%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV538+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:22 AM UTC 2025
% Result : Theorem 1.21s 1.38s
% Output : Proof 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV538+1 : TPTP v9.1.0. Released v9.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 07:42:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.21/1.38 % SZS status Theorem
% 1.21/1.38 % SZS output start Proof
% 1.21/1.38 tff(mem_type, type, (
% 1.21/1.38 mem: ( $i * $i ) > $o)).
% 1.21/1.38 tff(e_type, type, (
% 1.21/1.38 e: $i)).
% 1.21/1.38 tff(s_type, type, (
% 1.21/1.38 s: $i > $i)).
% 1.21/1.38 tff(n_type, type, (
% 1.21/1.38 n: $i > $i)).
% 1.21/1.38 tff(subq_type, type, (
% 1.21/1.38 subq: ( $i * $i ) > $o)).
% 1.21/1.38 tff(tptp_fun_Z_0_type, type, (
% 1.21/1.38 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 1.21/1.38 tff(p_type, type, (
% 1.21/1.38 p: $i > $i)).
% 1.21/1.38 tff(u_type, type, (
% 1.21/1.38 u: ( $i * $i ) > $i)).
% 1.21/1.38 tff(atleast2p_type, type, (
% 1.21/1.38 atleast2p: $i > $o)).
% 1.21/1.38 tff(a_type, type, (
% 1.21/1.38 a: ( $i * $i ) > $i)).
% 1.21/1.38 tff(disj_type, type, (
% 1.21/1.38 disj: ( $i * $i ) > $o)).
% 1.21/1.38 tff(tptp_fun_Z_1_type, type, (
% 1.21/1.38 tptp_fun_Z_1: ( $i * $i ) > $i)).
% 1.21/1.38 tff(atleast3p_type, type, (
% 1.21/1.38 atleast3p: $i > $o)).
% 1.21/1.38 tff(tptp_fun_Y_3_type, type, (
% 1.21/1.38 tptp_fun_Y_3: $i > $i)).
% 1.21/1.38 tff(tptp_fun_Y_2_type, type, (
% 1.21/1.38 tptp_fun_Y_2: $i > $i)).
% 1.21/1.38 tff(1,plain,
% 1.21/1.38 (^[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))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(2,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[1])).
% 1.21/1.38 tff(3,plain,
% 1.21/1.38 (^[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))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(4,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[3])).
% 1.21/1.38 tff(5,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[4, 2])).
% 1.21/1.38 tff(6,plain,
% 1.21/1.38 (^[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)))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(7,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[6])).
% 1.21/1.38 tff(8,plain,
% 1.21/1.38 (![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)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(9,plain,
% 1.21/1.38 (^[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))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(10,plain,
% 1.21/1.38 (![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)))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[9])).
% 1.21/1.38 tff(11,axiom,(![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : (mem(Z, X) => mem(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','subq_def')).
% 1.21/1.38 tff(12,plain,
% 1.21/1.38 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.21/1.38 tff(13,plain,
% 1.21/1.38 (![X: $i, Y: $i] : (subq(X, Y) <=> ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.21/1.38 tff(14,plain,(
% 1.21/1.38 ![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)))))),
% 1.21/1.38 inference(skolemize,[status(sab)],[13])).
% 1.21/1.38 tff(15,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.21/1.38 tff(16,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.21/1.38 tff(17,plain,
% 1.21/1.38 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(s(n(n(e))), e)) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e)))) | (~(subq(s(n(n(e))), e) | (~((~mem(tptp_fun_Z_0(e, s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(e, s(n(n(e)))), e)))))))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(18,plain,
% 1.21/1.38 (~((~((~subq(s(n(n(e))), e)) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e)))) | (~(subq(s(n(n(e))), e) | (~((~mem(tptp_fun_Z_0(e, s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(e, s(n(n(e)))), e))))))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.21/1.38 tff(19,plain,
% 1.21/1.38 (((~((~subq(s(n(n(e))), e)) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e)))) | (~(subq(s(n(n(e))), e) | (~((~mem(tptp_fun_Z_0(e, s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(e, s(n(n(e)))), e)))))) | ((~subq(s(n(n(e))), e)) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e)))),
% 1.21/1.38 inference(tautology,[status(thm)],[])).
% 1.21/1.38 tff(20,plain,
% 1.21/1.38 ((~subq(s(n(n(e))), e)) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.21/1.38 tff(21,plain,
% 1.21/1.38 (^[X: $i, Y: $i] : refl((mem(X, p(Y)) <=> subq(X, Y)) <=> (mem(X, p(Y)) <=> subq(X, Y)))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(22,plain,
% 1.21/1.38 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y)) <=> ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[21])).
% 1.21/1.38 tff(23,plain,
% 1.21/1.38 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y)) <=> ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(24,axiom,(![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','p_ax')).
% 1.21/1.38 tff(25,plain,
% 1.21/1.38 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.21/1.38 tff(26,plain,(
% 1.21/1.38 ![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.21/1.38 inference(skolemize,[status(sab)],[25])).
% 1.21/1.38 tff(27,plain,
% 1.21/1.38 (![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 1.21/1.38 tff(28,plain,
% 1.21/1.38 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(s(n(n(e))), p(e)) <=> subq(s(n(n(e))), e))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(29,plain,
% 1.21/1.38 (mem(s(n(n(e))), p(e)) <=> subq(s(n(n(e))), e)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 1.21/1.38 tff(30,assumption,(~mem(s(n(n(e))), p(e))), introduced(assumption)).
% 1.21/1.38 tff(31,plain,
% 1.21/1.38 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e))))) | (~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e)) | (~((~mem(tptp_fun_Z_0(p(e), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(p(e), u(p(s(n(n(e)))), s(n(n(n(e)))))), p(e))))))))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(32,plain,
% 1.21/1.38 (~((~((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e))))) | (~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e)) | (~((~mem(tptp_fun_Z_0(p(e), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(p(e), u(p(s(n(n(e)))), s(n(n(n(e)))))), p(e)))))))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[31, 16])).
% 1.21/1.38 tff(33,plain,
% 1.21/1.38 (((~((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e))))) | (~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e)) | (~((~mem(tptp_fun_Z_0(p(e), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(p(e), u(p(s(n(n(e)))), s(n(n(n(e)))))), p(e))))))) | ((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e))))),
% 1.21/1.38 inference(tautology,[status(thm)],[])).
% 1.21/1.38 tff(34,plain,
% 1.21/1.38 ((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e)))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 1.21/1.38 tff(35,assumption,(~(mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))))), introduced(assumption)).
% 1.21/1.38 tff(36,plain,
% 1.21/1.38 (^[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))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(37,plain,
% 1.21/1.38 (![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)))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[36])).
% 1.21/1.38 tff(38,plain,
% 1.21/1.38 (![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)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(39,plain,
% 1.21/1.38 (^[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))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(40,plain,
% 1.21/1.38 (![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)))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[39])).
% 1.21/1.38 tff(41,axiom,(![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Y) | mem(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','u_ax')).
% 1.21/1.38 tff(42,plain,
% 1.21/1.38 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.21/1.38 tff(43,plain,
% 1.21/1.38 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.21/1.38 tff(44,plain,(
% 1.21/1.38 ![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 1.21/1.38 inference(skolemize,[status(sab)],[43])).
% 1.21/1.38 tff(45,plain,
% 1.21/1.38 (![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 1.21/1.38 tff(46,plain,
% 1.21/1.38 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e))))))))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(47,plain,
% 1.21/1.38 ((mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, p(s(n(n(e))))))) <=> (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(48,plain,
% 1.21/1.38 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, p(s(n(n(e)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e))))))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[47])).
% 1.21/1.38 tff(49,plain,
% 1.21/1.38 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, p(s(n(n(e)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e))))))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[48, 46])).
% 1.21/1.38 tff(50,plain,
% 1.21/1.38 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, s(n(n(n(e))))) | mem(e, p(s(n(n(e)))))))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(51,plain,
% 1.21/1.38 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.21/1.38 tff(52,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[51, 45, 35])).
% 1.21/1.38 tff(53,plain,(mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(54,assumption,(~(mem(e, p(s(n(n(e))))) <=> subq(e, s(n(n(e)))))), introduced(assumption)).
% 1.21/1.38 tff(55,plain,
% 1.21/1.38 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(e, p(s(n(n(e))))) <=> subq(e, s(n(n(e)))))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(56,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[55, 27, 54])).
% 1.21/1.38 tff(57,plain,(mem(e, p(s(n(n(e))))) <=> subq(e, s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(58,assumption,((~((~subq(e, s(n(n(e))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, s(n(n(e))))))) | (~(subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e))))))))), introduced(assumption)).
% 1.21/1.38 tff(59,plain,
% 1.21/1.38 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(e, s(n(n(e))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, s(n(n(e))))))) | (~(subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e))))))))))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(60,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[59, 16, 58])).
% 1.21/1.38 tff(61,plain,(~((~((~subq(e, s(n(n(e))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, s(n(n(e))))))) | (~(subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(62,plain,
% 1.21/1.38 (((~((~subq(e, s(n(n(e))))) | ![Z: $i] : ((~mem(Z, e)) | mem(Z, s(n(n(e))))))) | (~(subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e))))))))) | (subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e)))))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(63,plain,
% 1.21/1.39 (subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 1.21/1.39 tff(64,assumption,(mem(tptp_fun_Z_0(s(n(n(e))), e), e)), introduced(assumption)).
% 1.21/1.39 tff(65,plain,
% 1.21/1.39 (^[X: $i] : refl((~mem(X, e)) <=> (~mem(X, e)))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(66,plain,
% 1.21/1.39 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[65])).
% 1.21/1.39 tff(67,plain,
% 1.21/1.39 (![X: $i] : (~mem(X, e)) <=> ![X: $i] : (~mem(X, e))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(68,axiom,(![X: $i] : (~mem(X, e))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','e_ax')).
% 1.21/1.39 tff(69,plain,
% 1.21/1.39 (![X: $i] : (~mem(X, e))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.21/1.39 tff(70,plain,(
% 1.21/1.39 ![X: $i] : (~mem(X, e))),
% 1.21/1.39 inference(skolemize,[status(sab)],[69])).
% 1.21/1.39 tff(71,plain,
% 1.21/1.39 (![X: $i] : (~mem(X, e))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.21/1.39 tff(72,plain,
% 1.21/1.39 ((~![X: $i] : (~mem(X, e))) | (~mem(tptp_fun_Z_0(s(n(n(e))), e), e))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(73,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[72, 71, 64])).
% 1.21/1.39 tff(74,plain,(~mem(tptp_fun_Z_0(s(n(n(e))), e), e)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(75,plain,
% 1.21/1.39 (((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), e), e)),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(76,plain,
% 1.21/1.39 ((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.21/1.39 tff(77,plain,
% 1.21/1.39 ((~(subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e)))))))) | subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e))))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(78,plain,
% 1.21/1.39 ((~(subq(e, s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), e), e)) | mem(tptp_fun_Z_0(s(n(n(e))), e), s(n(n(e)))))))) | subq(e, s(n(n(e))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[77, 76])).
% 1.21/1.39 tff(79,plain,
% 1.21/1.39 (subq(e, s(n(n(e))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[78, 63])).
