%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV097+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:31:30 AM UTC 2025
% Result : Theorem 145.47s 145.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV097+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:27:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 145.47/145.62 % SZS status Theorem
% 145.47/145.62 % SZS output start Proof
% 145.47/145.62 tff(use_type, type, (
% 145.47/145.62 use: $i)).
% 145.47/145.62 tff(a_select3_type, type, (
% 145.47/145.62 a_select3: ( $i * $i * $i ) > $i)).
% 145.47/145.62 tff(tptp_fun_F_13_type, type, (
% 145.47/145.62 tptp_fun_F_13: $i)).
% 145.47/145.62 tff(tptp_fun_E_14_type, type, (
% 145.47/145.62 tptp_fun_E_14: $i)).
% 145.47/145.62 tff(z_defuse_type, type, (
% 145.47/145.62 z_defuse: $i)).
% 145.47/145.62 tff(u_defuse_type, type, (
% 145.47/145.62 u_defuse: $i)).
% 145.47/145.62 tff(leq_type, type, (
% 145.47/145.62 leq: ( $i * $i ) > $o)).
% 145.47/145.62 tff(pv5_type, type, (
% 145.47/145.62 pv5: $i)).
% 145.47/145.62 tff(n2_type, type, (
% 145.47/145.62 n2: $i)).
% 145.47/145.62 tff(n0_type, type, (
% 145.47/145.62 n0: $i)).
% 145.47/145.62 tff(tptp_fun_H_15_type, type, (
% 145.47/145.62 tptp_fun_H_15: $i)).
% 145.47/145.62 tff(tptp_fun_G_16_type, type, (
% 145.47/145.62 tptp_fun_G_16: $i)).
% 145.47/145.62 tff(minus_type, type, (
% 145.47/145.62 minus: ( $i * $i ) > $i)).
% 145.47/145.62 tff(n1_type, type, (
% 145.47/145.62 n1: $i)).
% 145.47/145.62 tff(pred_type, type, (
% 145.47/145.62 pred: $i > $i)).
% 145.47/145.62 tff(succ_type, type, (
% 145.47/145.62 succ: $i > $i)).
% 145.47/145.62 tff(gt_type, type, (
% 145.47/145.62 gt: ( $i * $i ) > $o)).
% 145.47/145.62 tff(n999_type, type, (
% 145.47/145.62 n999: $i)).
% 145.47/145.62 tff(a_select2_type, type, (
% 145.47/145.62 a_select2: ( $i * $i ) > $i)).
% 145.47/145.62 tff(n5_type, type, (
% 145.47/145.62 n5: $i)).
% 145.47/145.62 tff(xinit_noise_defuse_type, type, (
% 145.47/145.62 xinit_noise_defuse: $i)).
% 145.47/145.62 tff(n4_type, type, (
% 145.47/145.62 n4: $i)).
% 145.47/145.62 tff(n3_type, type, (
% 145.47/145.62 n3: $i)).
% 145.47/145.62 tff(xinit_mean_defuse_type, type, (
% 145.47/145.62 xinit_mean_defuse: $i)).
% 145.47/145.62 tff(xinit_defuse_type, type, (
% 145.47/145.62 xinit_defuse: $i)).
% 145.47/145.62 tff(sigma_defuse_type, type, (
% 145.47/145.62 sigma_defuse: $i)).
% 145.47/145.62 tff(rho_defuse_type, type, (
% 145.47/145.62 rho_defuse: $i)).
% 145.47/145.62 tff(1,plain,
% 145.47/145.62 (^[X: $i] : refl((minus(X, n1) = pred(X)) <=> (minus(X, n1) = pred(X)))),
% 145.47/145.62 inference(bind,[status(th)],[])).
% 145.47/145.62 tff(2,plain,
% 145.47/145.62 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 145.47/145.62 inference(quant_intro,[status(thm)],[1])).
% 145.47/145.62 tff(3,plain,
% 145.47/145.62 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 145.47/145.62 inference(rewrite,[status(thm)],[])).
% 145.47/145.62 tff(4,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 145.47/145.62 tff(5,plain,
% 145.47/145.62 (![X: $i] : (minus(X, n1) = pred(X))),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[4, 3])).
% 145.47/145.62 tff(6,plain,(
% 145.47/145.62 ![X: $i] : (minus(X, n1) = pred(X))),
% 145.47/145.62 inference(skolemize,[status(sab)],[5])).
