 (mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[99, 253])).
% 1.22/1.39 tff(255,plain,
% 1.22/1.39 ($false),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[206, 254])).
% 1.22/1.39 tff(256,plain,(mem(a(e, e), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))) | (~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.39 tff(257,plain,
% 1.22/1.39 (~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[256, 202])).
% 1.22/1.39 tff(258,assumption,(~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e))))) <=> (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))))), introduced(assumption)).
% 1.22/1.39 tff(259,plain,
% 1.22/1.39 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e))))) <=> (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(260,plain,
% 1.22/1.39 ($false),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[259, 57, 258])).
% 1.22/1.39 tff(261,plain,(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e))))) <=> (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.39 tff(262,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e))))) <=> (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e))))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e)))))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(263,plain,
% 1.22/1.39 ((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e)))))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(n(n(e)))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(s(n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[262, 261])).
% 1.22/1.39 tff(264,plain,
% 1.22/1.39 (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[263, 257])).
% 1.22/1.39 tff(265,plain,
% 1.22/1.39 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e))))))) <=> (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e)))))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(266,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e))))))) <=> (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[265, 57])).
% 1.22/1.39 tff(267,plain,
% 1.22/1.39 ((~![X: $i] : (n(X) = a(X, X))) | (n(a(s(s(n(e))), n(n(e)))) = a(a(s(s(n(e))), n(n(e))), a(s(s(n(e))), n(n(e)))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(268,plain,
% 1.22/1.39 (n(a(s(s(n(e))), n(n(e)))) = a(a(s(s(n(e))), n(n(e))), a(s(s(n(e))), n(n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[267, 24])).
% 1.22/1.39 tff(269,plain,
% 1.22/1.39 (a(a(s(s(n(e))), n(n(e))), a(s(s(n(e))), n(n(e)))) = n(a(s(s(n(e))), n(n(e))))),
% 1.22/1.39 inference(symmetry,[status(thm)],[268])).
% 1.22/1.39 tff(270,plain,
% 1.22/1.39 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(s(n(e))), n(n(e))) = u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(271,plain,
% 1.22/1.39 (a(s(s(n(e))), n(n(e))) = u(s(s(n(e))), s(n(n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[270, 39])).
% 1.22/1.39 tff(272,plain,
% 1.22/1.39 (u(s(s(n(e))), s(n(n(e)))) = a(s(s(n(e))), n(n(e)))),
% 1.22/1.39 inference(symmetry,[status(thm)],[271])).
% 1.22/1.39 tff(273,plain,
% 1.22/1.39 (a(u(s(s(n(e))), s(n(n(e)))), u(s(s(n(e))), s(n(n(e))))) = a(a(s(s(n(e))), n(n(e))), a(s(s(n(e))), n(n(e))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[272, 272])).
% 1.22/1.39 tff(274,plain,
% 1.22/1.39 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(u(s(s(n(e))), s(n(n(e)))), u(s(s(n(e))), s(n(n(e))))) = u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e)))))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(275,plain,
% 1.22/1.39 (a(u(s(s(n(e))), s(n(n(e)))), u(s(s(n(e))), s(n(n(e))))) = u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[274, 39])).
% 1.22/1.39 tff(276,plain,
% 1.22/1.39 (u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e)))))) = a(u(s(s(n(e))), s(n(n(e)))), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(symmetry,[status(thm)],[275])).
% 1.22/1.39 tff(277,plain,
% 1.22/1.39 (u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e)))))) = n(a(s(s(n(e))), n(n(e))))),
% 1.22/1.39 inference(transitivity,[status(thm)],[276, 273, 269])).
% 1.22/1.39 tff(278,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e))))))) <=> mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[277])).
% 1.22/1.39 tff(279,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))) <=> mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e)))))))),
% 1.22/1.39 inference(symmetry,[status(thm)],[278])).
% 1.22/1.39 tff(280,plain,
% 1.22/1.39 (((~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), p(s(s(n(e)))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e))))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(281,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), n(a(s(s(n(e))), n(n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[280, 188])).
% 1.22/1.39 tff(282,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e)))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[281, 279])).
% 1.22/1.39 tff(283,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e))))))) <=> (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e)))))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(u(s(s(n(e))), s(n(n(e)))), s(u(s(s(n(e))), s(n(n(e)))))))) | (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(284,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[283, 282, 266])).
% 1.22/1.39 tff(285,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e))))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(286,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[285, 284])).
% 1.22/1.39 tff(287,plain,
% 1.22/1.39 (mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[286, 264])).
% 1.22/1.39 tff(288,plain,
% 1.22/1.39 ((~(mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e)))))) <=> (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = u(s(s(n(e))), s(n(n(e))))))) | (~mem(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))), s(u(s(s(n(e))), s(n(n(e))))))) | (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(289,plain,
% 1.22/1.39 (tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))) = u(s(s(n(e))), s(n(n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[288, 287, 11])).
% 1.22/1.39 tff(290,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))) <=> mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[289])).
% 1.22/1.39 tff(291,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e))))) <=> mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))),
% 1.22/1.39 inference(symmetry,[status(thm)],[290])).
% 1.22/1.39 tff(292,assumption,(~(mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), s(s(n(e))))))), introduced(assumption)).
% 1.22/1.39 tff(293,plain,
% 1.22/1.39 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), s(s(n(e))))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(294,plain,
% 1.22/1.39 ($false),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[293, 57, 292])).
% 1.22/1.39 tff(295,plain,(mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), s(s(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.39 tff(296,plain,
% 1.22/1.39 (s(n(n(e))) = s(a(n(e), n(e)))),
% 1.22/1.39 inference(symmetry,[status(thm)],[233])).
% 1.22/1.39 tff(297,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), s(n(n(e)))) <=> mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[296])).
% 1.22/1.39 tff(298,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> mem(a(n(e), n(e)), s(n(n(e))))),
% 1.22/1.39 inference(symmetry,[status(thm)],[297])).