% 1.21/1.39 tff(80,plain,
% 1.21/1.39 ((~(mem(e, p(s(n(n(e))))) <=> subq(e, s(n(n(e)))))) | mem(e, p(s(n(n(e))))) | (~subq(e, s(n(n(e)))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(81,plain,
% 1.21/1.39 ((~(mem(e, p(s(n(n(e))))) <=> subq(e, s(n(n(e)))))) | mem(e, p(s(n(n(e)))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 1.21/1.39 tff(82,plain,
% 1.21/1.39 (mem(e, p(s(n(n(e)))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[81, 57])).
% 1.21/1.39 tff(83,plain,
% 1.21/1.39 ((mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))) | (~mem(e, p(s(n(n(e))))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(84,plain,
% 1.21/1.39 (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[83, 82])).
% 1.21/1.39 tff(85,plain,
% 1.21/1.39 ((~(mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))))) | mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~(mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(86,plain,
% 1.21/1.39 ((~(mem(e, u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(e, p(s(n(n(e))))) | mem(e, s(n(n(n(e)))))))) | mem(e, u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[85, 84])).
% 1.21/1.39 tff(87,plain,
% 1.21/1.39 (mem(e, u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[86, 53])).
% 1.21/1.39 tff(88,assumption,(~mem(a(e, e), s(a(e, e)))), introduced(assumption)).
% 1.21/1.39 tff(89,plain,
% 1.21/1.39 (^[X: $i, Y: $i] : refl((mem(X, s(Y)) <=> (X = Y)) <=> (mem(X, s(Y)) <=> (X = Y)))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(90,plain,
% 1.21/1.39 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[89])).
% 1.21/1.39 tff(91,plain,
% 1.21/1.39 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(92,axiom,(![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','s_ax')).
% 1.21/1.39 tff(93,plain,
% 1.21/1.39 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.21/1.39 tff(94,plain,(
% 1.21/1.39 ![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.21/1.39 inference(skolemize,[status(sab)],[93])).
% 1.21/1.39 tff(95,plain,
% 1.21/1.39 (![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[94, 90])).
% 1.21/1.39 tff(96,plain,
% 1.21/1.39 (((~![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))))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(97,plain,
% 1.21/1.39 ((mem(a(e, e), s(a(e, e))) <=> $true) <=> mem(a(e, e), s(a(e, e)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(98,plain,
% 1.21/1.39 ((a(e, e) = a(e, e)) <=> $true),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(99,plain,
% 1.21/1.39 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> (mem(a(e, e), s(a(e, e))) <=> $true)),
% 1.21/1.39 inference(monotonicity,[status(thm)],[98])).
% 1.21/1.39 tff(100,plain,
% 1.21/1.39 ((mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e))) <=> mem(a(e, e), s(a(e, e)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[99, 97])).
% 1.21/1.39 tff(101,plain,
% 1.21/1.39 (((~![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))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[100])).
% 1.21/1.39 tff(102,plain,
% 1.21/1.39 (((~![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))))),
% 1.21/1.39 inference(transitivity,[status(thm)],[101, 96])).
% 1.21/1.39 tff(103,plain,
% 1.21/1.39 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(e, e))) <=> (a(e, e) = a(e, e)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(104,plain,
% 1.21/1.39 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(e, e), s(a(e, e)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.21/1.39 tff(105,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[104, 95, 88])).
% 1.21/1.39 tff(106,plain,(mem(a(e, e), s(a(e, e)))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(107,plain,
% 1.21/1.39 (^[X: $i] : refl((n(X) = a(X, X)) <=> (n(X) = a(X, X)))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(108,plain,
% 1.21/1.39 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[107])).
% 1.21/1.39 tff(109,plain,
% 1.21/1.39 (![X: $i] : (n(X) = a(X, X)) <=> ![X: $i] : (n(X) = a(X, X))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(110,axiom,(![X: $i] : (n(X) = a(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','n_def')).
% 1.21/1.39 tff(111,plain,
% 1.21/1.39 (![X: $i] : (n(X) = a(X, X))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.21/1.39 tff(112,plain,(
% 1.21/1.39 ![X: $i] : (n(X) = a(X, X))),
% 1.21/1.39 inference(skolemize,[status(sab)],[111])).
% 1.21/1.39 tff(113,plain,
% 1.21/1.39 (![X: $i] : (n(X) = a(X, X))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.21/1.39 tff(114,plain,
% 1.21/1.39 ((~![X: $i] : (n(X) = a(X, X))) | (n(e) = a(e, e))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(115,plain,
% 1.21/1.39 (n(e) = a(e, e)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[114, 113])).
% 1.21/1.39 tff(116,plain,
% 1.21/1.39 (a(e, e) = n(e)),
% 1.21/1.39 inference(symmetry,[status(thm)],[115])).
% 1.21/1.39 tff(117,plain,
% 1.21/1.39 (s(a(e, e)) = s(n(e))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[116])).
% 1.21/1.39 tff(118,plain,
% 1.21/1.39 (mem(a(e, e), s(a(e, e))) <=> mem(a(e, e), s(n(e)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[117])).
% 1.21/1.39 tff(119,plain,
% 1.21/1.39 (mem(a(e, e), s(n(e))) <=> mem(a(e, e), s(a(e, e)))),
% 1.21/1.39 inference(symmetry,[status(thm)],[118])).
% 1.21/1.39 tff(120,plain,
% 1.21/1.39 ((~mem(a(e, e), s(n(e)))) <=> (~mem(a(e, e), s(a(e, e))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[119])).
% 1.21/1.39 tff(121,assumption,(~mem(a(e, e), s(n(e)))), introduced(assumption)).
% 1.21/1.39 tff(122,plain,
% 1.21/1.39 (~mem(a(e, e), s(a(e, e)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.21/1.39 tff(123,assumption,(mem(a(e, e), s(a(e, e)))), introduced(assumption)).
% 1.21/1.39 tff(124,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[123, 122])).
% 1.21/1.39 tff(125,plain,((~mem(a(e, e), s(a(e, e)))) | mem(a(e, e), s(n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(126,plain,
% 1.21/1.39 (mem(a(e, e), s(n(e)))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[125, 106])).
% 1.21/1.39 tff(127,plain,
% 1.21/1.39 ((mem(a(e, e), s(s(s(n(e))))) | mem(a(e, e), s(n(e)))) | (~mem(a(e, e), s(n(e))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(128,plain,
% 1.21/1.39 (mem(a(e, e), s(s(s(n(e))))) | mem(a(e, e), s(n(e)))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.21/1.39 tff(129,assumption,(~(mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))) <=> (mem(a(e, e), s(s(s(n(e))))) | mem(a(e, e), s(n(e)))))), introduced(assumption)).
% 1.21/1.39 tff(130,plain,
% 1.21/1.39 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))) <=> (mem(a(e, e), s(s(s(n(e))))) | mem(a(e, e), s(n(e)))))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(131,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[130, 45, 129])).
% 1.21/1.39 tff(132,plain,(mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))) <=> (mem(a(e, e), s(s(s(n(e))))) | mem(a(e, e), s(n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(133,plain,
% 1.21/1.39 ((~(mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))) <=> (mem(a(e, e), s(s(s(n(e))))) | mem(a(e, e), s(n(e)))))) | mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))) | (~(mem(a(e, e), s(s(s(n(e))))) | mem(a(e, e), s(n(e)))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(134,plain,
% 1.21/1.39 (mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))) | (~(mem(a(e, e), s(s(s(n(e))))) | mem(a(e, e), s(n(e)))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[133, 132])).
% 1.21/1.39 tff(135,plain,
% 1.21/1.39 (mem(a(e, e), u(s(n(e)), s(s(s(n(e))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[134, 128])).
% 1.21/1.39 tff(136,plain,
% 1.21/1.39 (^[X: $i, Y: $i] : refl((a(X, Y) = u(X, s(Y))) <=> (a(X, Y) = u(X, s(Y))))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(137,plain,
% 1.21/1.39 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[136])).
% 1.21/1.39 tff(138,plain,
% 1.21/1.39 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y))) <=> ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(139,axiom,(![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','a_def')).
% 1.21/1.39 tff(140,plain,
% 1.21/1.39 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.21/1.39 tff(141,plain,(
% 1.21/1.39 ![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.21/1.39 inference(skolemize,[status(sab)],[140])).
% 1.21/1.39 tff(142,plain,
% 1.21/1.39 (![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[141, 137])).
% 1.21/1.39 tff(143,plain,
% 1.21/1.39 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(p(s(n(n(e)))), n(n(n(e)))) = u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(144,plain,
% 1.21/1.39 (a(p(s(n(n(e)))), n(n(n(e)))) = u(p(s(n(n(e)))), s(n(n(n(e)))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[143, 142])).
% 1.21/1.39 tff(145,plain,
% 1.21/1.39 (u(p(s(n(n(e)))), s(n(n(n(e))))) = a(p(s(n(n(e)))), n(n(n(e))))),
% 1.21/1.39 inference(symmetry,[status(thm)],[144])).
% 1.21/1.39 tff(146,plain,
% 1.21/1.39 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(s(n(e)), s(s(n(e)))) = u(s(n(e)), s(s(s(n(e))))))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(147,plain,
% 1.21/1.39 (a(s(n(e)), s(s(n(e)))) = u(s(n(e)), s(s(s(n(e)))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[146, 142])).
% 1.21/1.39 tff(148,plain,
% 1.21/1.39 (u(s(n(e)), s(s(s(n(e))))) = a(s(n(e)), s(s(n(e))))),
% 1.21/1.39 inference(symmetry,[status(thm)],[147])).
% 1.21/1.39 tff(149,plain,
% 1.21/1.39 (u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) = u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[148, 145])).
% 1.21/1.39 tff(150,plain,
% 1.21/1.39 (mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[149])).
% 1.21/1.39 tff(151,plain,
% 1.21/1.39 (mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) <=> mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.39 inference(symmetry,[status(thm)],[150])).
% 1.21/1.39 tff(152,plain,
% 1.21/1.39 ((~mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) <=> (~mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[151])).
% 1.21/1.39 tff(153,assumption,(~mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))), introduced(assumption)).
% 1.21/1.39 tff(154,plain,
% 1.21/1.39 (~mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.21/1.39 tff(155,plain,
% 1.21/1.39 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(s(s(n(e))))))))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(156,plain,
% 1.21/1.39 (mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[155, 45])).
% 1.21/1.39 tff(157,assumption,(mem(a(e, e), u(s(n(e)), s(s(s(n(e))))))), introduced(assumption)).
% 1.21/1.39 tff(158,plain,
% 1.21/1.39 ((mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(s(s(n(e))))))) | (~mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(159,plain,
% 1.21/1.39 (mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(s(s(n(e))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[158, 157])).
% 1.21/1.39 tff(160,plain,
% 1.21/1.39 ((~(mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(s(s(n(e))))))))) | mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~(mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(s(s(n(e))))))))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(161,plain,
% 1.21/1.39 ((~(mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(a(e, e), u(s(n(e)), s(s(s(n(e))))))))) | mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[160, 159])).
% 1.21/1.39 tff(162,plain,
% 1.21/1.39 (mem(a(e, e), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[161, 156])).
% 1.21/1.39 tff(163,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[162, 154])).