% 145.47/145.62 tff(7,plain,
% 145.47/145.62 (![X: $i] : (minus(X, n1) = pred(X))),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[6, 2])).
% 145.47/145.62 tff(8,plain,
% 145.47/145.62 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(pv5, n1) = pred(pv5))),
% 145.47/145.62 inference(quant_inst,[status(thm)],[])).
% 145.47/145.62 tff(9,plain,
% 145.47/145.62 (minus(pv5, n1) = pred(pv5)),
% 145.47/145.62 inference(unit_resolution,[status(thm)],[8, 7])).
% 145.47/145.62 tff(10,plain,
% 145.47/145.62 (pred(pv5) = minus(pv5, n1)),
% 145.47/145.62 inference(symmetry,[status(thm)],[9])).
% 145.47/145.62 tff(11,plain,
% 145.47/145.62 (leq(H!15, pred(pv5)) <=> leq(H!15, minus(pv5, n1))),
% 145.47/145.62 inference(monotonicity,[status(thm)],[10])).
% 145.47/145.62 tff(12,plain,
% 145.47/145.62 (leq(H!15, minus(pv5, n1)) <=> leq(H!15, pred(pv5))),
% 145.47/145.62 inference(symmetry,[status(thm)],[11])).
% 145.47/145.62 tff(13,assumption,(~((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))))), introduced(assumption)).
% 145.47/145.62 tff(14,plain,
% 145.47/145.62 (((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))) | leq(H!15, minus(pv5, n1))),
% 145.47/145.62 inference(tautology,[status(thm)],[])).
% 145.47/145.62 tff(15,plain,
% 145.47/145.62 (leq(H!15, minus(pv5, n1))),
% 145.47/145.62 inference(unit_resolution,[status(thm)],[14, 13])).
% 145.47/145.62 tff(16,plain,
% 145.47/145.62 (leq(H!15, pred(pv5))),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[15, 12])).
% 145.47/145.62 tff(17,plain,
% 145.47/145.62 (^[X: $i, Y: $i] : refl((leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> (leq(succ(X), succ(Y)) <=> leq(X, Y)))),
% 145.47/145.62 inference(bind,[status(th)],[])).
% 145.47/145.62 tff(18,plain,
% 145.47/145.62 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 145.47/145.62 inference(quant_intro,[status(thm)],[17])).
% 145.47/145.62 tff(19,plain,
% 145.47/145.62 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 145.47/145.62 inference(rewrite,[status(thm)],[])).
% 145.47/145.62 tff(20,axiom,(![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_succ_succ')).
% 145.47/145.62 tff(21,plain,
% 145.47/145.62 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[20, 19])).
% 145.47/145.62 tff(22,plain,(
% 145.47/145.62 ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 145.47/145.62 inference(skolemize,[status(sab)],[21])).
% 145.47/145.62 tff(23,plain,
% 145.47/145.62 (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[22, 18])).
% 145.47/145.62 tff(24,plain,
% 145.47/145.62 ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(pred(pv5)), succ(pv5)) <=> leq(pred(pv5), pv5))),
% 145.47/145.62 inference(quant_inst,[status(thm)],[])).
% 145.47/145.62 tff(25,plain,
% 145.47/145.62 (leq(succ(pred(pv5)), succ(pv5)) <=> leq(pred(pv5), pv5)),
% 145.47/145.62 inference(unit_resolution,[status(thm)],[24, 23])).
% 145.47/145.62 tff(26,plain,
% 145.47/145.62 (![X: $i] : (succ(pred(X)) = X) <=> ![X: $i] : (succ(pred(X)) = X)),
% 145.47/145.62 inference(rewrite,[status(thm)],[])).
% 145.47/145.62 tff(27,plain,
% 145.47/145.62 (![X: $i] : (succ(pred(X)) = X) <=> ![X: $i] : (succ(pred(X)) = X)),
% 145.47/145.62 inference(rewrite,[status(thm)],[])).
% 145.47/145.62 tff(28,axiom,(![X: $i] : (succ(pred(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','succ_pred')).
% 145.47/145.62 tff(29,plain,
% 145.47/145.62 (![X: $i] : (succ(pred(X)) = X)),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[28, 27])).
% 145.47/145.62 tff(30,plain,(
% 145.47/145.62 ![X: $i] : (succ(pred(X)) = X)),
% 145.47/145.62 inference(skolemize,[status(sab)],[29])).
% 145.47/145.62 tff(31,plain,
% 145.47/145.62 (![X: $i] : (succ(pred(X)) = X)),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[30, 26])).