% 1.22/1.39 tff(299,plain,
% 1.22/1.39 (((~![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)))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(300,plain,
% 1.22/1.39 ((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))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(301,plain,
% 1.22/1.39 ((a(n(e), n(e)) = a(n(e), n(e))) <=> $true),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(302,plain,
% 1.22/1.39 ((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)),
% 1.22/1.39 inference(monotonicity,[status(thm)],[301])).
% 1.22/1.39 tff(303,plain,
% 1.22/1.39 ((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))))),
% 1.22/1.39 inference(transitivity,[status(thm)],[302, 300])).
% 1.22/1.39 tff(304,plain,
% 1.22/1.39 (((~![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)))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[303])).
% 1.22/1.39 tff(305,plain,
% 1.22/1.39 (((~![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)))))),
% 1.22/1.39 inference(transitivity,[status(thm)],[304, 299])).
% 1.22/1.39 tff(306,plain,
% 1.22/1.39 ((~![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))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(307,plain,
% 1.22/1.39 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.22/1.39 tff(308,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[307, 8])).
% 1.22/1.39 tff(309,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), s(n(n(e))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[308, 298])).
% 1.22/1.39 tff(310,plain,
% 1.22/1.39 ((mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), s(s(n(e))))) | (~mem(a(n(e), n(e)), s(n(n(e)))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(311,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), s(s(n(e))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[310, 309])).
% 1.22/1.39 tff(312,plain,
% 1.22/1.39 ((~(mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), s(s(n(e))))))) | mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e))))) | (~(mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), s(s(n(e))))))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(313,plain,
% 1.22/1.39 ((~(mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), s(s(n(e))))))) | mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[312, 311])).
% 1.22/1.39 tff(314,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[313, 295])).
% 1.22/1.39 tff(315,plain,
% 1.22/1.39 (mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[314, 291])).
% 1.22/1.39 tff(316,assumption,(~mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))), introduced(assumption)).
% 1.22/1.39 tff(317,plain,
% 1.22/1.39 ($false),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[316, 315])).
% 1.22/1.39 tff(318,plain,(mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.39 tff(319,assumption,(~(mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e))))), introduced(assumption)).
% 1.22/1.40 tff(320,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(321,plain,
% 1.22/1.40 ($false),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[320, 8, 319])).
% 1.22/1.40 tff(322,plain,(mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.40 tff(323,assumption,(a(n(e), n(e)) = s(n(e))), introduced(assumption)).
% 1.22/1.40 tff(324,plain,
% 1.22/1.40 (s(n(e)) = a(n(e), n(e))),
% 1.22/1.40 inference(symmetry,[status(thm)],[323])).
% 1.22/1.40 tff(325,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), s(a(e, e))) <=> (tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))) = a(e, e)))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(326,plain,
% 1.22/1.40 (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), s(a(e, e))) <=> (tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))) = a(e, e))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[325, 8])).
% 1.22/1.40 tff(327,assumption,(s(n(e)) = a(n(e), n(e))), introduced(assumption)).
% 1.22/1.40 tff(328,plain,
% 1.22/1.40 (s(a(e, e)) = a(n(e), n(e))),
% 1.22/1.40 inference(transitivity,[status(thm)],[82, 327])).
% 1.22/1.40 tff(329,plain,
% 1.22/1.40 (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), s(a(e, e))) <=> mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[328])).
% 1.22/1.40 tff(330,plain,
% 1.22/1.40 (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e))) <=> mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), s(a(e, e)))),
% 1.22/1.40 inference(symmetry,[status(thm)],[329])).
% 1.22/1.40 tff(331,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(tptp_fun_Y_2(s(n(e)))))))) | (~(subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))) | (~((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))))))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(332,plain,
% 1.22/1.40 (~((~((~subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(tptp_fun_Y_2(s(n(e)))))))) | (~(subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))) | (~((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e))))))))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[331, 141])).
% 1.22/1.40 tff(333,plain,
% 1.22/1.40 (((~((~subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e)))))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(tptp_fun_Y_2(s(n(e)))))))) | (~(subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))) | (~((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))))))) | (subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))) | (~((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e))))))))),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.40 tff(334,plain,
% 1.22/1.40 (subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))) | (~((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[333, 332])).
% 1.22/1.40 tff(335,plain,
% 1.22/1.40 (a(n(e), n(e)) = s(n(e))),
% 1.22/1.40 inference(symmetry,[status(thm)],[327])).
% 1.22/1.40 tff(336,plain,
% 1.22/1.40 (subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))) <=> subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[335])).
% 1.22/1.40 tff(337,plain,
% 1.22/1.40 (subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))) <=> subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e)))))),
% 1.22/1.40 inference(symmetry,[status(thm)],[336])).
% 1.22/1.40 tff(338,plain,
% 1.22/1.40 ((~subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))) <=> (~subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[337])).
% 1.22/1.40 tff(339,plain,
% 1.22/1.40 (subq(a(n(e), n(e)), p(e)) <=> subq(s(n(e)), p(e))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[335])).
% 1.22/1.40 tff(340,plain,
% 1.22/1.40 (subq(s(n(e)), p(e)) <=> subq(a(n(e), n(e)), p(e))),
% 1.22/1.40 inference(symmetry,[status(thm)],[339])).
% 1.22/1.40 tff(341,assumption,(subq(s(n(e)), p(e))), introduced(assumption)).
% 1.22/1.40 tff(342,plain,
% 1.22/1.40 (subq(a(n(e), n(e)), p(e))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[341, 340])).