% 1.21/1.39 tff(164,plain,(mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~mem(a(e, e), u(s(n(e)), s(s(s(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(165,plain,
% 1.21/1.39 (mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[164, 135])).
% 1.21/1.39 tff(166,plain,
% 1.21/1.39 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(e)) = a(n(e), n(e)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(167,plain,
% 1.21/1.39 (n(n(e)) = a(n(e), n(e))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[166, 113])).
% 1.21/1.39 tff(168,plain,
% 1.21/1.39 (a(n(e), n(e)) = n(n(e))),
% 1.21/1.39 inference(symmetry,[status(thm)],[167])).
% 1.21/1.39 tff(169,plain,
% 1.21/1.39 (s(a(n(e), n(e))) = s(n(n(e)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[168])).
% 1.21/1.39 tff(170,plain,
% 1.21/1.39 (mem(e, s(a(n(e), n(e)))) <=> mem(e, s(n(n(e))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[169])).
% 1.21/1.39 tff(171,plain,
% 1.21/1.39 (mem(e, s(n(n(e)))) <=> mem(e, s(a(n(e), n(e))))),
% 1.21/1.39 inference(symmetry,[status(thm)],[170])).
% 1.21/1.39 tff(172,assumption,(mem(e, s(n(n(e))))), introduced(assumption)).
% 1.21/1.39 tff(173,plain,
% 1.21/1.39 (mem(e, s(a(n(e), n(e))))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.21/1.39 tff(174,plain,
% 1.21/1.39 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e))))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(175,plain,
% 1.21/1.39 (mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e)))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[174, 95])).
% 1.21/1.39 tff(176,assumption,(e = a(n(e), n(e))), introduced(assumption)).
% 1.21/1.39 tff(177,plain,
% 1.21/1.39 (mem(a(n(e), n(e)), e) <=> mem(a(n(e), n(e)), a(n(e), n(e)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[176])).
% 1.21/1.39 tff(178,plain,
% 1.21/1.39 (mem(a(n(e), n(e)), a(n(e), n(e))) <=> mem(a(n(e), n(e)), e)),
% 1.21/1.39 inference(symmetry,[status(thm)],[177])).
% 1.21/1.39 tff(179,plain,
% 1.21/1.39 (a(n(e), n(e)) = e),
% 1.21/1.39 inference(symmetry,[status(thm)],[176])).
% 1.21/1.39 tff(180,plain,
% 1.21/1.39 (mem(a(n(e), n(e)), a(n(e), n(e))) <=> mem(e, a(n(e), n(e)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[179])).
% 1.21/1.39 tff(181,plain,
% 1.21/1.39 (mem(e, a(n(e), n(e))) <=> mem(a(n(e), n(e)), a(n(e), n(e)))),
% 1.21/1.39 inference(symmetry,[status(thm)],[180])).
% 1.21/1.39 tff(182,plain,
% 1.21/1.39 (a(a(e, e), a(e, e)) = a(n(e), n(e))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[116, 116])).
% 1.21/1.39 tff(183,plain,
% 1.21/1.39 ((~![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))))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(184,plain,
% 1.21/1.39 (a(a(e, e), a(e, e)) = u(a(e, e), s(a(e, e)))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[183, 142])).
% 1.21/1.39 tff(185,plain,
% 1.21/1.39 (u(a(e, e), s(a(e, e))) = a(a(e, e), a(e, e))),
% 1.21/1.39 inference(symmetry,[status(thm)],[184])).
% 1.21/1.39 tff(186,plain,
% 1.21/1.39 (s(n(e)) = s(a(e, e))),
% 1.21/1.39 inference(symmetry,[status(thm)],[117])).
% 1.21/1.39 tff(187,plain,
% 1.21/1.39 (u(a(e, e), s(n(e))) = u(a(e, e), s(a(e, e)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[186])).
% 1.21/1.39 tff(188,plain,
% 1.21/1.39 (u(a(e, e), s(n(e))) = a(n(e), n(e))),
% 1.21/1.39 inference(transitivity,[status(thm)],[187, 185, 182])).
% 1.21/1.39 tff(189,plain,
% 1.21/1.39 (mem(e, u(a(e, e), s(n(e)))) <=> mem(e, a(n(e), n(e)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[188])).
% 1.21/1.39 tff(190,plain,
% 1.21/1.39 (mem(e, a(n(e), n(e))) <=> mem(e, u(a(e, e), s(n(e))))),
% 1.21/1.39 inference(symmetry,[status(thm)],[189])).
% 1.21/1.39 tff(191,plain,
% 1.21/1.39 ((~mem(e, a(n(e), n(e)))) <=> (~mem(e, u(a(e, e), s(n(e)))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[190])).
% 1.21/1.39 tff(192,assumption,(~mem(e, a(n(e), n(e)))), introduced(assumption)).
% 1.21/1.39 tff(193,plain,
% 1.21/1.39 (~mem(e, u(a(e, e), s(n(e))))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[192, 191])).
% 1.21/1.39 tff(194,plain,
% 1.21/1.39 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(195,plain,
% 1.21/1.39 ((mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, s(n(e))) | mem(e, a(e, e)))) <=> (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(196,plain,
% 1.21/1.39 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, s(n(e))) | mem(e, a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[195])).
% 1.21/1.39 tff(197,plain,
% 1.21/1.39 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, s(n(e))) | mem(e, a(e, e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))))),
% 1.21/1.39 inference(transitivity,[status(thm)],[196, 194])).
% 1.21/1.39 tff(198,plain,
% 1.21/1.39 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, s(n(e))) | mem(e, a(e, e))))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(199,plain,
% 1.21/1.39 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.21/1.39 tff(200,plain,
% 1.21/1.39 (mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e))))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[199, 45])).
% 1.21/1.39 tff(201,plain,
% 1.21/1.39 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(e, e) = u(e, s(e)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(202,plain,
% 1.21/1.39 (a(e, e) = u(e, s(e))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[201, 142])).
% 1.21/1.39 tff(203,plain,
% 1.21/1.39 (u(e, s(e)) = a(e, e)),
% 1.21/1.39 inference(symmetry,[status(thm)],[202])).
% 1.21/1.39 tff(204,plain,
% 1.21/1.39 (mem(e, u(e, s(e))) <=> mem(e, a(e, e))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[203])).
% 1.21/1.39 tff(205,plain,
% 1.21/1.39 (mem(e, a(e, e)) <=> mem(e, u(e, s(e)))),
% 1.21/1.39 inference(symmetry,[status(thm)],[204])).
% 1.21/1.39 tff(206,plain,
% 1.21/1.39 ((~mem(e, a(e, e))) <=> (~mem(e, u(e, s(e))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[205])).
% 1.21/1.39 tff(207,assumption,(~mem(e, a(e, e))), introduced(assumption)).
% 1.21/1.39 tff(208,plain,
% 1.21/1.39 (~mem(e, u(e, s(e)))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.21/1.39 tff(209,plain,
% 1.21/1.39 ((~![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)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(210,plain,
% 1.21/1.39 (mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[209, 45])).
% 1.21/1.39 tff(211,assumption,(~mem(e, s(e))), introduced(assumption)).
% 1.21/1.39 tff(212,plain,
% 1.21/1.39 (((~![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)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(213,plain,
% 1.21/1.39 ((mem(e, s(e)) <=> $true) <=> mem(e, s(e))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(214,plain,
% 1.21/1.39 ((e = e) <=> $true),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(215,plain,
% 1.21/1.39 ((mem(e, s(e)) <=> (e = e)) <=> (mem(e, s(e)) <=> $true)),
% 1.21/1.39 inference(monotonicity,[status(thm)],[214])).
% 1.21/1.39 tff(216,plain,
% 1.21/1.39 ((mem(e, s(e)) <=> (e = e)) <=> mem(e, s(e))),
% 1.21/1.39 inference(transitivity,[status(thm)],[215, 213])).
% 1.21/1.39 tff(217,plain,
% 1.21/1.39 (((~![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)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[216])).
% 1.21/1.39 tff(218,plain,
% 1.21/1.39 (((~![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)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[217, 212])).
% 1.21/1.39 tff(219,plain,
% 1.21/1.39 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(e, s(e)) <=> (e = e))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(220,plain,
% 1.21/1.39 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(e, s(e))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.21/1.39 tff(221,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[220, 95, 211])).
% 1.21/1.39 tff(222,plain,(mem(e, s(e))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(223,plain,
% 1.21/1.39 ((mem(e, s(e)) | mem(e, e)) | (~mem(e, s(e)))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(224,plain,
% 1.21/1.39 (mem(e, s(e)) | mem(e, e)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[223, 222])).
% 1.21/1.39 tff(225,plain,
% 1.21/1.39 ((~(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)))),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(226,plain,
% 1.21/1.39 ((~(mem(e, u(e, s(e))) <=> (mem(e, s(e)) | mem(e, e)))) | mem(e, u(e, s(e)))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[225, 224])).
% 1.21/1.40 tff(227,plain,
% 1.21/1.40 (mem(e, u(e, s(e)))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[226, 210])).
% 1.21/1.40 tff(228,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[227, 208])).
% 1.21/1.40 tff(229,plain,(mem(e, a(e, e))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(230,plain,
% 1.21/1.40 ((mem(e, a(e, e)) | mem(e, s(n(e)))) | (~mem(e, a(e, e)))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(231,plain,
% 1.21/1.40 (mem(e, a(e, e)) | mem(e, s(n(e)))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[230, 229])).
% 1.21/1.40 tff(232,plain,
% 1.21/1.40 ((~(mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))) | mem(e, u(a(e, e), s(n(e)))) | (~(mem(e, a(e, e)) | mem(e, s(n(e)))))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(233,plain,
% 1.21/1.40 ((~(mem(e, u(a(e, e), s(n(e)))) <=> (mem(e, a(e, e)) | mem(e, s(n(e)))))) | mem(e, u(a(e, e), s(n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[232, 231])).
% 1.21/1.40 tff(234,plain,
% 1.21/1.40 (mem(e, u(a(e, e), s(n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[233, 200])).
% 1.21/1.40 tff(235,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[234, 193])).
% 1.21/1.40 tff(236,plain,(mem(e, a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(237,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), a(n(e), n(e)))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[236, 181])).
% 1.21/1.40 tff(238,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), e)),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[237, 178])).
% 1.21/1.40 tff(239,assumption,(mem(a(n(e), n(e)), e)), introduced(assumption)).
% 1.21/1.40 tff(240,plain,
% 1.21/1.40 ((~![X: $i] : (~mem(X, e))) | (~mem(a(n(e), n(e)), e))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(241,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[240, 71, 239])).
% 1.21/1.40 tff(242,plain,(~mem(a(n(e), n(e)), e)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(243,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[242, 238])).
% 1.21/1.40 tff(244,plain,(~(e = a(n(e), n(e)))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(245,plain,
% 1.21/1.40 ((~(mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e))))) | (~mem(e, s(a(n(e), n(e))))) | (e = a(n(e), n(e)))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(246,plain,
% 1.21/1.40 ((~(mem(e, s(a(n(e), n(e)))) <=> (e = a(n(e), n(e))))) | (~mem(e, s(a(n(e), n(e)))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[245, 244])).