% 145.47/145.62 tff(32,plain,
% 145.47/145.62 ((~![X: $i] : (succ(pred(X)) = X)) | (succ(pred(pv5)) = pv5)),
% 145.47/145.62 inference(quant_inst,[status(thm)],[])).
% 145.47/145.62 tff(33,plain,
% 145.47/145.62 (succ(pred(pv5)) = pv5),
% 145.47/145.62 inference(unit_resolution,[status(thm)],[32, 31])).
% 145.47/145.62 tff(34,plain,
% 145.47/145.62 (leq(succ(pred(pv5)), succ(pv5)) <=> leq(pv5, succ(pv5))),
% 145.47/145.62 inference(monotonicity,[status(thm)],[33])).
% 145.47/145.62 tff(35,plain,
% 145.47/145.62 (leq(pv5, succ(pv5)) <=> leq(succ(pred(pv5)), succ(pv5))),
% 145.47/145.62 inference(symmetry,[status(thm)],[34])).
% 145.47/145.62 tff(36,plain,
% 145.47/145.62 (^[X: $i] : refl(gt(succ(X), X) <=> gt(succ(X), X))),
% 145.47/145.62 inference(bind,[status(th)],[])).
% 145.47/145.62 tff(37,plain,
% 145.47/145.62 (![X: $i] : gt(succ(X), X) <=> ![X: $i] : gt(succ(X), X)),
% 145.47/145.62 inference(quant_intro,[status(thm)],[36])).
% 145.47/145.62 tff(38,plain,
% 145.47/145.62 (![X: $i] : gt(succ(X), X) <=> ![X: $i] : gt(succ(X), X)),
% 145.47/145.62 inference(rewrite,[status(thm)],[])).
% 145.47/145.62 tff(39,axiom,(![X: $i] : gt(succ(X), X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','gt_succ')).
% 145.47/145.62 tff(40,plain,
% 145.47/145.62 (![X: $i] : gt(succ(X), X)),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[39, 38])).
% 145.47/145.62 tff(41,plain,(
% 145.47/145.62 ![X: $i] : gt(succ(X), X)),
% 145.47/145.62 inference(skolemize,[status(sab)],[40])).
% 145.47/145.62 tff(42,plain,
% 145.47/145.62 (![X: $i] : gt(succ(X), X)),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[41, 37])).
% 145.47/145.62 tff(43,plain,
% 145.47/145.62 ((~![X: $i] : gt(succ(X), X)) | gt(succ(pv5), pv5)),
% 145.47/145.62 inference(quant_inst,[status(thm)],[])).
% 145.47/145.62 tff(44,plain,
% 145.47/145.62 (gt(succ(pv5), pv5)),
% 145.47/145.62 inference(unit_resolution,[status(thm)],[43, 42])).
% 145.47/145.62 tff(45,plain,
% 145.47/145.62 (^[X: $i, Y: $i] : refl(((~gt(Y, X)) | leq(X, Y)) <=> ((~gt(Y, X)) | leq(X, Y)))),
% 145.47/145.62 inference(bind,[status(th)],[])).
% 145.47/145.62 tff(46,plain,
% 145.47/145.62 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 145.47/145.62 inference(quant_intro,[status(thm)],[45])).
% 145.47/145.62 tff(47,plain,
% 145.47/145.62 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 145.47/145.62 inference(rewrite,[status(thm)],[])).
% 145.47/145.62 tff(48,plain,
% 145.47/145.62 (^[X: $i, Y: $i] : rewrite((gt(Y, X) => leq(X, Y)) <=> ((~gt(Y, X)) | leq(X, Y)))),
% 145.47/145.62 inference(bind,[status(th)],[])).
% 145.47/145.62 tff(49,plain,
% 145.47/145.62 (![X: $i, Y: $i] : (gt(Y, X) => leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 145.47/145.62 inference(quant_intro,[status(thm)],[48])).
% 145.47/145.62 tff(50,axiom,(![X: $i, Y: $i] : (gt(Y, X) => leq(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt1')).
% 145.47/145.62 tff(51,plain,
% 145.47/145.62 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[50, 49])).
% 145.47/145.62 tff(52,plain,
% 145.47/145.62 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 145.47/145.62 inference(modus_ponens,[status(thm)],[51, 47])).
% 145.47/145.62 tff(53,plain,(
% 145.47/145.62 ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 145.47/145.62 inference(skolemize,[status(sab)],[52])).