% 1.22/1.40 tff(343,plain,
% 1.22/1.40 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~((~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))) | subq(a(n(e), n(e)), p(e))))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~((~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))) | subq(a(n(e), n(e)), p(e)))))))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(344,plain,
% 1.22/1.40 ((~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~(subq(a(n(e), n(e)), p(e)) | (~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))))))) <=> (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~((~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))) | subq(a(n(e), n(e)), p(e))))))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(345,plain,
% 1.22/1.40 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~(subq(a(n(e), n(e)), p(e)) | (~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e))))))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~((~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))) | subq(a(n(e), n(e)), p(e)))))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[344])).
% 1.22/1.40 tff(346,plain,
% 1.22/1.40 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~(subq(a(n(e), n(e)), p(e)) | (~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e))))))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~((~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))) | subq(a(n(e), n(e)), p(e)))))))),
% 1.22/1.40 inference(transitivity,[status(thm)],[345, 343])).
% 1.22/1.40 tff(347,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~(subq(a(n(e), n(e)), p(e)) | (~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e))))))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(348,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~((~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))) | subq(a(n(e), n(e)), p(e))))))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[347, 346])).
% 1.22/1.40 tff(349,plain,
% 1.22/1.40 (~((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~((~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))) | subq(a(n(e), n(e)), p(e)))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[348, 141])).
% 1.22/1.40 tff(350,plain,
% 1.22/1.40 (((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~((~((~mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(e), a(n(e), n(e))), p(e)))) | subq(a(n(e), n(e)), p(e))))) | ((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.40 tff(351,plain,
% 1.22/1.40 ((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e)))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[350, 349])).
% 1.22/1.40 tff(352,assumption,(![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e)))), introduced(assumption)).
% 1.22/1.40 tff(353,assumption,(~(mem(a(e, e), p(e)) <=> subq(a(e, e), e))), introduced(assumption)).
% 1.22/1.40 tff(354,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(a(e, e), p(e)) <=> subq(a(e, e), e))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(355,plain,
% 1.22/1.40 ($false),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[354, 152, 353])).
% 1.22/1.40 tff(356,plain,(mem(a(e, e), p(e)) <=> subq(a(e, e), e)), inference(lemma,lemma(discharge,[]))).
% 1.22/1.40 tff(357,assumption,((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e)))), introduced(assumption)).
% 1.22/1.40 tff(358,plain,
% 1.22/1.40 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e)))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e))))))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(359,plain,
% 1.22/1.40 ((~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~(subq(a(e, e), e) | (~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))))))) <=> (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e)))))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(360,plain,
% 1.22/1.40 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~(subq(a(e, e), e) | (~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e)))))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e))))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[359])).
% 1.22/1.40 tff(361,plain,
% 1.22/1.40 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~(subq(a(e, e), e) | (~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e)))))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e))))))),
% 1.22/1.40 inference(transitivity,[status(thm)],[360, 358])).
% 1.22/1.40 tff(362,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~(subq(a(e, e), e) | (~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e)))))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(363,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e)))))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.22/1.40 tff(364,plain,
% 1.22/1.40 ($false),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[363, 141, 357])).
% 1.22/1.40 tff(365,plain,(~((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.40 tff(366,plain,
% 1.22/1.40 (((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~((~((~mem(tptp_fun_Z_0(e, a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(e, a(e, e)), e))) | subq(a(e, e), e)))) | ((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.40 tff(367,plain,
% 1.22/1.40 ((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[366, 365])).
% 1.22/1.40 tff(368,assumption,(![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e))), introduced(assumption)).
% 1.22/1.40 tff(369,plain,
% 1.22/1.40 ((~![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, u(s(s(n(e))), s(n(n(e)))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e)))))))) | (~(subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e)))))))))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(370,plain,
% 1.22/1.40 (~((~((~subq(e, u(s(s(n(e))), s(n(n(e)))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e)))))))) | (~(subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e))))))))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[369, 141])).
% 1.22/1.40 tff(371,plain,
% 1.22/1.40 (((~((~subq(e, u(s(s(n(e))), s(n(n(e)))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e)))))))) | (~(subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e)))))))))) | ((~subq(e, u(s(s(n(e))), s(n(n(e)))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e)))))))),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.40 tff(372,plain,
% 1.22/1.40 ((~subq(e, u(s(s(n(e))), s(n(n(e)))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[371, 370])).
% 1.22/1.40 tff(373,plain,
% 1.22/1.40 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(e, p(u(s(s(n(e))), s(n(n(e)))))) <=> subq(e, u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(374,plain,
% 1.22/1.40 (mem(e, p(u(s(s(n(e))), s(n(n(e)))))) <=> subq(e, u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[373, 152])).
% 1.22/1.40 tff(375,plain,
% 1.22/1.40 (u(s(s(n(e))), s(n(n(e)))) = tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))),
% 1.22/1.40 inference(symmetry,[status(thm)],[289])).
% 1.22/1.40 tff(376,plain,
% 1.22/1.40 (p(u(s(s(n(e))), s(n(n(e))))) = p(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[375])).
% 1.22/1.40 tff(377,plain,
% 1.22/1.40 (mem(e, p(u(s(s(n(e))), s(n(n(e)))))) <=> mem(e, p(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[376])).
% 1.22/1.40 tff(378,plain,
% 1.22/1.40 (mem(e, p(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) <=> mem(e, p(u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.40 inference(symmetry,[status(thm)],[377])).
% 1.22/1.40 tff(379,plain,
% 1.22/1.40 ((~mem(e, p(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))))) <=> (~mem(e, p(u(s(s(n(e))), s(n(n(e)))))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[378])).
% 1.22/1.40 tff(380,assumption,(~mem(e, p(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))))), introduced(assumption)).
% 1.22/1.40 tff(381,plain,
% 1.22/1.40 (~mem(e, p(u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[380, 379])).
% 1.22/1.40 tff(382,plain,
% 1.22/1.40 ((~(mem(e, p(u(s(s(n(e))), s(n(n(e)))))) <=> subq(e, u(s(s(n(e))), s(n(n(e))))))) | mem(e, p(u(s(s(n(e))), s(n(n(e)))))) | (~subq(e, u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.40 tff(383,plain,
% 1.22/1.40 (~subq(e, u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[382, 381, 374])).