% 1.21/1.40 tff(247,plain,
% 1.21/1.40 (~mem(e, s(a(n(e), n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[246, 175])).
% 1.21/1.40 tff(248,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[247, 173])).
% 1.21/1.40 tff(249,plain,(~mem(e, s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(250,assumption,(~mem(e, s(n(n(e))))), introduced(assumption)).
% 1.21/1.40 tff(251,assumption,(![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))), introduced(assumption)).
% 1.21/1.40 tff(252,plain,
% 1.21/1.40 (((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))) | ((~mem(e, a(e, e))) | mem(e, s(n(n(e)))))) <=> ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))) | (~mem(e, a(e, e))) | mem(e, s(n(n(e)))))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(253,plain,
% 1.21/1.40 ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))) | ((~mem(e, a(e, e))) | mem(e, s(n(n(e)))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(254,plain,
% 1.21/1.40 ((~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))) | (~mem(e, a(e, e))) | mem(e, s(n(n(e))))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.21/1.40 tff(255,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[254, 251, 250, 229])).
% 1.21/1.40 tff(256,plain,(mem(e, s(n(n(e)))) | (~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(257,plain,
% 1.21/1.40 (~![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[256, 249])).
% 1.21/1.40 tff(258,assumption,((~((~subq(a(e, e), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e))))))) | (~(subq(a(e, e), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(n(e))), a(e, e)), s(n(n(e))))))))), introduced(assumption)).
% 1.21/1.40 tff(259,plain,
% 1.21/1.40 ((~![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), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e))))))) | (~(subq(a(e, e), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(n(e))), a(e, e)), s(n(n(e))))))))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(260,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[259, 16, 258])).
% 1.21/1.40 tff(261,plain,(~((~((~subq(a(e, e), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e))))))) | (~(subq(a(e, e), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(n(e))), a(e, e)), s(n(n(e)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(262,plain,
% 1.21/1.40 (((~((~subq(a(e, e), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e))))))) | (~(subq(a(e, e), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), a(e, e)), a(e, e))) | mem(tptp_fun_Z_0(s(n(n(e))), a(e, e)), s(n(n(e))))))))) | ((~subq(a(e, e), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e))))))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(263,plain,
% 1.21/1.40 ((~subq(a(e, e), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[262, 261])).
% 1.21/1.40 tff(264,plain,
% 1.21/1.40 ((~((~subq(a(e, e), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e))))))) | (~subq(a(e, e), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(265,plain,
% 1.21/1.40 ((~subq(a(e, e), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, a(e, e))) | mem(Z, s(n(n(e)))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[264, 263])).
% 1.21/1.40 tff(266,plain,
% 1.21/1.40 (~subq(a(e, e), s(n(n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[265, 257])).
% 1.21/1.40 tff(267,assumption,(~(mem(a(e, e), p(s(n(n(e))))) <=> subq(a(e, e), s(n(n(e)))))), introduced(assumption)).
% 1.21/1.40 tff(268,plain,
% 1.21/1.40 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(a(e, e), p(s(n(n(e))))) <=> subq(a(e, e), s(n(n(e)))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(269,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[268, 27, 267])).
% 1.21/1.40 tff(270,plain,(mem(a(e, e), p(s(n(n(e))))) <=> subq(a(e, e), s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(271,plain,
% 1.21/1.40 ((~(mem(a(e, e), p(s(n(n(e))))) <=> subq(a(e, e), s(n(n(e)))))) | (~mem(a(e, e), p(s(n(n(e)))))) | subq(a(e, e), s(n(n(e))))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(272,plain,
% 1.21/1.40 ((~mem(a(e, e), p(s(n(n(e)))))) | subq(a(e, e), s(n(n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[271, 270])).
% 1.21/1.40 tff(273,plain,
% 1.21/1.40 (~mem(a(e, e), p(s(n(n(e)))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[272, 266])).
% 1.21/1.40 tff(274,plain,
% 1.21/1.40 ((~![X: $i] : (n(X) = a(X, X))) | (n(n(n(e))) = a(n(n(e)), n(n(e))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(275,plain,
% 1.21/1.40 (n(n(n(e))) = a(n(n(e)), n(n(e)))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[274, 113])).
% 1.21/1.40 tff(276,plain,
% 1.21/1.40 (a(n(n(e)), n(n(e))) = n(n(n(e)))),
% 1.21/1.40 inference(symmetry,[status(thm)],[275])).
% 1.21/1.40 tff(277,plain,
% 1.21/1.40 (s(a(n(n(e)), n(n(e)))) = s(n(n(n(e))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[276])).
% 1.21/1.40 tff(278,plain,
% 1.21/1.40 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(a(e, e))) <=> (tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))) = a(e, e)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(279,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(a(e, e))) <=> (tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))) = a(e, e))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[278, 95])).
% 1.21/1.40 tff(280,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(a(e, e))) <=> mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[117])).
% 1.21/1.40 tff(281,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e))) <=> mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(a(e, e)))),
% 1.21/1.40 inference(symmetry,[status(thm)],[280])).
% 1.21/1.40 tff(282,assumption,(~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))), introduced(assumption)).
% 1.21/1.40 tff(283,plain,
% 1.21/1.40 (((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(284,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[283, 282])).
% 1.21/1.40 tff(285,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(a(e, e)))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[284, 281])).
% 1.21/1.40 tff(286,plain,
% 1.21/1.40 ((~(mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(a(e, e))) <=> (tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))) = a(e, e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(a(e, e)))) | (tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))) = a(e, e))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(287,plain,
% 1.21/1.40 (tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))) = a(e, e)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[286, 285, 279])).
% 1.21/1.40 tff(288,plain,
% 1.21/1.40 (a(e, e) = tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e)))),
% 1.21/1.40 inference(symmetry,[status(thm)],[287])).
% 1.21/1.40 tff(289,plain,
% 1.21/1.40 (mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e)))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[288, 277])).
% 1.21/1.40 tff(290,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) <=> mem(a(e, e), s(a(n(n(e)), n(n(e)))))),
% 1.21/1.40 inference(symmetry,[status(thm)],[289])).
% 1.21/1.40 tff(291,plain,
% 1.21/1.40 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e)))))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(292,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e))))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[291, 45])).
% 1.21/1.40 tff(293,plain,
% 1.21/1.40 (((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(294,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[293, 282])).
% 1.21/1.40 tff(295,plain,
% 1.21/1.40 ((~(mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e)))))))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e))))))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(296,plain,
% 1.21/1.40 ((~(mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e)))))))) | (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e))))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[295, 294])).
% 1.21/1.40 tff(297,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e)))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[296, 292])).
% 1.21/1.40 tff(298,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e))))) <=> mem(a(e, e), p(s(n(n(e)))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[287])).
% 1.21/1.40 tff(299,plain,
% 1.21/1.40 (mem(a(e, e), p(s(n(n(e))))) <=> mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e)))))),
% 1.21/1.40 inference(symmetry,[status(thm)],[298])).
% 1.21/1.40 tff(300,plain,
% 1.21/1.40 ((~mem(a(e, e), p(s(n(n(e)))))) <=> (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e))))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[299])).
% 1.21/1.40 tff(301,assumption,(~mem(a(e, e), p(s(n(n(e)))))), introduced(assumption)).
% 1.21/1.40 tff(302,plain,
% 1.21/1.40 (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e)))))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[301, 300])).
% 1.21/1.40 tff(303,plain,
% 1.21/1.40 ((~(mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e))))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e))))) | mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), p(s(n(n(e)))))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(304,plain,
% 1.21/1.40 (mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(n(n(e)))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[303, 302, 297])).
% 1.21/1.40 tff(305,plain,
% 1.21/1.40 (mem(a(e, e), s(a(n(n(e)), n(n(e)))))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[304, 290])).
% 1.21/1.40 tff(306,plain,
% 1.21/1.40 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> (a(e, e) = a(n(n(e)), n(n(e)))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(307,plain,
% 1.21/1.40 (mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> (a(e, e) = a(n(n(e)), n(n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[306, 95])).
% 1.21/1.40 tff(308,plain,
% 1.21/1.40 (s(n(n(e))) = s(a(n(e), n(e)))),
% 1.21/1.40 inference(symmetry,[status(thm)],[169])).
% 1.21/1.40 tff(309,plain,
% 1.21/1.40 (u(a(n(e), n(e)), s(n(n(e)))) = u(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[308])).
% 1.21/1.40 tff(310,plain,
% 1.21/1.40 (u(a(n(e), n(e)), s(a(n(e), n(e)))) = u(a(n(e), n(e)), s(n(n(e))))),
% 1.21/1.40 inference(symmetry,[status(thm)],[309])).
% 1.21/1.40 tff(311,plain,
% 1.21/1.40 ((~![X: $i, Y: $i] : (a(X, Y) = u(X, s(Y)))) | (a(a(n(e), n(e)), a(n(e), n(e))) = u(a(n(e), n(e)), s(a(n(e), n(e)))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(312,plain,
% 1.21/1.40 (a(a(n(e), n(e)), a(n(e), n(e))) = u(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[311, 142])).
% 1.21/1.40 tff(313,plain,
% 1.21/1.40 (a(a(n(e), n(e)), a(n(e), n(e))) = a(n(n(e)), n(n(e)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[168, 168])).
% 1.21/1.40 tff(314,plain,
% 1.21/1.40 (a(n(n(e)), n(n(e))) = a(a(n(e), n(e)), a(n(e), n(e)))),
% 1.21/1.40 inference(symmetry,[status(thm)],[313])).
% 1.21/1.40 tff(315,assumption,(a(e, e) = a(n(n(e)), n(n(e)))), introduced(assumption)).
% 1.21/1.40 tff(316,plain,
% 1.21/1.40 (u(e, s(e)) = u(a(n(e), n(e)), s(n(n(e))))),
% 1.21/1.40 inference(transitivity,[status(thm)],[203, 315, 314, 312, 310])).
% 1.21/1.40 tff(317,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), u(e, s(e))) <=> mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e)))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[316])).
% 1.21/1.40 tff(318,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> mem(a(n(e), n(e)), u(e, s(e)))),
% 1.21/1.40 inference(symmetry,[status(thm)],[317])).
% 1.21/1.40 tff(319,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), s(a(n(e), n(e)))) <=> mem(a(n(e), n(e)), s(n(n(e))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[169])).
% 1.21/1.40 tff(320,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), s(n(n(e)))) <=> mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.21/1.40 inference(symmetry,[status(thm)],[319])).
% 1.21/1.40 tff(321,plain,
% 1.21/1.40 ((~mem(a(n(e), n(e)), s(n(n(e))))) <=> (~mem(a(n(e), n(e)), s(a(n(e), n(e)))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[320])).
% 1.21/1.40 tff(322,assumption,(~mem(a(n(e), n(e)), s(n(n(e))))), introduced(assumption)).
% 1.21/1.40 tff(323,plain,
% 1.21/1.40 (~mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.21/1.40 tff(324,plain,
% 1.21/1.40 (((~![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)))))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(325,plain,
% 1.21/1.40 ((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))))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(326,plain,
% 1.21/1.40 ((a(n(e), n(e)) = a(n(e), n(e))) <=> $true),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(327,plain,
% 1.21/1.40 ((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)),
% 1.21/1.40 inference(monotonicity,[status(thm)],[326])).