% 145.47/145.63 tff(54,plain,
% 145.47/145.63 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 145.47/145.63 inference(modus_ponens,[status(thm)],[53, 46])).
% 145.47/145.63 tff(55,plain,
% 145.47/145.63 (((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(succ(pv5), pv5)) | leq(pv5, succ(pv5)))) <=> ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(succ(pv5), pv5)) | leq(pv5, succ(pv5)))),
% 145.47/145.63 inference(rewrite,[status(thm)],[])).
% 145.47/145.63 tff(56,plain,
% 145.47/145.63 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(succ(pv5), pv5)) | leq(pv5, succ(pv5)))),
% 145.47/145.63 inference(quant_inst,[status(thm)],[])).
% 145.47/145.63 tff(57,plain,
% 145.47/145.63 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(succ(pv5), pv5)) | leq(pv5, succ(pv5))),
% 145.47/145.63 inference(modus_ponens,[status(thm)],[56, 55])).
% 145.47/145.63 tff(58,plain,
% 145.47/145.63 (leq(pv5, succ(pv5))),
% 145.47/145.63 inference(unit_resolution,[status(thm)],[57, 54, 44])).
% 145.47/145.63 tff(59,plain,
% 145.47/145.63 (leq(succ(pred(pv5)), succ(pv5))),
% 145.47/145.63 inference(modus_ponens,[status(thm)],[58, 35])).
% 145.47/145.63 tff(60,plain,
% 145.47/145.63 ((~(leq(succ(pred(pv5)), succ(pv5)) <=> leq(pred(pv5), pv5))) | (~leq(succ(pred(pv5)), succ(pv5))) | leq(pred(pv5), pv5)),
% 145.47/145.63 inference(tautology,[status(thm)],[])).
% 145.47/145.63 tff(61,plain,
% 145.47/145.63 (leq(pred(pv5), pv5)),
% 145.47/145.63 inference(unit_resolution,[status(thm)],[60, 59, 25])).
% 145.47/145.63 tff(62,plain,
% 145.47/145.63 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 145.47/145.63 inference(rewrite,[status(thm)],[])).
% 145.47/145.63 tff(63,plain,
% 145.47/145.63 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 145.47/145.63 inference(bind,[status(th)],[])).
% 145.47/145.63 tff(64,plain,
% 145.47/145.63 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 145.47/145.63 inference(quant_intro,[status(thm)],[63])).
% 145.47/145.63 tff(65,plain,
% 145.47/145.63 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 145.47/145.63 inference(rewrite,[status(thm)],[])).
% 145.47/145.63 tff(66,plain,
% 145.47/145.63 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 145.47/145.63 inference(bind,[status(th)],[])).
% 145.47/145.63 tff(67,plain,
% 145.47/145.63 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 145.47/145.63 inference(quant_intro,[status(thm)],[66])).
% 145.47/145.63 tff(68,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 145.47/145.63 tff(69,plain,
% 145.47/145.63 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 145.47/145.63 inference(modus_ponens,[status(thm)],[68, 67])).
% 145.47/145.63 tff(70,plain,
% 145.47/145.63 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 145.47/145.63 inference(modus_ponens,[status(thm)],[69, 65])).
% 145.47/145.63 tff(71,plain,(
% 145.47/145.63 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 145.47/145.63 inference(skolemize,[status(sab)],[70])).
% 145.47/145.63 tff(72,plain,
% 145.47/145.63 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 145.47/145.63 inference(modus_ponens,[status(thm)],[71, 64])).
% 145.47/145.63 tff(73,plain,
% 145.47/145.63 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 145.47/145.63 inference(modus_ponens,[status(thm)],[72, 62])).
% 145.47/145.63 tff(74,plain,
% 145.47/145.63 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))) | leq(H!15, pv5))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))) | leq(H!15, pv5))),
% 145.47/145.63 inference(rewrite,[status(thm)],[])).
% 145.47/145.63 tff(75,plain,
% 145.47/145.63 ((leq(H!15, pv5) | (~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5)))) <=> ((~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))) | leq(H!15, pv5))),
% 145.47/145.63 inference(rewrite,[status(thm)],[])).
% 145.47/145.63 tff(76,plain,
% 145.47/145.63 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(H!15, pv5) | (~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))) | leq(H!15, pv5)))),
% 145.47/145.63 inference(monotonicity,[status(thm)],[75])).
% 145.47/145.63 tff(77,plain,
% 145.47/145.63 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(H!15, pv5) | (~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))) | leq(H!15, pv5))),
% 145.47/145.63 inference(transitivity,[status(thm)],[76, 74])).