% 1.22/1.40 tff(384,plain,
% 1.22/1.40 (((~((~subq(e, u(s(s(n(e))), s(n(n(e)))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e)))))))) | (~(subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e)))))))))) | (subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e))))))))),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.40 tff(385,plain,
% 1.22/1.40 (subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e)))))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[384, 370])).
% 1.22/1.40 tff(386,assumption,(mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)), introduced(assumption)).
% 1.22/1.40 tff(387,plain,
% 1.22/1.40 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(388,plain,
% 1.22/1.40 ($false),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[387, 111, 386])).
% 1.22/1.40 tff(389,plain,(~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)), inference(lemma,lemma(discharge,[]))).
% 1.22/1.40 tff(390,plain,
% 1.22/1.40 (((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e)))))) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.40 tff(391,plain,
% 1.22/1.40 ((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[390, 389])).
% 1.22/1.40 tff(392,plain,
% 1.22/1.40 ((~(subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e))))))))) | subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e)))))))),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(393,plain,
% 1.22/1.41 ((~(subq(e, u(s(s(n(e))), s(n(n(e))))) | (~((~mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), e)) | mem(tptp_fun_Z_0(u(s(s(n(e))), s(n(n(e)))), e), u(s(s(n(e))), s(n(n(e))))))))) | subq(e, u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[392, 391])).
% 1.22/1.41 tff(394,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[393, 385, 383])).
% 1.22/1.41 tff(395,plain,(mem(e, p(tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(396,plain,
% 1.22/1.41 (mem(e, p(u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[395, 378])).
% 1.22/1.41 tff(397,plain,
% 1.22/1.41 ((~(mem(e, p(u(s(s(n(e))), s(n(n(e)))))) <=> subq(e, u(s(s(n(e))), s(n(n(e))))))) | (~mem(e, p(u(s(s(n(e))), s(n(n(e))))))) | subq(e, u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(398,plain,
% 1.22/1.41 (subq(e, u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[397, 396, 374])).
% 1.22/1.41 tff(399,plain,
% 1.22/1.41 ((~((~subq(e, u(s(s(n(e))), s(n(n(e)))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e)))))))) | (~subq(e, u(s(s(n(e))), s(n(n(e)))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(400,plain,
% 1.22/1.41 (![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[399, 398, 372])).
% 1.22/1.41 tff(401,plain,
% 1.22/1.41 (mem(e, u(s(s(n(e))), s(n(n(e))))) <=> mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[375])).
% 1.22/1.41 tff(402,plain,
% 1.22/1.41 (mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e)))))) <=> mem(e, u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.41 inference(symmetry,[status(thm)],[401])).
% 1.22/1.41 tff(403,plain,
% 1.22/1.41 ((~mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) <=> (~mem(e, u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[402])).
% 1.22/1.41 tff(404,assumption,(mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))), introduced(assumption)).
% 1.22/1.41 tff(405,plain,
% 1.22/1.41 (((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | ((~mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(e, s(s(n(e)))))) <=> ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | (~mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(e, s(s(n(e)))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(406,plain,
% 1.22/1.41 ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | ((~mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(e, s(s(n(e)))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(407,plain,
% 1.22/1.41 ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | (~mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(e, s(s(n(e))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[406, 405])).
% 1.22/1.41 tff(408,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[407, 196, 118, 404])).
% 1.22/1.41 tff(409,plain,(~mem(e, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(410,plain,
% 1.22/1.41 (~mem(e, u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[409, 403])).
% 1.22/1.41 tff(411,plain,
% 1.22/1.41 (((~![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e))))))) | ((~mem(e, e)) | mem(e, u(s(s(n(e))), s(n(n(e))))))) <=> ((~![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e))))))) | (~mem(e, e)) | mem(e, u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(412,plain,
% 1.22/1.41 ((~![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e))))))) | ((~mem(e, e)) | mem(e, u(s(s(n(e))), s(n(n(e))))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(413,plain,
% 1.22/1.41 ((~![Z: $i] : ((~mem(Z, e)) | mem(Z, u(s(s(n(e))), s(n(n(e))))))) | (~mem(e, e)) | mem(e, u(s(s(n(e))), s(n(n(e)))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.22/1.41 tff(414,plain,
% 1.22/1.41 (~mem(e, e)),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[413, 410, 400])).
% 1.22/1.41 tff(415,plain,
% 1.22/1.41 (((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e))) | ((~mem(e, a(e, e))) | mem(e, e))) <=> ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e))) | (~mem(e, a(e, e))) | mem(e, e))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(416,plain,
% 1.22/1.41 ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e))) | ((~mem(e, a(e, e))) | mem(e, e))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(417,plain,
% 1.22/1.41 ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e))) | (~mem(e, a(e, e))) | mem(e, e)),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[416, 415])).
% 1.22/1.41 tff(418,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[417, 76, 414, 368])).
% 1.22/1.41 tff(419,plain,(~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(420,plain,
% 1.22/1.41 ((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(421,plain,
% 1.22/1.41 ((~((~subq(a(e, e), e)) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, e)))) | (~subq(a(e, e), e))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[420, 419])).
% 1.22/1.41 tff(422,plain,
% 1.22/1.41 (~subq(a(e, e), e)),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[421, 367])).
% 1.22/1.41 tff(423,plain,
% 1.22/1.41 ((~(mem(a(e, e), p(e)) <=> subq(a(e, e), e))) | (~mem(a(e, e), p(e))) | subq(a(e, e), e)),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(424,plain,
% 1.22/1.41 ((~(mem(a(e, e), p(e)) <=> subq(a(e, e), e))) | (~mem(a(e, e), p(e)))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[423, 422])).
% 1.22/1.41 tff(425,plain,
% 1.22/1.41 (~mem(a(e, e), p(e))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[424, 356])).