% 1.21/1.40 tff(328,plain,
% 1.21/1.40 ((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))))),
% 1.21/1.40 inference(transitivity,[status(thm)],[327, 325])).
% 1.21/1.40 tff(329,plain,
% 1.21/1.40 (((~![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)))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[328])).
% 1.21/1.40 tff(330,plain,
% 1.21/1.40 (((~![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)))))),
% 1.21/1.40 inference(transitivity,[status(thm)],[329, 324])).
% 1.21/1.40 tff(331,plain,
% 1.21/1.40 ((~![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))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(332,plain,
% 1.21/1.40 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[331, 330])).
% 1.21/1.40 tff(333,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), s(a(n(e), n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[332, 95])).
% 1.21/1.40 tff(334,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[333, 323])).
% 1.21/1.40 tff(335,plain,(mem(a(n(e), n(e)), s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(336,plain,
% 1.21/1.40 ((mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e))))) | (~mem(a(n(e), n(e)), s(n(n(e)))))),
% 1.21/1.40 inference(tautology,[status(thm)],[])).
% 1.21/1.40 tff(337,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[336, 335])).
% 1.21/1.40 tff(338,plain,
% 1.21/1.40 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e)))))))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(339,plain,
% 1.21/1.40 ((mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e))))) <=> (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e))))))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(340,plain,
% 1.21/1.40 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e)))))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[339])).
% 1.21/1.40 tff(341,plain,
% 1.21/1.40 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e)))))))),
% 1.21/1.40 inference(transitivity,[status(thm)],[340, 338])).
% 1.21/1.40 tff(342,plain,
% 1.21/1.40 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), s(n(n(e)))) | mem(a(n(e), n(e)), a(n(e), n(e)))))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(343,plain,
% 1.21/1.40 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e))))))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.21/1.40 tff(344,plain,
% 1.21/1.40 (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e)))))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[343, 45])).
% 1.21/1.40 tff(345,plain,
% 1.21/1.40 ((~(mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) <=> (mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e))))))) | mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) | (~(mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e))))))),
% 1.21/1.41 inference(tautology,[status(thm)],[])).
% 1.21/1.41 tff(346,plain,
% 1.21/1.41 (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e))))) | (~(mem(a(n(e), n(e)), a(n(e), n(e))) | mem(a(n(e), n(e)), s(n(n(e))))))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[345, 344])).
% 1.21/1.41 tff(347,plain,
% 1.21/1.41 (mem(a(n(e), n(e)), u(a(n(e), n(e)), s(n(n(e)))))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[346, 337])).
% 1.21/1.41 tff(348,plain,
% 1.21/1.41 (mem(a(n(e), n(e)), u(e, s(e)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[347, 318])).
% 1.21/1.41 tff(349,plain,
% 1.21/1.41 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(350,plain,
% 1.21/1.41 ((mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e))) <=> (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(351,plain,
% 1.21/1.41 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[350])).
% 1.21/1.41 tff(352,plain,
% 1.21/1.41 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e)))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))))),
% 1.21/1.41 inference(transitivity,[status(thm)],[351, 349])).
% 1.21/1.41 tff(353,plain,
% 1.21/1.41 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), s(e)) | mem(a(n(e), n(e)), e)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(354,plain,
% 1.21/1.41 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.21/1.41 tff(355,plain,
% 1.21/1.41 (mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[354, 45])).
% 1.21/1.41 tff(356,assumption,(~(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))), introduced(assumption)).
% 1.21/1.41 tff(357,plain,
% 1.21/1.41 ((~![X: $i, Y: $i] : (mem(X, s(Y)) <=> (X = Y))) | (mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(358,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[357, 95, 356])).
% 1.21/1.41 tff(359,plain,(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(360,assumption,(a(n(e), n(e)) = e), introduced(assumption)).
% 1.21/1.41 tff(361,plain,
% 1.21/1.41 (e = a(n(e), n(e))),
% 1.21/1.41 inference(symmetry,[status(thm)],[360])).
% 1.21/1.41 tff(362,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[244, 361])).
% 1.21/1.41 tff(363,plain,(~(a(n(e), n(e)) = e)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(364,plain,
% 1.21/1.41 ((~(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))) | (~mem(a(n(e), n(e)), s(e))) | (a(n(e), n(e)) = e)),
% 1.21/1.41 inference(tautology,[status(thm)],[])).
% 1.21/1.41 tff(365,plain,
% 1.21/1.41 ((~(mem(a(n(e), n(e)), s(e)) <=> (a(n(e), n(e)) = e))) | (~mem(a(n(e), n(e)), s(e)))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[364, 363])).
% 1.21/1.41 tff(366,plain,
% 1.21/1.41 (~mem(a(n(e), n(e)), s(e))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[365, 359])).
% 1.21/1.41 tff(367,plain,
% 1.21/1.41 ((~(mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))) | mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))),
% 1.21/1.41 inference(tautology,[status(thm)],[])).
% 1.21/1.41 tff(368,plain,
% 1.21/1.41 (~(mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[367, 242, 366])).
% 1.21/1.41 tff(369,plain,
% 1.21/1.41 ((~(mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))) | (~mem(a(n(e), n(e)), u(e, s(e)))) | (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e)))),
% 1.21/1.41 inference(tautology,[status(thm)],[])).
% 1.21/1.41 tff(370,plain,
% 1.21/1.41 ((~(mem(a(n(e), n(e)), u(e, s(e))) <=> (mem(a(n(e), n(e)), e) | mem(a(n(e), n(e)), s(e))))) | (~mem(a(n(e), n(e)), u(e, s(e))))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[369, 368])).
% 1.21/1.41 tff(371,plain,
% 1.21/1.41 (~mem(a(n(e), n(e)), u(e, s(e)))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[370, 355])).
% 1.21/1.41 tff(372,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[371, 348])).
% 1.21/1.41 tff(373,plain,(~(a(e, e) = a(n(n(e)), n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(374,plain,
% 1.21/1.41 ((~(mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> (a(e, e) = a(n(n(e)), n(n(e)))))) | (~mem(a(e, e), s(a(n(n(e)), n(n(e)))))) | (a(e, e) = a(n(n(e)), n(n(e))))),
% 1.21/1.41 inference(tautology,[status(thm)],[])).
% 1.21/1.41 tff(375,plain,
% 1.21/1.41 ((~(mem(a(e, e), s(a(n(n(e)), n(n(e))))) <=> (a(e, e) = a(n(n(e)), n(n(e)))))) | (~mem(a(e, e), s(a(n(n(e)), n(n(e))))))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[374, 373])).
% 1.21/1.41 tff(376,plain,
% 1.21/1.41 (~mem(a(e, e), s(a(n(n(e)), n(n(e)))))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[375, 307])).
% 1.21/1.41 tff(377,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[376, 305])).
% 1.21/1.41 tff(378,plain,(((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | mem(a(e, e), p(s(n(n(e)))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(379,plain,
% 1.21/1.41 ((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[378, 273])).
% 1.21/1.41 tff(380,plain,
% 1.21/1.41 (^[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))))))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(381,plain,
% 1.21/1.41 (![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)))))))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[380])).
% 1.21/1.41 tff(382,plain,
% 1.21/1.41 (^[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))))))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(383,plain,
% 1.21/1.41 (![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)))))))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[382])).
% 1.21/1.41 tff(384,plain,
% 1.21/1.41 (![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)))))))),
% 1.21/1.41 inference(transitivity,[status(thm)],[383, 381])).
% 1.21/1.41 tff(385,plain,
% 1.21/1.41 (^[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)))))))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(386,plain,
% 1.21/1.41 (![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)))))))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[385])).
% 1.21/1.41 tff(387,plain,
% 1.21/1.41 (^[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)))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(388,plain,
% 1.21/1.41 (![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))))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[387])).
% 1.21/1.41 tff(389,plain,
% 1.21/1.41 (![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)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(390,plain,
% 1.21/1.41 (^[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)))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(391,plain,
% 1.21/1.41 (![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)))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[390])).
% 1.21/1.41 tff(392,axiom,(![X: $i, Y: $i] : (disj(X, Y) <=> (~?[Z: $i] : (mem(Z, X) & mem(Z, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','disj_def')).
% 1.21/1.41 tff(393,plain,
% 1.21/1.41 (![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.21/1.41 tff(394,plain,
% 1.21/1.41 (![X: $i, Y: $i] : (~(?[Z: $i] : (mem(Z, X) & mem(Z, Y)) <=> disj(X, Y)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[393, 389])).
% 1.21/1.41 tff(395,plain,(
% 1.21/1.41 ![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))))),
% 1.21/1.41 inference(skolemize,[status(sab)],[394])).
% 1.21/1.41 tff(396,plain,
% 1.21/1.41 (![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))))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[395, 388])).
% 1.21/1.41 tff(397,plain,
% 1.21/1.41 (![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)))))))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[396, 386])).
% 1.21/1.41 tff(398,plain,
% 1.21/1.41 (![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)))))))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[397, 384])).
% 1.21/1.41 tff(399,plain,
% 1.21/1.41 (((~![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)))))))) | (~((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(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)))))))) | (~((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))))))))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(400,plain,
% 1.21/1.41 ((~((~(disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))))))) <=> (~((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))))))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(401,plain,
% 1.21/1.41 (((~![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(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(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)))))))) | (~((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))))))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[400])).
% 1.21/1.41 tff(402,plain,
% 1.21/1.41 (((~![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(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(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)))))))) | (~((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))))))))),
% 1.21/1.41 inference(transitivity,[status(thm)],[401, 399])).
% 1.21/1.41 tff(403,plain,
% 1.21/1.41 ((~![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(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))))))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(404,plain,
% 1.21/1.41 ((~![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)))))))) | (~((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))))))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.21/1.41 tff(405,plain,
% 1.21/1.41 (~((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))))))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[404, 398])).
% 1.21/1.42 tff(406,plain,
% 1.21/1.42 (((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))))) | ((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(tautology,[status(thm)],[])).
% 1.21/1.42 tff(407,plain,
% 1.21/1.42 ((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[406, 405])).
% 1.21/1.42 tff(408,plain,
% 1.21/1.42 ((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.42 inference(tautology,[status(thm)],[])).
% 1.21/1.42 tff(409,plain,
% 1.21/1.42 ((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[408, 407])).
% 1.21/1.42 tff(410,plain,
% 1.21/1.42 (disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[409, 379])).
% 1.21/1.42 tff(411,plain,
% 1.21/1.42 (((~((~((~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), s(n(e)))) | (~mem(tptp_fun_Z_1(u(p(s(n(n(e)))), s(n(n(n(e))))), s(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))))) | disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))))) | ((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))))),
% 1.21/1.42 inference(tautology,[status(thm)],[])).
% 1.21/1.42 tff(412,plain,
% 1.21/1.42 ((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[411, 405])).
% 1.21/1.42 tff(413,plain,
% 1.21/1.42 ((~((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))))) | (~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.42 inference(tautology,[status(thm)],[])).
% 1.21/1.42 tff(414,plain,
% 1.21/1.42 ((~disj(s(n(e)), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[413, 412])).
% 1.21/1.42 tff(415,plain,
% 1.21/1.42 (![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[414, 410])).