% 145.47/145.63 tff(78,plain,
% 145.47/145.63 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(H!15, pv5) | (~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))))),
% 145.47/145.63 inference(quant_inst,[status(thm)],[])).
% 145.47/145.63 tff(79,plain,
% 145.47/145.63 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pred(pv5), pv5)) | (~leq(H!15, pred(pv5))) | leq(H!15, pv5)),
% 145.47/145.63 inference(modus_ponens,[status(thm)],[78, 77])).
% 145.47/145.63 tff(80,plain,
% 145.47/145.63 ((~leq(H!15, pred(pv5))) | leq(H!15, pv5)),
% 145.47/145.63 inference(unit_resolution,[status(thm)],[79, 73, 61])).
% 145.47/145.63 tff(81,plain,
% 145.47/145.63 (leq(H!15, pv5)),
% 145.47/145.63 inference(unit_resolution,[status(thm)],[80, 16])).
% 145.47/145.63 tff(82,plain,
% 145.47/145.63 (((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))) | ((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))),
% 145.47/145.63 inference(tautology,[status(thm)],[])).
% 145.47/145.63 tff(83,plain,
% 145.47/145.63 ((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))),
% 145.47/145.63 inference(unit_resolution,[status(thm)],[82, 13])).
% 145.47/145.63 tff(84,plain,
% 145.47/145.63 (((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))) | leq(G!16, n2)),
% 145.47/145.63 inference(tautology,[status(thm)],[])).
% 145.47/145.63 tff(85,plain,
% 145.47/145.63 (leq(G!16, n2)),
% 145.47/145.63 inference(unit_resolution,[status(thm)],[84, 13])).
% 145.47/145.63 tff(86,plain,
% 145.47/145.63 (((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))) | leq(n0, H!15)),
% 145.47/145.63 inference(tautology,[status(thm)],[])).
% 145.47/145.63 tff(87,plain,
% 145.47/145.63 (leq(n0, H!15)),
% 145.47/145.63 inference(unit_resolution,[status(thm)],[86, 13])).
% 145.47/145.63 tff(88,plain,
% 145.47/145.63 (((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))) | leq(n0, G!16)),
% 145.47/145.63 inference(tautology,[status(thm)],[])).
% 145.47/145.63 tff(89,plain,
% 145.47/145.63 (leq(n0, G!16)),
% 145.47/145.63 inference(unit_resolution,[status(thm)],[88, 13])).
% 145.47/145.63 tff(90,plain,
% 145.47/145.63 (^[A: $i, B: $i] : refl(((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use))))) <=> ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use))))))),
% 145.47/145.63 inference(bind,[status(th)],[])).
% 145.47/145.63 tff(91,plain,
% 145.47/145.63 (![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use))))) <=> ![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))),
% 145.47/145.63 inference(quant_intro,[status(thm)],[90])).
% 145.47/145.63 tff(92,plain,
% 145.47/145.63 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5)) <=> (~((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5))))), ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) <=> (~(~((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5))))))), rewrite((~(~((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5))))) <=> ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)))), ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) <=> ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5))))), rewrite(((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)) <=> (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use))))), (((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))) <=> (((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5))) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use))))))), rewrite((((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5))) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use))))) <=> ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))), (((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))) <=> ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))))),
% 145.47/145.63 inference(bind,[status(th)],[])).
% 145.47/145.63 tff(93,plain,
% 145.47/145.63 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))) <=> ![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))),
% 145.47/145.63 inference(quant_intro,[status(thm)],[92])).
% 145.47/145.63 tff(94,plain,
% 145.47/145.63 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))) <=> ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 145.47/145.63 inference(rewrite,[status(thm)],[])).
% 145.47/145.63 tff(95,plain,
% 145.47/145.63 ((~((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pv5)) => ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, minus(pv5, n1))) => ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))) => (((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, minus(n999, n1))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, n2)) & leq(H, minus(pv5, n1))) => ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use)))))) <=> (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))) | ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use))))))),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(96,axiom,(~((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pv5)) => ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, minus(pv5, n1))) => ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))) => (((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, minus(n999, n1))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, n2)) & leq(H, minus(pv5, n1))) => ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0009')).
% 145.47/145.64 tff(97,plain,
% 145.47/145.64 (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))) | ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use)))))),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[96, 95])).