% 1.22/1.41 tff(426,plain,
% 1.22/1.41 (u(a(e, e), s(n(e))) = a(n(e), n(e))),
% 1.22/1.41 inference(transitivity,[status(thm)],[214, 212, 209])).
% 1.22/1.41 tff(427,plain,
% 1.22/1.41 (mem(a(e, e), u(a(e, e), s(n(e)))) <=> mem(a(e, e), a(n(e), n(e)))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[426])).
% 1.22/1.41 tff(428,plain,
% 1.22/1.41 (mem(a(e, e), a(n(e), n(e))) <=> mem(a(e, e), u(a(e, e), s(n(e))))),
% 1.22/1.41 inference(symmetry,[status(thm)],[427])).
% 1.22/1.41 tff(429,plain,
% 1.22/1.41 ((~mem(a(e, e), a(n(e), n(e)))) <=> (~mem(a(e, e), u(a(e, e), s(n(e)))))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[428])).
% 1.22/1.41 tff(430,assumption,(~mem(a(e, e), a(n(e), n(e)))), introduced(assumption)).
% 1.22/1.41 tff(431,plain,
% 1.22/1.41 (~mem(a(e, e), u(a(e, e), s(n(e))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[430, 429])).
% 1.22/1.41 tff(432,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[226, 431])).
% 1.22/1.41 tff(433,plain,(mem(a(e, e), a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(434,plain,
% 1.22/1.41 (((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e)))) | ((~mem(a(e, e), a(n(e), n(e)))) | mem(a(e, e), p(e)))) <=> ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e)))) | (~mem(a(e, e), a(n(e), n(e)))) | mem(a(e, e), p(e)))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(435,plain,
% 1.22/1.41 ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e)))) | ((~mem(a(e, e), a(n(e), n(e)))) | mem(a(e, e), p(e)))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(436,plain,
% 1.22/1.41 ((~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e)))) | (~mem(a(e, e), a(n(e), n(e)))) | mem(a(e, e), p(e))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[435, 434])).
% 1.22/1.41 tff(437,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[436, 433, 425, 352])).
% 1.22/1.41 tff(438,plain,(~![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(439,plain,
% 1.22/1.41 ((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e)))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(440,plain,
% 1.22/1.41 ((~((~subq(a(n(e), n(e)), p(e))) | ![Z: $i] : ((~mem(Z, a(n(e), n(e)))) | mem(Z, p(e))))) | (~subq(a(n(e), n(e)), p(e)))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[439, 438])).
% 1.22/1.41 tff(441,plain,
% 1.22/1.41 (~subq(a(n(e), n(e)), p(e))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[440, 351])).
% 1.22/1.41 tff(442,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[441, 342])).
% 1.22/1.41 tff(443,plain,((~subq(s(n(e)), p(e))) | (~(s(n(e)) = a(n(e), n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(444,plain,
% 1.22/1.41 (~subq(s(n(e)), p(e))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[443, 327])).
% 1.22/1.41 tff(445,plain,
% 1.22/1.41 (a(n(e), n(e)) = s(a(e, e))),
% 1.22/1.41 inference(transitivity,[status(thm)],[335, 213])).
% 1.22/1.41 tff(446,plain,
% 1.22/1.41 (u(a(e, e), a(n(e), n(e))) = u(a(e, e), s(a(e, e)))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[445])).
% 1.22/1.41 tff(447,plain,
% 1.22/1.41 (u(a(e, e), a(n(e), n(e))) = s(n(e))),
% 1.22/1.41 inference(transitivity,[status(thm)],[446, 212, 209, 335])).
% 1.22/1.41 tff(448,plain,
% 1.22/1.41 (mem(e, u(a(e, e), a(n(e), n(e)))) <=> mem(e, s(n(e)))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[447])).
% 1.22/1.41 tff(449,plain,
% 1.22/1.41 (mem(e, s(n(e))) <=> mem(e, u(a(e, e), a(n(e), n(e))))),
% 1.22/1.41 inference(symmetry,[status(thm)],[448])).
% 1.22/1.41 tff(450,plain,
% 1.22/1.41 ((~mem(e, s(n(e)))) <=> (~mem(e, u(a(e, e), a(n(e), n(e)))))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[449])).
% 1.22/1.41 tff(451,assumption,(~mem(e, s(n(e)))), introduced(assumption)).
% 1.22/1.41 tff(452,plain,
% 1.22/1.41 (~mem(e, u(a(e, e), a(n(e), n(e))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[451, 450])).
% 1.22/1.41 tff(453,plain,
% 1.22/1.41 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), 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), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), n(e))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(454,plain,
% 1.22/1.41 ((mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(n(e), n(e))) | mem(e, a(e, e)))) <=> (mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), n(e)))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(455,plain,
% 1.22/1.41 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(n(e), 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), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), n(e))))))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[454])).
% 1.22/1.41 tff(456,plain,
% 1.22/1.41 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(n(e), 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), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), n(e))))))),
% 1.22/1.41 inference(transitivity,[status(thm)],[455, 453])).
% 1.22/1.41 tff(457,plain,
% 1.22/1.41 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(n(e), n(e))) | mem(e, a(e, e))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(458,plain,
% 1.22/1.41 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), n(e)))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[457, 456])).
% 1.22/1.41 tff(459,plain,
% 1.22/1.41 (mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), n(e))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[458, 57])).
% 1.22/1.41 tff(460,plain,
% 1.22/1.41 ((mem(e, a(e, e)) | mem(e, a(n(e), n(e)))) | (~mem(e, a(e, e)))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(461,plain,
% 1.22/1.41 (mem(e, a(e, e)) | mem(e, a(n(e), n(e)))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[460, 76])).