% 1.21/1.42 tff(416,plain,
% 1.21/1.42 (((~![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))) | ((~mem(a(e, e), s(n(e)))) | (~mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e))))))))) <=> ((~![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))) | (~mem(a(e, e), s(n(e)))) | (~mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(417,plain,
% 1.21/1.42 ((~![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))) | ((~mem(a(e, e), s(n(e)))) | (~mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(418,plain,
% 1.21/1.42 ((~![Z: $i] : ((~mem(Z, s(n(e)))) | (~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))) | (~mem(a(e, e), s(n(e)))) | (~mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.21/1.42 tff(419,plain,
% 1.21/1.42 (~mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[418, 415, 126])).
% 1.21/1.42 tff(420,assumption,(mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))), introduced(assumption)).
% 1.21/1.42 tff(421,assumption,(~mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e))))))), introduced(assumption)).
% 1.21/1.42 tff(422,assumption,(![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))), introduced(assumption)).
% 1.21/1.42 tff(423,plain,
% 1.21/1.42 (((~![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))) | ((~mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))))) <=> ((~![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(424,plain,
% 1.21/1.42 ((~![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))) | ((~mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(425,plain,
% 1.21/1.42 ((~![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))) | (~mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.21/1.42 tff(426,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[425, 422, 421, 420])).
% 1.21/1.42 tff(427,plain,((~![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))) | mem(a(e, e), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~mem(a(e, e), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(428,plain,
% 1.21/1.42 (~![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[427, 419, 165])).
% 1.21/1.42 tff(429,plain,
% 1.21/1.42 ((~![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(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))) | (~(subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(tptp_fun_Z_0(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))))))))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(430,plain,
% 1.21/1.42 (~((~((~subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))) | (~(subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(tptp_fun_Z_0(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[429, 16])).
% 1.21/1.42 tff(431,plain,
% 1.21/1.42 (((~((~subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))) | (~(subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(tptp_fun_Z_0(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))))))) | ((~subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.42 inference(tautology,[status(thm)],[])).
% 1.21/1.42 tff(432,plain,
% 1.21/1.42 ((~subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[431, 430])).
% 1.21/1.42 tff(433,plain,
% 1.21/1.42 ((~((~subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))))) | (~subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(tautology,[status(thm)],[])).
% 1.21/1.42 tff(434,plain,
% 1.21/1.42 ((~subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(Z, u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[433, 432])).
% 1.21/1.42 tff(435,plain,
% 1.21/1.42 (~subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[434, 428])).
% 1.21/1.42 tff(436,assumption,((~((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | (~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))), introduced(assumption)).
% 1.21/1.42 tff(437,plain,
% 1.21/1.42 ((~![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(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | (~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(438,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[437, 16, 436])).
% 1.21/1.42 tff(439,plain,(~((~((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | (~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(440,plain,
% 1.21/1.42 (((~((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | (~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))),
% 1.21/1.42 inference(tautology,[status(thm)],[])).
% 1.21/1.42 tff(441,plain,
% 1.21/1.42 (subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[440, 439])).
% 1.21/1.42 tff(442,plain,
% 1.21/1.42 (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[149])).
% 1.21/1.42 tff(443,plain,
% 1.21/1.42 (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) <=> mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.42 inference(symmetry,[status(thm)],[442])).
% 1.21/1.42 tff(444,plain,
% 1.21/1.42 ((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) <=> (~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[443])).
% 1.21/1.42 tff(445,assumption,(~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))), introduced(assumption)).
% 1.21/1.42 tff(446,plain,
% 1.21/1.42 (((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))),
% 1.21/1.43 inference(tautology,[status(thm)],[])).
% 1.21/1.43 tff(447,plain,
% 1.21/1.43 (~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[446, 445])).
% 1.21/1.43 tff(448,plain,
% 1.21/1.43 (~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[447, 444])).
% 1.21/1.43 tff(449,plain,
% 1.21/1.43 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(s(n(e)), s(s(s(n(e))))))))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(450,plain,
% 1.21/1.43 (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(s(n(e)), s(s(s(n(e)))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[449, 45])).
% 1.21/1.43 tff(451,plain,
% 1.21/1.43 (((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.43 inference(tautology,[status(thm)],[])).
% 1.21/1.43 tff(452,plain,
% 1.21/1.43 (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[451, 445])).
% 1.21/1.43 tff(453,plain,
% 1.21/1.43 ((mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(s(n(e)), s(s(s(n(e))))))) | (~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.43 inference(tautology,[status(thm)],[])).
% 1.21/1.43 tff(454,plain,
% 1.21/1.43 (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(s(n(e)), s(s(s(n(e))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[453, 452])).
% 1.21/1.43 tff(455,plain,
% 1.21/1.43 ((~(mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(s(n(e)), s(s(s(n(e))))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~(mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(s(n(e)), s(s(s(n(e))))))))),
% 1.21/1.43 inference(tautology,[status(thm)],[])).
% 1.21/1.43 tff(456,plain,
% 1.21/1.43 ((~(mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) <=> (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(s(n(e)), s(s(s(n(e))))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[455, 454])).
% 1.21/1.43 tff(457,plain,
% 1.21/1.43 (mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(u(s(n(e)), s(s(s(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[456, 450])).
% 1.21/1.43 tff(458,plain,
% 1.21/1.43 ($false),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[457, 448])).
% 1.21/1.43 tff(459,plain,((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.43 tff(460,plain,
% 1.21/1.43 ((~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.43 inference(tautology,[status(thm)],[])).
% 1.21/1.43 tff(461,plain,
% 1.21/1.43 ((~(subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | (~((~mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(tptp_fun_Z_0(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[460, 459])).
% 1.21/1.43 tff(462,plain,
% 1.21/1.43 (subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[461, 441])).
% 1.21/1.43 tff(463,plain,
% 1.21/1.43 (^[X: $i] : refl((~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))))) <=> (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))))))),
% 1.21/1.43 inference(bind,[status(th)],[])).
% 1.21/1.43 tff(464,plain,
% 1.21/1.43 (![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))))) <=> ![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))),
% 1.21/1.43 inference(quant_intro,[status(thm)],[463])).
% 1.21/1.43 tff(465,plain,
% 1.21/1.43 (^[X: $i] : rewrite((~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))))) <=> (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))))))),
% 1.21/1.43 inference(bind,[status(th)],[])).
% 1.21/1.43 tff(466,plain,
% 1.21/1.43 (![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))))) <=> ![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))),
% 1.21/1.43 inference(quant_intro,[status(thm)],[465])).
% 1.21/1.43 tff(467,plain,
% 1.21/1.43 (![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))))) <=> ![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))),
% 1.21/1.43 inference(transitivity,[status(thm)],[466, 464])).
% 1.21/1.43 tff(468,plain,
% 1.21/1.43 (^[X: $i] : trans(monotonicity(rewrite(((~atleast3p(X)) | (subq(tptp_fun_Y_3(X), X) & atleast2p(tptp_fun_Y_3(X)) & (~subq(X, tptp_fun_Y_3(X))))) <=> ((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))), rewrite((atleast3p(X) | ![Y: $i] : (~(subq(Y, X) & atleast2p(Y) & (~subq(X, Y))))) <=> (atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))), ((((~atleast3p(X)) | (subq(tptp_fun_Y_3(X), X) & atleast2p(tptp_fun_Y_3(X)) & (~subq(X, tptp_fun_Y_3(X))))) & (atleast3p(X) | ![Y: $i] : (~(subq(Y, X) & atleast2p(Y) & (~subq(X, Y)))))) <=> (((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X)))))) & (atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))))), rewrite((((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X)))))) & (atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y))))) <=> (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))), ((((~atleast3p(X)) | (subq(tptp_fun_Y_3(X), X) & atleast2p(tptp_fun_Y_3(X)) & (~subq(X, tptp_fun_Y_3(X))))) & (atleast3p(X) | ![Y: $i] : (~(subq(Y, X) & atleast2p(Y) & (~subq(X, Y)))))) <=> (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))))),
% 1.21/1.43 inference(bind,[status(th)],[])).
% 1.21/1.43 tff(469,plain,
% 1.21/1.43 (![X: $i] : (((~atleast3p(X)) | (subq(tptp_fun_Y_3(X), X) & atleast2p(tptp_fun_Y_3(X)) & (~subq(X, tptp_fun_Y_3(X))))) & (atleast3p(X) | ![Y: $i] : (~(subq(Y, X) & atleast2p(Y) & (~subq(X, Y)))))) <=> ![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))),
% 1.21/1.43 inference(quant_intro,[status(thm)],[468])).
% 1.21/1.43 tff(470,plain,
% 1.21/1.43 (![X: $i] : (atleast3p(X) <=> ?[Y: $i] : (subq(Y, X) & atleast2p(Y) & (~subq(X, Y)))) <=> ![X: $i] : (atleast3p(X) <=> ?[Y: $i] : (subq(Y, X) & atleast2p(Y) & (~subq(X, Y))))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(471,plain,
% 1.21/1.43 (^[X: $i] : rewrite((atleast3p(X) <=> ?[Y: $i] : ((subq(Y, X) & atleast2p(Y)) & (~subq(X, Y)))) <=> (atleast3p(X) <=> ?[Y: $i] : (subq(Y, X) & atleast2p(Y) & (~subq(X, Y)))))),
% 1.21/1.43 inference(bind,[status(th)],[])).
% 1.21/1.43 tff(472,plain,
% 1.21/1.43 (![X: $i] : (atleast3p(X) <=> ?[Y: $i] : ((subq(Y, X) & atleast2p(Y)) & (~subq(X, Y)))) <=> ![X: $i] : (atleast3p(X) <=> ?[Y: $i] : (subq(Y, X) & atleast2p(Y) & (~subq(X, Y))))),
% 1.21/1.43 inference(quant_intro,[status(thm)],[471])).
% 1.21/1.43 tff(473,axiom,(![X: $i] : (atleast3p(X) <=> ?[Y: $i] : ((subq(Y, X) & atleast2p(Y)) & (~subq(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','atleast3p_def')).
% 1.21/1.43 tff(474,plain,
% 1.21/1.43 (![X: $i] : (atleast3p(X) <=> ?[Y: $i] : (subq(Y, X) & atleast2p(Y) & (~subq(X, Y))))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[473, 472])).
% 1.21/1.43 tff(475,plain,
% 1.21/1.43 (![X: $i] : (atleast3p(X) <=> ?[Y: $i] : (subq(Y, X) & atleast2p(Y) & (~subq(X, Y))))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[474, 470])).
% 1.21/1.43 tff(476,plain,(
% 1.21/1.43 ![X: $i] : (((~atleast3p(X)) | (subq(tptp_fun_Y_3(X), X) & atleast2p(tptp_fun_Y_3(X)) & (~subq(X, tptp_fun_Y_3(X))))) & (atleast3p(X) | ![Y: $i] : (~(subq(Y, X) & atleast2p(Y) & (~subq(X, Y))))))),
% 1.21/1.43 inference(skolemize,[status(sab)],[475])).
% 1.21/1.43 tff(477,plain,
% 1.21/1.43 (![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[476, 469])).
% 1.21/1.43 tff(478,plain,
% 1.21/1.43 (![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[477, 467])).