% 145.47/145.64 tff(98,plain,
% 145.47/145.64 ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))),
% 145.47/145.64 inference(or_elim,[status(thm)],[97])).
% 145.47/145.64 tff(99,plain,
% 145.47/145.64 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(100,plain,
% 145.47/145.64 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[99, 94])).
% 145.47/145.64 tff(101,plain,(
% 145.47/145.64 ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pv5))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 145.47/145.64 inference(skolemize,[status(sab)],[100])).
% 145.47/145.64 tff(102,plain,
% 145.47/145.64 (![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[101, 93])).
% 145.47/145.64 tff(103,plain,
% 145.47/145.64 (![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[102, 91])).
% 145.47/145.64 tff(104,plain,
% 145.47/145.64 (((~![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))) | ((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))) | (~leq(H!15, pv5)))) <=> ((~![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))) | (~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))) | (~leq(H!15, pv5)))),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(105,plain,
% 145.47/145.64 (((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, pv5)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))) <=> ((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))) | (~leq(H!15, pv5)))),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(106,plain,
% 145.47/145.64 (((~![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))) | ((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, pv5)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))))) <=> ((~![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))) | ((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))) | (~leq(H!15, pv5))))),
% 145.47/145.64 inference(monotonicity,[status(thm)],[105])).
% 145.47/145.64 tff(107,plain,
% 145.47/145.64 (((~![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))) | ((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, pv5)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))))) <=> ((~![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))) | (~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))) | (~leq(H!15, pv5)))),
% 145.47/145.64 inference(transitivity,[status(thm)],[106, 104])).
% 145.47/145.64 tff(108,plain,
% 145.47/145.64 ((~![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))) | ((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, pv5)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))))),
% 145.47/145.64 inference(quant_inst,[status(thm)],[])).
% 145.47/145.64 tff(109,plain,
% 145.47/145.64 ((~![A: $i, B: $i] : ((~leq(n0, A)) | (~leq(n0, B)) | (~leq(A, n2)) | (~leq(B, pv5)) | (~((~(a_select3(u_defuse, A, B) = use)) | (~(a_select3(z_defuse, A, B) = use)))))) | (~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))) | (~leq(H!15, pv5))),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[108, 107])).
% 145.47/145.64 tff(110,plain,
% 145.47/145.64 ($false),
% 145.47/145.64 inference(unit_resolution,[status(thm)],[109, 103, 89, 87, 85, 83, 81])).
% 145.47/145.64 tff(111,plain,((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))), inference(lemma,lemma(discharge,[]))).
% 145.47/145.64 tff(112,plain,
% 145.47/145.64 (leq(pv5, minus(n999, n1)) <=> leq(pv5, minus(n999, n1))),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(113,plain,
% 145.47/145.64 (leq(pv5, minus(n999, n1))),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(114,plain,
% 145.47/145.64 (leq(pv5, minus(n999, n1))),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[113, 112])).
% 145.47/145.64 tff(115,plain,
% 145.47/145.64 (leq(n0, pv5) <=> leq(n0, pv5)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(116,plain,
% 145.47/145.64 (leq(n0, pv5)),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(117,plain,
% 145.47/145.64 (leq(n0, pv5)),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[116, 115])).
% 145.47/145.64 tff(118,plain,
% 145.47/145.64 ((a_select2(xinit_noise_defuse, n5) = use) <=> (a_select2(xinit_noise_defuse, n5) = use)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(119,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n5) = use),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(120,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n5) = use),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[119, 118])).
% 145.47/145.64 tff(121,plain,
% 145.47/145.64 ((a_select2(xinit_noise_defuse, n4) = use) <=> (a_select2(xinit_noise_defuse, n4) = use)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(122,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n4) = use),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(123,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n4) = use),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[122, 121])).
% 145.47/145.64 tff(124,plain,
% 145.47/145.64 ((a_select2(xinit_noise_defuse, n3) = use) <=> (a_select2(xinit_noise_defuse, n3) = use)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(125,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n3) = use),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(126,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n3) = use),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[125, 124])).
% 145.47/145.64 tff(127,plain,
% 145.47/145.64 ((a_select2(xinit_noise_defuse, n2) = use) <=> (a_select2(xinit_noise_defuse, n2) = use)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(128,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n2) = use),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(129,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n2) = use),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[128, 127])).
% 145.47/145.64 tff(130,plain,
% 145.47/145.64 ((a_select2(xinit_noise_defuse, n1) = use) <=> (a_select2(xinit_noise_defuse, n1) = use)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(131,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n1) = use),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(132,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n1) = use),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[131, 130])).