% 1.22/1.41 tff(462,plain,
% 1.22/1.41 ((~(mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), n(e)))))) | mem(e, u(a(e, e), a(n(e), n(e)))) | (~(mem(e, a(e, e)) | mem(e, a(n(e), n(e)))))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(463,plain,
% 1.22/1.41 ((~(mem(e, u(a(e, e), a(n(e), n(e)))) <=> (mem(e, a(e, e)) | mem(e, a(n(e), n(e)))))) | mem(e, u(a(e, e), a(n(e), n(e))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[462, 461])).
% 1.22/1.41 tff(464,plain,
% 1.22/1.41 (mem(e, u(a(e, e), a(n(e), n(e))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[463, 459])).
% 1.22/1.41 tff(465,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[464, 452])).
% 1.22/1.41 tff(466,plain,(mem(e, s(n(e))) | (~(s(n(e)) = a(n(e), n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(467,plain,
% 1.22/1.41 (mem(e, s(n(e)))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[466, 327])).
% 1.22/1.41 tff(468,assumption,(~subq(s(n(e)), p(e))), introduced(assumption)).
% 1.22/1.41 tff(469,assumption,(mem(e, s(n(e)))), introduced(assumption)).
% 1.22/1.41 tff(470,assumption,(![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))), introduced(assumption)).
% 1.22/1.41 tff(471,plain,
% 1.22/1.41 (((~![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))) | ((~mem(e, s(n(e)))) | subq(s(n(e)), p(e)))) <=> ((~![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))) | (~mem(e, s(n(e)))) | subq(s(n(e)), p(e)))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(472,plain,
% 1.22/1.41 ((~![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))) | ((~mem(e, s(n(e)))) | subq(s(n(e)), p(e)))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(473,plain,
% 1.22/1.41 ((~![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))) | (~mem(e, s(n(e)))) | subq(s(n(e)), p(e))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.22/1.41 tff(474,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[473, 470, 469, 468])).
% 1.22/1.41 tff(475,plain,((~![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))) | (~mem(e, s(n(e)))) | subq(s(n(e)), p(e))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(476,plain,
% 1.22/1.41 (~![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[475, 467, 444])).
% 1.22/1.41 tff(477,plain,
% 1.22/1.41 (^[X: $i] : refl((~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))))) <=> (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))))))),
% 1.22/1.41 inference(bind,[status(th)],[])).
% 1.22/1.41 tff(478,plain,
% 1.22/1.41 (![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))))) <=> ![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))),
% 1.22/1.41 inference(quant_intro,[status(thm)],[477])).
% 1.22/1.41 tff(479,plain,
% 1.22/1.41 (^[X: $i] : rewrite((~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))))) <=> (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))))))),
% 1.22/1.41 inference(bind,[status(th)],[])).
% 1.22/1.41 tff(480,plain,
% 1.22/1.41 (![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))))) <=> ![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))),
% 1.22/1.41 inference(quant_intro,[status(thm)],[479])).
% 1.22/1.41 tff(481,plain,
% 1.22/1.41 (![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))))) <=> ![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))),
% 1.22/1.41 inference(transitivity,[status(thm)],[480, 478])).
% 1.22/1.41 tff(482,plain,
% 1.22/1.41 (^[X: $i] : trans(monotonicity(rewrite(((~atleast2p(X)) | (mem(tptp_fun_Y_2(X), X) & (~subq(X, p(tptp_fun_Y_2(X)))))) <=> ((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))), rewrite((atleast2p(X) | ![Y: $i] : (~(mem(Y, X) & (~subq(X, p(Y)))))) <=> (atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))), ((((~atleast2p(X)) | (mem(tptp_fun_Y_2(X), X) & (~subq(X, p(tptp_fun_Y_2(X)))))) & (atleast2p(X) | ![Y: $i] : (~(mem(Y, X) & (~subq(X, p(Y))))))) <=> (((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X)))))) & (atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))))), rewrite((((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X)))))) & (atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y))))) <=> (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))), ((((~atleast2p(X)) | (mem(tptp_fun_Y_2(X), X) & (~subq(X, p(tptp_fun_Y_2(X)))))) & (atleast2p(X) | ![Y: $i] : (~(mem(Y, X) & (~subq(X, p(Y))))))) <=> (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))))),
% 1.22/1.41 inference(bind,[status(th)],[])).
% 1.22/1.41 tff(483,plain,
% 1.22/1.41 (![X: $i] : (((~atleast2p(X)) | (mem(tptp_fun_Y_2(X), X) & (~subq(X, p(tptp_fun_Y_2(X)))))) & (atleast2p(X) | ![Y: $i] : (~(mem(Y, X) & (~subq(X, p(Y))))))) <=> ![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))),
% 1.22/1.41 inference(quant_intro,[status(thm)],[482])).
% 1.22/1.41 tff(484,plain,
% 1.22/1.41 (![X: $i] : (atleast2p(X) <=> ?[Y: $i] : (mem(Y, X) & (~subq(X, p(Y))))) <=> ![X: $i] : (atleast2p(X) <=> ?[Y: $i] : (mem(Y, X) & (~subq(X, p(Y)))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(485,axiom,(![X: $i] : (atleast2p(X) <=> ?[Y: $i] : (mem(Y, X) & (~subq(X, p(Y)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax','atleast2p_def')).
% 1.22/1.41 tff(486,plain,
% 1.22/1.41 (![X: $i] : (atleast2p(X) <=> ?[Y: $i] : (mem(Y, X) & (~subq(X, p(Y)))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.22/1.41 tff(487,plain,(
% 1.22/1.41 ![X: $i] : (((~atleast2p(X)) | (mem(tptp_fun_Y_2(X), X) & (~subq(X, p(tptp_fun_Y_2(X)))))) & (atleast2p(X) | ![Y: $i] : (~(mem(Y, X) & (~subq(X, p(Y)))))))),
% 1.22/1.41 inference(skolemize,[status(sab)],[486])).
% 1.22/1.41 tff(488,plain,
% 1.22/1.41 (![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[487, 483])).