% 1.21/1.43 tff(479,plain,
% 1.21/1.43 (((~![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))) | (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~((~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))))) <=> ((~![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))) | (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~((~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(480,plain,
% 1.21/1.43 ((~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~(subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~atleast2p(Y))))))) <=> (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~((~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(481,plain,
% 1.21/1.43 (((~![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))) | (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~(subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~atleast2p(Y)))))))) <=> ((~![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))) | (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~((~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[480])).
% 1.21/1.43 tff(482,plain,
% 1.21/1.43 (((~![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))) | (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~(subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~atleast2p(Y)))))))) <=> ((~![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))) | (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~((~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))))),
% 1.21/1.43 inference(transitivity,[status(thm)],[481, 479])).
% 1.21/1.43 tff(483,plain,
% 1.21/1.43 ((~![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))) | (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~(subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~atleast2p(Y)))))))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(484,plain,
% 1.21/1.43 ((~![X: $i] : (~((~((~atleast3p(X)) | (~(subq(X, tptp_fun_Y_3(X)) | (~subq(tptp_fun_Y_3(X), X)) | (~atleast2p(tptp_fun_Y_3(X))))))) | (~(atleast3p(X) | ![Y: $i] : (subq(X, Y) | (~subq(Y, X)) | (~atleast2p(Y)))))))) | (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~((~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.21/1.43 tff(485,plain,
% 1.21/1.43 (~((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~((~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[484, 478])).
% 1.21/1.43 tff(486,plain,
% 1.21/1.43 (((~((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | (~((~atleast2p(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) | (~subq(tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), tptp_fun_Y_3(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))))) | (atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))),
% 1.21/1.44 inference(tautology,[status(thm)],[])).
% 1.21/1.44 tff(487,plain,
% 1.21/1.44 (atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[486, 485])).
% 1.21/1.44 tff(488,plain,
% 1.21/1.44 ((~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))) <=> (~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(489,axiom,(~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','atleast3_2323')).
% 1.21/1.44 tff(490,plain,
% 1.21/1.44 (~atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[489, 488])).
% 1.21/1.44 tff(491,plain,
% 1.21/1.44 ((~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))) | atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.44 inference(tautology,[status(thm)],[])).
% 1.21/1.44 tff(492,plain,
% 1.21/1.44 ((~(atleast3p(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))) | ![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[491, 490])).
% 1.21/1.44 tff(493,plain,
% 1.21/1.44 (![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[492, 487])).
% 1.21/1.44 tff(494,plain,
% 1.21/1.44 (((~![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) <=> ((~![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(495,plain,
% 1.21/1.44 (((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))) <=> (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(496,plain,
% 1.21/1.44 (((~![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | ((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) <=> ((~![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))))),
% 1.21/1.44 inference(monotonicity,[status(thm)],[495])).
% 1.21/1.44 tff(497,plain,
% 1.21/1.44 (((~![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | ((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) <=> ((~![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.44 inference(transitivity,[status(thm)],[496, 494])).
% 1.21/1.44 tff(498,plain,
% 1.21/1.44 ((~![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | ((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))),
% 1.21/1.44 inference(quant_inst,[status(thm)],[])).
% 1.21/1.44 tff(499,plain,
% 1.21/1.44 ((~![Y: $i] : ((~atleast2p(Y)) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), Y) | (~subq(Y, u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))))))) | subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[498, 497])).
% 1.21/1.44 tff(500,plain,
% 1.21/1.44 (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e)))))))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[499, 493])).
% 1.21/1.44 tff(501,plain,
% 1.21/1.44 (subq(u(a(s(n(e)), s(s(n(e)))), a(p(s(n(n(e)))), n(n(n(e))))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[500, 462])).
% 1.21/1.44 tff(502,plain,
% 1.21/1.44 (~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[501, 435])).
% 1.21/1.44 tff(503,assumption,((~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e))))))))))))), introduced(assumption)).
% 1.21/1.44 tff(504,plain,
% 1.21/1.44 (^[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))))))))),
% 1.21/1.44 inference(bind,[status(th)],[])).
% 1.21/1.44 tff(505,plain,
% 1.21/1.44 (![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)))))))),
% 1.21/1.44 inference(quant_intro,[status(thm)],[504])).
% 1.21/1.44 tff(506,plain,
% 1.21/1.44 (^[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))))))))),
% 1.21/1.44 inference(bind,[status(th)],[])).
% 1.21/1.44 tff(507,plain,
% 1.21/1.44 (![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)))))))),
% 1.21/1.44 inference(quant_intro,[status(thm)],[506])).
% 1.21/1.44 tff(508,plain,
% 1.21/1.44 (![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)))))))),
% 1.21/1.44 inference(transitivity,[status(thm)],[507, 505])).
% 1.21/1.44 tff(509,plain,
% 1.21/1.44 (^[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)))))))))),
% 1.21/1.44 inference(bind,[status(th)],[])).
% 1.21/1.44 tff(510,plain,
% 1.21/1.44 (![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)))))))),
% 1.21/1.44 inference(quant_intro,[status(thm)],[509])).
% 1.21/1.44 tff(511,plain,
% 1.21/1.44 (![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)))))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(512,axiom,(![X: $i] : (atleast2p(X) <=> ?[Y: $i] : (mem(Y, X) & (~subq(X, p(Y)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax','atleast2p_def')).
% 1.21/1.44 tff(513,plain,
% 1.21/1.44 (![X: $i] : (atleast2p(X) <=> ?[Y: $i] : (mem(Y, X) & (~subq(X, p(Y)))))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[512, 511])).
% 1.21/1.44 tff(514,plain,(
% 1.21/1.44 ![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)))))))),
% 1.21/1.44 inference(skolemize,[status(sab)],[513])).
% 1.21/1.44 tff(515,plain,
% 1.21/1.44 (![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)))))))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[514, 510])).
% 1.21/1.44 tff(516,plain,
% 1.21/1.44 (![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)))))))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[515, 508])).
% 1.21/1.44 tff(517,plain,
% 1.21/1.44 (((~![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(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(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(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))))))))))))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(518,plain,
% 1.21/1.44 ((~((~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))))))))) | (~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))))) <=> (~((~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e))))))))))))))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(519,plain,
% 1.21/1.44 (((~![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(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))))))))) | (~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(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(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))))))))))))),
% 1.21/1.44 inference(monotonicity,[status(thm)],[518])).
% 1.21/1.44 tff(520,plain,
% 1.21/1.44 (((~![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(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))))))))) | (~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(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(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))))))))))))),
% 1.21/1.44 inference(transitivity,[status(thm)],[519, 517])).
% 1.21/1.44 tff(521,plain,
% 1.21/1.44 ((~![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(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))))))))) | (~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))))))),
% 1.21/1.44 inference(quant_inst,[status(thm)],[])).
% 1.21/1.44 tff(522,plain,
% 1.21/1.44 ((~![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(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e))))))))))))))),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.21/1.44 tff(523,plain,
% 1.21/1.44 ($false),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[522, 516, 503])).
% 1.21/1.44 tff(524,plain,(~((~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.44 tff(525,plain,
% 1.21/1.44 (((~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | (~((~atleast2p(u(p(s(n(n(e)))), s(n(n(n(e))))))) | (~((~mem(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e)))))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(tptp_fun_Y_2(u(p(s(n(n(e)))), s(n(n(n(e))))))))))))) | (atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))),
% 1.21/1.44 inference(tautology,[status(thm)],[])).
% 1.21/1.44 tff(526,plain,
% 1.21/1.44 (atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[525, 524])).
% 1.21/1.44 tff(527,plain,
% 1.21/1.44 ((~(atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y))))) | atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))),
% 1.21/1.44 inference(tautology,[status(thm)],[])).
% 1.21/1.44 tff(528,plain,
% 1.21/1.44 (atleast2p(u(p(s(n(n(e)))), s(n(n(n(e)))))) | ![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[527, 526])).
% 1.21/1.44 tff(529,plain,
% 1.21/1.44 (![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[528, 502])).
% 1.21/1.44 tff(530,plain,
% 1.21/1.44 (((~![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))) | ((~mem(e, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e)))) <=> ((~![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))) | (~mem(e, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e)))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(531,plain,
% 1.21/1.44 ((~![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))) | ((~mem(e, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e)))),
% 1.21/1.44 inference(quant_inst,[status(thm)],[])).
% 1.21/1.44 tff(532,plain,
% 1.21/1.44 ((~![Y: $i] : ((~mem(Y, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(Y)))) | (~mem(e, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))),
% 1.21/1.45 inference(modus_ponens,[status(thm)],[531, 530])).
% 1.21/1.45 tff(533,plain,
% 1.21/1.45 ((~mem(e, u(p(s(n(n(e)))), s(n(n(n(e))))))) | subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[532, 529])).
% 1.21/1.45 tff(534,plain,
% 1.21/1.45 (subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[533, 87])).
% 1.21/1.45 tff(535,plain,
% 1.21/1.45 ((~((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e))))) | (~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e)))),
% 1.21/1.45 inference(tautology,[status(thm)],[])).
% 1.21/1.45 tff(536,plain,
% 1.21/1.45 ((~((~subq(u(p(s(n(n(e)))), s(n(n(n(e))))), p(e))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e))))) | ![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e)))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[535, 534])).
% 1.21/1.45 tff(537,plain,
% 1.21/1.45 (![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e)))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[536, 34])).
% 1.21/1.45 tff(538,assumption,(~(mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))))), introduced(assumption)).
% 1.21/1.45 tff(539,plain,
% 1.21/1.45 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e))))))))),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(540,plain,
% 1.21/1.45 ((mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), s(n(n(n(e))))) | mem(s(n(n(e))), p(s(n(n(e))))))) <=> (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))))),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(541,plain,
% 1.21/1.45 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), s(n(n(n(e))))) | mem(s(n(n(e))), p(s(n(n(e)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e))))))))),
% 1.21/1.45 inference(monotonicity,[status(thm)],[540])).
% 1.21/1.45 tff(542,plain,
% 1.21/1.45 (((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), s(n(n(n(e))))) | mem(s(n(n(e))), p(s(n(n(e)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e))))))))),
% 1.21/1.45 inference(transitivity,[status(thm)],[541, 539])).
% 1.21/1.45 tff(543,plain,
% 1.21/1.45 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), s(n(n(n(e))))) | mem(s(n(n(e))), p(s(n(n(e)))))))),
% 1.21/1.45 inference(quant_inst,[status(thm)],[])).
% 1.21/1.45 tff(544,plain,
% 1.21/1.45 ((~![X: $i, Y: $i, Z: $i] : (mem(X, u(Y, Z)) <=> (mem(X, Z) | mem(X, Y)))) | (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))))),
% 1.21/1.45 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.21/1.45 tff(545,plain,
% 1.21/1.45 ($false),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[544, 45, 538])).
% 1.21/1.45 tff(546,plain,(mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.45 tff(547,plain,
% 1.21/1.45 ((~![X: $i, Y: $i] : (mem(X, p(Y)) <=> subq(X, Y))) | (mem(s(n(n(e))), p(s(n(n(e))))) <=> subq(s(n(n(e))), s(n(n(e)))))),
% 1.21/1.45 inference(quant_inst,[status(thm)],[])).