% 145.47/145.64 tff(133,plain,
% 145.47/145.64 ((a_select2(xinit_noise_defuse, n0) = use) <=> (a_select2(xinit_noise_defuse, n0) = use)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(134,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n0) = use),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(135,plain,
% 145.47/145.64 (a_select2(xinit_noise_defuse, n0) = use),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[134, 133])).
% 145.47/145.64 tff(136,plain,
% 145.47/145.64 ((a_select2(xinit_mean_defuse, n5) = use) <=> (a_select2(xinit_mean_defuse, n5) = use)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(137,plain,
% 145.47/145.64 (a_select2(xinit_mean_defuse, n5) = use),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(138,plain,
% 145.47/145.64 (a_select2(xinit_mean_defuse, n5) = use),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[137, 136])).
% 145.47/145.64 tff(139,plain,
% 145.47/145.64 ((a_select2(xinit_mean_defuse, n4) = use) <=> (a_select2(xinit_mean_defuse, n4) = use)),
% 145.47/145.64 inference(rewrite,[status(thm)],[])).
% 145.47/145.64 tff(140,plain,
% 145.47/145.64 (a_select2(xinit_mean_defuse, n4) = use),
% 145.47/145.64 inference(and_elim,[status(thm)],[98])).
% 145.47/145.64 tff(141,plain,
% 145.47/145.64 (a_select2(xinit_mean_defuse, n4) = use),
% 145.47/145.64 inference(modus_ponens,[status(thm)],[140, 139])).
% 145.47/145.64 tff(142,plain,
% 145.47/145.64 ((a_select2(xinit_mean_defuse, n3) = use) <=> (a_select2(xinit_mean_defuse, n3) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(143,plain,
% 145.47/145.65 (a_select2(xinit_mean_defuse, n3) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(144,plain,
% 145.47/145.65 (a_select2(xinit_mean_defuse, n3) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[143, 142])).
% 145.47/145.65 tff(145,plain,
% 145.47/145.65 ((a_select2(xinit_mean_defuse, n2) = use) <=> (a_select2(xinit_mean_defuse, n2) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(146,plain,
% 145.47/145.65 (a_select2(xinit_mean_defuse, n2) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(147,plain,
% 145.47/145.65 (a_select2(xinit_mean_defuse, n2) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[146, 145])).
% 145.47/145.65 tff(148,plain,
% 145.47/145.65 ((a_select2(xinit_mean_defuse, n1) = use) <=> (a_select2(xinit_mean_defuse, n1) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(149,plain,
% 145.47/145.65 (a_select2(xinit_mean_defuse, n1) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(150,plain,
% 145.47/145.65 (a_select2(xinit_mean_defuse, n1) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[149, 148])).
% 145.47/145.65 tff(151,plain,
% 145.47/145.65 ((a_select2(xinit_mean_defuse, n0) = use) <=> (a_select2(xinit_mean_defuse, n0) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(152,plain,
% 145.47/145.65 (a_select2(xinit_mean_defuse, n0) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(153,plain,
% 145.47/145.65 (a_select2(xinit_mean_defuse, n0) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[152, 151])).
% 145.47/145.65 tff(154,plain,
% 145.47/145.65 ((a_select2(xinit_defuse, n5) = use) <=> (a_select2(xinit_defuse, n5) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(155,plain,
% 145.47/145.65 (a_select2(xinit_defuse, n5) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(156,plain,
% 145.47/145.65 (a_select2(xinit_defuse, n5) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[155, 154])).
% 145.47/145.65 tff(157,plain,
% 145.47/145.65 ((a_select2(xinit_defuse, n4) = use) <=> (a_select2(xinit_defuse, n4) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(158,plain,
% 145.47/145.65 (a_select2(xinit_defuse, n4) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(159,plain,
% 145.47/145.65 (a_select2(xinit_defuse, n4) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[158, 157])).
% 145.47/145.65 tff(160,plain,
% 145.47/145.65 ((a_select2(xinit_defuse, n3) = use) <=> (a_select2(xinit_defuse, n3) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(161,plain,
% 145.47/145.65 (a_select2(xinit_defuse, n3) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(162,plain,
% 145.47/145.65 (a_select2(xinit_defuse, n3) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[161, 160])).