% 1.22/1.41 tff(489,plain,
% 1.22/1.41 (![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[488, 481])).
% 1.22/1.41 tff(490,plain,
% 1.22/1.41 (((~![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))) | (~((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))))))))) <=> ((~![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))) | (~((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(491,plain,
% 1.22/1.41 ((~((~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))) | (~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))))) <=> (~((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(492,plain,
% 1.22/1.41 (((~![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))) | (~((~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))) | (~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))))))) <=> ((~![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))) | (~((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))))))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[491])).
% 1.22/1.41 tff(493,plain,
% 1.22/1.41 (((~![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))) | (~((~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))) | (~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))))))) <=> ((~![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))) | (~((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))))))),
% 1.22/1.41 inference(transitivity,[status(thm)],[492, 490])).
% 1.22/1.41 tff(494,plain,
% 1.22/1.41 ((~![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))) | (~((~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))) | (~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(495,plain,
% 1.22/1.41 ((~![X: $i] : (~((~((~atleast2p(X)) | (~((~mem(tptp_fun_Y_2(X), X)) | subq(X, p(tptp_fun_Y_2(X))))))) | (~(atleast2p(X) | ![Y: $i] : ((~mem(Y, X)) | subq(X, p(Y)))))))) | (~((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[494, 493])).
% 1.22/1.41 tff(496,plain,
% 1.22/1.41 (~((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[495, 489])).
% 1.22/1.41 tff(497,plain,
% 1.22/1.41 (((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))))))) | (atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(498,plain,
% 1.22/1.41 (atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[497, 496])).
% 1.22/1.41 tff(499,plain,
% 1.22/1.41 ((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(500,plain,
% 1.22/1.41 (atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y)))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[499, 498])).
% 1.22/1.41 tff(501,plain,
% 1.22/1.41 (atleast2p(s(n(e)))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[500, 476])).
% 1.22/1.41 tff(502,plain,
% 1.22/1.41 (((~(atleast2p(s(n(e))) | ![Y: $i] : ((~mem(Y, s(n(e)))) | subq(s(n(e)), p(Y))))) | (~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))))))) | ((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(503,plain,
% 1.22/1.41 ((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[502, 496])).
% 1.22/1.41 tff(504,plain,
% 1.22/1.41 ((~((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))))) | (~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(505,plain,
% 1.22/1.41 ((~atleast2p(s(n(e)))) | (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[504, 503])).
% 1.22/1.41 tff(506,plain,
% 1.22/1.41 (~((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[505, 501])).
% 1.22/1.41 tff(507,plain,
% 1.22/1.41 (((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))) | (~subq(s(n(e)), p(tptp_fun_Y_2(s(n(e))))))),
% 1.22/1.41 inference(tautology,[status(thm)],[])).
% 1.22/1.41 tff(508,plain,
% 1.22/1.41 (~subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[507, 506])).
% 1.22/1.41 tff(509,plain,
% 1.22/1.41 (~subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e)))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[508, 338])).
% 1.22/1.41 tff(510,plain,
% 1.22/1.41 ((~(subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))) | (~((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e))))))))) | subq(a(n(e), n(e)), p(tptp_fun_Y_2(s(n(e))))) | (~((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(511,plain,
% 1.22/1.42 (~((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e))))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[510, 509, 334])).
% 1.22/1.42 tff(512,plain,
% 1.22/1.42 (((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(513,plain,
% 1.22/1.42 (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[512, 511])).
% 1.22/1.42 tff(514,plain,
% 1.22/1.42 (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), s(a(e, e)))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[513, 330])).
% 1.22/1.42 tff(515,plain,
% 1.22/1.42 ((~(mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), s(a(e, e))) <=> (tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))) = a(e, e)))) | (~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), s(a(e, e)))) | (tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))) = a(e, e))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(516,plain,
% 1.22/1.42 (tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))) = a(e, e)),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[515, 514, 326])).
% 1.22/1.42 tff(517,plain,
% 1.22/1.42 (mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))) <=> mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[516])).
% 1.22/1.42 tff(518,plain,
% 1.22/1.42 (mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e)) <=> mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))),
% 1.22/1.42 inference(symmetry,[status(thm)],[517])).
% 1.22/1.42 tff(519,plain,
% 1.22/1.42 ((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))) <=> (~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[518])).
% 1.22/1.42 tff(520,plain,
% 1.22/1.42 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(Z, a(e, e))))) | (~(subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)) | (~((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))))))))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(521,plain,
% 1.22/1.42 (~((~((~subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(Z, a(e, e))))) | (~(subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)) | (~((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e)))))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[520, 141])).
% 1.22/1.42 tff(522,plain,
% 1.22/1.42 (((~((~subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e))) | ![Z: $i] : ((~mem(Z, tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(Z, a(e, e))))) | (~(subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)) | (~((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))))))) | (subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)) | (~((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e)))))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(523,plain,
% 1.22/1.42 (subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)) | (~((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[522, 521])).
% 1.22/1.42 tff(524,plain,
% 1.22/1.42 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(a(e, e))) <=> subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(525,plain,
% 1.22/1.42 (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(a(e, e))) <=> subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[524, 152])).
% 1.22/1.42 tff(526,plain,
% 1.22/1.42 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Y_2(s(n(e))), s(a(e, e))) <=> (tptp_fun_Y_2(s(n(e))) = a(e, e)))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(527,plain,
% 1.22/1.42 (mem(tptp_fun_Y_2(s(n(e))), s(a(e, e))) <=> (tptp_fun_Y_2(s(n(e))) = a(e, e))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[526, 8])).
% 1.22/1.42 tff(528,plain,
% 1.22/1.42 (mem(tptp_fun_Y_2(s(n(e))), s(a(e, e))) <=> mem(tptp_fun_Y_2(s(n(e))), s(n(e)))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[82])).