% 1.21/1.45 tff(548,plain,
% 1.21/1.45 (mem(s(n(n(e))), p(s(n(n(e))))) <=> subq(s(n(n(e))), s(n(n(e))))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[547, 27])).
% 1.21/1.45 tff(549,assumption,(~subq(s(n(n(e))), s(n(n(e))))), introduced(assumption)).
% 1.21/1.45 tff(550,plain,
% 1.21/1.45 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | subq(s(n(n(e))), s(n(n(e))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | subq(s(n(n(e))), s(n(n(e)))))),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(551,plain,
% 1.21/1.45 ((~(~subq(s(n(n(e))), s(n(n(e)))))) <=> subq(s(n(n(e))), s(n(n(e))))),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(552,plain,
% 1.21/1.45 (($false | (~subq(s(n(n(e))), s(n(n(e)))))) <=> (~subq(s(n(n(e))), s(n(n(e)))))),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(553,plain,
% 1.21/1.45 ((~(subq(s(n(n(e))), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e)))))))) <=> (~subq(s(n(n(e))), s(n(n(e)))))),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(554,plain,
% 1.21/1.45 ((~$true) <=> $false),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(555,plain,
% 1.21/1.45 (((~subq(s(n(n(e))), s(n(n(e))))) | $true) <=> $true),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(556,plain,
% 1.21/1.45 (![Z: $i] : $true <=> $true),
% 1.21/1.45 inference(elim_unused_vars,[status(thm)],[])).
% 1.21/1.45 tff(557,plain,
% 1.21/1.45 (![Z: $i] : $true <=> ![Z: $i] : $true),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(558,plain,
% 1.21/1.45 (![Z: $i] : $true <=> $true),
% 1.21/1.45 inference(transitivity,[status(thm)],[557, 556])).
% 1.21/1.45 tff(559,plain,
% 1.21/1.45 (^[Z: $i] : rewrite(((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))) <=> $true)),
% 1.21/1.45 inference(bind,[status(th)],[])).
% 1.21/1.45 tff(560,plain,
% 1.21/1.45 (![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))) <=> ![Z: $i] : $true),
% 1.21/1.45 inference(quant_intro,[status(thm)],[559])).
% 1.21/1.45 tff(561,plain,
% 1.21/1.45 (![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))) <=> $true),
% 1.21/1.45 inference(transitivity,[status(thm)],[560, 558])).
% 1.21/1.45 tff(562,plain,
% 1.21/1.45 (((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e)))))) <=> ((~subq(s(n(n(e))), s(n(n(e))))) | $true)),
% 1.21/1.45 inference(monotonicity,[status(thm)],[561])).
% 1.21/1.45 tff(563,plain,
% 1.21/1.45 (((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e)))))) <=> $true),
% 1.21/1.45 inference(transitivity,[status(thm)],[562, 555])).
% 1.21/1.45 tff(564,plain,
% 1.21/1.45 ((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) <=> (~$true)),
% 1.21/1.45 inference(monotonicity,[status(thm)],[563])).
% 1.21/1.45 tff(565,plain,
% 1.21/1.45 ((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) <=> $false),
% 1.21/1.45 inference(transitivity,[status(thm)],[564, 554])).
% 1.21/1.45 tff(566,plain,
% 1.21/1.45 (((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) | (~(subq(s(n(n(e))), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))))))) <=> ($false | (~subq(s(n(n(e))), s(n(n(e))))))),
% 1.21/1.45 inference(monotonicity,[status(thm)],[565, 553])).
% 1.21/1.45 tff(567,plain,
% 1.21/1.45 (((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) | (~(subq(s(n(n(e))), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))))))) <=> (~subq(s(n(n(e))), s(n(n(e)))))),
% 1.21/1.45 inference(transitivity,[status(thm)],[566, 552])).
% 1.21/1.45 tff(568,plain,
% 1.21/1.45 ((~((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) | (~(subq(s(n(n(e))), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e)))))))))) <=> (~(~subq(s(n(n(e))), s(n(n(e))))))),
% 1.21/1.45 inference(monotonicity,[status(thm)],[567])).
% 1.21/1.45 tff(569,plain,
% 1.21/1.45 ((~((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) | (~(subq(s(n(n(e))), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e)))))))))) <=> subq(s(n(n(e))), s(n(n(e))))),
% 1.21/1.45 inference(transitivity,[status(thm)],[568, 551])).
% 1.21/1.45 tff(570,plain,
% 1.21/1.45 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) | (~(subq(s(n(n(e))), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))))))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | subq(s(n(n(e))), s(n(n(e)))))),
% 1.21/1.45 inference(monotonicity,[status(thm)],[569])).
% 1.21/1.45 tff(571,plain,
% 1.21/1.45 (((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) | (~(subq(s(n(n(e))), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))))))))) <=> ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | subq(s(n(n(e))), s(n(n(e)))))),
% 1.21/1.45 inference(transitivity,[status(thm)],[570, 550])).
% 1.21/1.45 tff(572,plain,
% 1.21/1.45 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~subq(s(n(n(e))), s(n(n(e))))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, s(n(n(e))))))) | (~(subq(s(n(n(e))), s(n(n(e)))) | (~((~mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))) | mem(tptp_fun_Z_0(s(n(n(e))), s(n(n(e)))), s(n(n(e))))))))))),
% 1.21/1.45 inference(quant_inst,[status(thm)],[])).
% 1.21/1.45 tff(573,plain,
% 1.21/1.45 ((~![X: $i, Y: $i] : (~((~((~subq(X, Y)) | ![Z: $i] : ((~mem(Z, X)) | mem(Z, Y)))) | (~(subq(X, Y) | (~((~mem(tptp_fun_Z_0(Y, X), X)) | mem(tptp_fun_Z_0(Y, X), Y)))))))) | subq(s(n(n(e))), s(n(n(e))))),
% 1.21/1.45 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.21/1.45 tff(574,plain,
% 1.21/1.45 ($false),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[573, 16, 549])).
% 1.21/1.45 tff(575,plain,(subq(s(n(n(e))), s(n(n(e))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.45 tff(576,plain,
% 1.21/1.45 ((~(mem(s(n(n(e))), p(s(n(n(e))))) <=> subq(s(n(n(e))), s(n(n(e)))))) | mem(s(n(n(e))), p(s(n(n(e))))) | (~subq(s(n(n(e))), s(n(n(e)))))),
% 1.21/1.45 inference(tautology,[status(thm)],[])).
% 1.21/1.45 tff(577,plain,
% 1.21/1.45 ((~(mem(s(n(n(e))), p(s(n(n(e))))) <=> subq(s(n(n(e))), s(n(n(e)))))) | mem(s(n(n(e))), p(s(n(n(e)))))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[576, 575])).
% 1.21/1.45 tff(578,plain,
% 1.21/1.45 (mem(s(n(n(e))), p(s(n(n(e)))))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[577, 548])).
% 1.21/1.45 tff(579,plain,
% 1.21/1.45 ((mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))) | (~mem(s(n(n(e))), p(s(n(n(e))))))),
% 1.21/1.45 inference(tautology,[status(thm)],[])).
% 1.21/1.45 tff(580,plain,
% 1.21/1.45 (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[579, 578])).
% 1.21/1.45 tff(581,plain,
% 1.21/1.45 ((~(mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))))) | mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) | (~(mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))))),
% 1.21/1.45 inference(tautology,[status(thm)],[])).
% 1.21/1.45 tff(582,plain,
% 1.21/1.45 ((~(mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e)))))) <=> (mem(s(n(n(e))), p(s(n(n(e))))) | mem(s(n(n(e))), s(n(n(n(e)))))))) | mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[581, 580])).
% 1.21/1.45 tff(583,plain,
% 1.21/1.45 (mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[582, 546])).
% 1.21/1.45 tff(584,plain,
% 1.21/1.45 (((~![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e)))) | ((~mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(s(n(n(e))), p(e)))) <=> ((~![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e)))) | (~mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(s(n(n(e))), p(e)))),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(585,plain,
% 1.21/1.45 ((~![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e)))) | ((~mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(s(n(n(e))), p(e)))),
% 1.21/1.45 inference(quant_inst,[status(thm)],[])).
% 1.21/1.45 tff(586,plain,
% 1.21/1.45 ((~![Z: $i] : ((~mem(Z, u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(Z, p(e)))) | (~mem(s(n(n(e))), u(p(s(n(n(e)))), s(n(n(n(e))))))) | mem(s(n(n(e))), p(e))),
% 1.21/1.45 inference(modus_ponens,[status(thm)],[585, 584])).
% 1.21/1.45 tff(587,plain,
% 1.21/1.45 ($false),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[586, 583, 537, 30])).
% 1.21/1.45 tff(588,plain,(mem(s(n(n(e))), p(e))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.45 tff(589,plain,
% 1.21/1.45 ((~(mem(s(n(n(e))), p(e)) <=> subq(s(n(n(e))), e))) | (~mem(s(n(n(e))), p(e))) | subq(s(n(n(e))), e)),
% 1.21/1.45 inference(tautology,[status(thm)],[])).
% 1.21/1.45 tff(590,plain,
% 1.21/1.45 ((~(mem(s(n(n(e))), p(e)) <=> subq(s(n(n(e))), e))) | subq(s(n(n(e))), e)),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[589, 588])).
% 1.21/1.45 tff(591,plain,
% 1.21/1.45 (subq(s(n(n(e))), e)),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[590, 29])).
% 1.21/1.45 tff(592,plain,
% 1.21/1.45 ((~((~subq(s(n(n(e))), e)) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e)))) | (~subq(s(n(n(e))), e)) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e))),
% 1.21/1.45 inference(tautology,[status(thm)],[])).
% 1.21/1.45 tff(593,plain,
% 1.21/1.45 ((~((~subq(s(n(n(e))), e)) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e)))) | ![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[592, 591])).
% 1.21/1.45 tff(594,plain,
% 1.21/1.45 (![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e))),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[593, 20])).
% 1.21/1.45 tff(595,plain,
% 1.21/1.45 (((~![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e))) | ((~mem(a(n(e), n(e)), s(n(n(e))))) | mem(a(n(e), n(e)), e))) <=> ((~![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e))) | (~mem(a(n(e), n(e)), s(n(n(e))))) | mem(a(n(e), n(e)), e))),
% 1.21/1.45 inference(rewrite,[status(thm)],[])).
% 1.21/1.45 tff(596,plain,
% 1.21/1.45 ((~![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e))) | ((~mem(a(n(e), n(e)), s(n(n(e))))) | mem(a(n(e), n(e)), e))),
% 1.21/1.45 inference(quant_inst,[status(thm)],[])).
% 1.21/1.45 tff(597,plain,
% 1.21/1.45 ((~![Z: $i] : ((~mem(Z, s(n(n(e))))) | mem(Z, e))) | (~mem(a(n(e), n(e)), s(n(n(e))))) | mem(a(n(e), n(e)), e)),
% 1.21/1.45 inference(modus_ponens,[status(thm)],[596, 595])).
% 1.21/1.45 tff(598,plain,
% 1.21/1.45 ($false),
% 1.21/1.45 inference(unit_resolution,[status(thm)],[597, 335, 242, 594])).
% 1.21/1.45 % SZS output end Proof
% 1.21/1.45 % E exiting
%------------------------------------------------------------------------------