% 1.22/1.42 tff(529,plain,
% 1.22/1.42 (mem(tptp_fun_Y_2(s(n(e))), s(n(e))) <=> mem(tptp_fun_Y_2(s(n(e))), s(a(e, e)))),
% 1.22/1.42 inference(symmetry,[status(thm)],[528])).
% 1.22/1.42 tff(530,plain,
% 1.22/1.42 (((~mem(tptp_fun_Y_2(s(n(e))), s(n(e)))) | subq(s(n(e)), p(tptp_fun_Y_2(s(n(e)))))) | mem(tptp_fun_Y_2(s(n(e))), s(n(e)))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(531,plain,
% 1.22/1.42 (mem(tptp_fun_Y_2(s(n(e))), s(n(e)))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[530, 506])).
% 1.22/1.42 tff(532,plain,
% 1.22/1.42 (mem(tptp_fun_Y_2(s(n(e))), s(a(e, e)))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[531, 529])).
% 1.22/1.42 tff(533,plain,
% 1.22/1.42 ((~(mem(tptp_fun_Y_2(s(n(e))), s(a(e, e))) <=> (tptp_fun_Y_2(s(n(e))) = a(e, e)))) | (~mem(tptp_fun_Y_2(s(n(e))), s(a(e, e)))) | (tptp_fun_Y_2(s(n(e))) = a(e, e))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(534,plain,
% 1.22/1.42 (tptp_fun_Y_2(s(n(e))) = a(e, e)),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[533, 532, 527])).
% 1.22/1.42 tff(535,plain,
% 1.22/1.42 (p(tptp_fun_Y_2(s(n(e)))) = p(a(e, e))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[534])).
% 1.22/1.42 tff(536,plain,
% 1.22/1.42 (p(a(e, e)) = p(tptp_fun_Y_2(s(n(e))))),
% 1.22/1.42 inference(symmetry,[status(thm)],[535])).
% 1.22/1.42 tff(537,plain,
% 1.22/1.42 (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(a(e, e))) <=> mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[536])).
% 1.22/1.42 tff(538,plain,
% 1.22/1.42 (mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e))))) <=> mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(a(e, e)))),
% 1.22/1.42 inference(symmetry,[status(thm)],[537])).
% 1.22/1.42 tff(539,plain,
% 1.22/1.42 ((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))) <=> (~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(a(e, e))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[538])).
% 1.22/1.42 tff(540,plain,
% 1.22/1.42 (((~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(n(e), n(e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))) | (~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e))))))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(541,plain,
% 1.22/1.42 (~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(tptp_fun_Y_2(s(n(e)))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[540, 511])).
% 1.22/1.42 tff(542,plain,
% 1.22/1.42 (~mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(a(e, e)))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[541, 539])).
% 1.22/1.42 tff(543,plain,
% 1.22/1.42 ((~(mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(a(e, e))) <=> subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)))) | mem(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), p(a(e, e))) | (~subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(544,plain,
% 1.22/1.42 (~subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[543, 542, 525])).
% 1.22/1.42 tff(545,plain,
% 1.22/1.42 ((~(subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)) | (~((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e)))))) | subq(tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))), a(e, e)) | (~((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(546,plain,
% 1.22/1.42 (~((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e)))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[545, 544, 523])).
% 1.22/1.42 tff(547,plain,
% 1.22/1.42 (((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))) | (~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e)))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(548,plain,
% 1.22/1.42 (~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[547, 546])).
% 1.22/1.42 tff(549,plain,
% 1.22/1.42 (~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[548, 519])).
% 1.22/1.42 tff(550,plain,
% 1.22/1.42 (((~mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), a(e, e))) | mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(551,plain,
% 1.22/1.42 (mem(tptp_fun_Z_0(a(e, e), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e)))), tptp_fun_Z_0(p(tptp_fun_Y_2(s(n(e)))), a(n(e), n(e))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[550, 546])).
% 1.22/1.42 tff(552,plain,
% 1.22/1.42 ($false),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[551, 549])).
% 1.22/1.42 tff(553,plain,(~(s(n(e)) = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.42 tff(554,plain,
% 1.22/1.42 ($false),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[553, 324])).
% 1.22/1.42 tff(555,plain,(~(a(n(e), n(e)) = s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.42 tff(556,plain,
% 1.22/1.42 ((~(mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e))))) | (~mem(a(n(e), n(e)), s(s(n(e))))) | (a(n(e), n(e)) = s(n(e)))),
% 1.22/1.42 inference(tautology,[status(thm)],[])).
% 1.22/1.42 tff(557,plain,
% 1.22/1.42 ((~(mem(a(n(e), n(e)), s(s(n(e)))) <=> (a(n(e), n(e)) = s(n(e))))) | (~mem(a(n(e), n(e)), s(s(n(e)))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[556, 555])).
% 1.22/1.42 tff(558,plain,
% 1.22/1.42 (~mem(a(n(e), n(e)), s(s(n(e))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[557, 322])).
% 1.22/1.42 tff(559,plain,
% 1.22/1.42 (((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | ((~mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(a(n(e), n(e)), s(s(n(e)))))) <=> ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | (~mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(a(n(e), n(e)), s(s(n(e)))))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(560,plain,
% 1.22/1.42 ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | ((~mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(a(n(e), n(e)), s(s(n(e)))))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(561,plain,
% 1.22/1.42 ((~![Z: $i] : ((~mem(Z, tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(Z, s(s(n(e)))))) | (~mem(a(n(e), n(e)), tptp_fun_Z_1(n(a(s(s(n(e))), n(n(e)))), p(s(s(n(e))))))) | mem(a(n(e), n(e)), s(s(n(e))))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[560, 559])).
% 1.22/1.42 tff(562,plain,
% 1.22/1.42 ($false),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[561, 196, 558, 318])).
% 1.22/1.42 % SZS output end Proof
% 1.22/1.42 % E exiting
%------------------------------------------------------------------------------