% 145.47/145.65 tff(163,plain,
% 145.47/145.65 ((a_select3(u_defuse, n2, n0) = use) <=> (a_select3(u_defuse, n2, n0) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(164,plain,
% 145.47/145.65 (a_select3(u_defuse, n2, n0) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(165,plain,
% 145.47/145.65 (a_select3(u_defuse, n2, n0) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[164, 163])).
% 145.47/145.65 tff(166,plain,
% 145.47/145.65 ((a_select3(u_defuse, n1, n0) = use) <=> (a_select3(u_defuse, n1, n0) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(167,plain,
% 145.47/145.65 (a_select3(u_defuse, n1, n0) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(168,plain,
% 145.47/145.65 (a_select3(u_defuse, n1, n0) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[167, 166])).
% 145.47/145.65 tff(169,plain,
% 145.47/145.65 ((a_select3(u_defuse, n0, n0) = use) <=> (a_select3(u_defuse, n0, n0) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(170,plain,
% 145.47/145.65 (a_select3(u_defuse, n0, n0) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(171,plain,
% 145.47/145.65 (a_select3(u_defuse, n0, n0) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[170, 169])).
% 145.47/145.65 tff(172,plain,
% 145.47/145.65 ((a_select2(sigma_defuse, n5) = use) <=> (a_select2(sigma_defuse, n5) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(173,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n5) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(174,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n5) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[173, 172])).
% 145.47/145.65 tff(175,plain,
% 145.47/145.65 ((a_select2(sigma_defuse, n4) = use) <=> (a_select2(sigma_defuse, n4) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(176,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n4) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(177,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n4) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[176, 175])).
% 145.47/145.65 tff(178,plain,
% 145.47/145.65 ((a_select2(sigma_defuse, n3) = use) <=> (a_select2(sigma_defuse, n3) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(179,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n3) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(180,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n3) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[179, 178])).
% 145.47/145.65 tff(181,plain,
% 145.47/145.65 ((a_select2(sigma_defuse, n2) = use) <=> (a_select2(sigma_defuse, n2) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(182,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n2) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(183,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n2) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[182, 181])).
% 145.47/145.65 tff(184,plain,
% 145.47/145.65 ((a_select2(sigma_defuse, n1) = use) <=> (a_select2(sigma_defuse, n1) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(185,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n1) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(186,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n1) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[185, 184])).
% 145.47/145.65 tff(187,plain,
% 145.47/145.65 ((a_select2(sigma_defuse, n0) = use) <=> (a_select2(sigma_defuse, n0) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(188,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n0) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(189,plain,
% 145.47/145.65 (a_select2(sigma_defuse, n0) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[188, 187])).
% 145.47/145.65 tff(190,plain,
% 145.47/145.65 ((a_select2(rho_defuse, n2) = use) <=> (a_select2(rho_defuse, n2) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(191,plain,
% 145.47/145.65 (a_select2(rho_defuse, n2) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(192,plain,
% 145.47/145.65 (a_select2(rho_defuse, n2) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[191, 190])).
% 145.47/145.65 tff(193,plain,
% 145.47/145.65 ((a_select2(rho_defuse, n1) = use) <=> (a_select2(rho_defuse, n1) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(194,plain,
% 145.47/145.65 (a_select2(rho_defuse, n1) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(195,plain,
% 145.47/145.65 (a_select2(rho_defuse, n1) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[194, 193])).
% 145.47/145.65 tff(196,plain,
% 145.47/145.65 ((a_select2(rho_defuse, n0) = use) <=> (a_select2(rho_defuse, n0) = use)),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(197,plain,
% 145.47/145.65 (a_select2(rho_defuse, n0) = use),
% 145.47/145.65 inference(and_elim,[status(thm)],[98])).
% 145.47/145.65 tff(198,plain,
% 145.47/145.65 (a_select2(rho_defuse, n0) = use),
% 145.47/145.65 inference(modus_ponens,[status(thm)],[197, 196])).
% 145.47/145.65 tff(199,plain,
% 145.47/145.65 (((~(a_select2(rho_defuse, n0) = use)) | (~(a_select2(rho_defuse, n1) = use)) | (~(a_select2(rho_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(xinit_mean_defuse, n0) = use)) | (~(a_select2(xinit_mean_defuse, n1) = use)) | (~(a_select2(xinit_mean_defuse, n2) = use)) | (~(a_select2(xinit_mean_defuse, n3) = use)) | (~(a_select2(xinit_mean_defuse, n4) = use)) | (~(a_select2(xinit_mean_defuse, n5) = use)) | (~(a_select2(xinit_noise_defuse, n0) = use)) | (~(a_select2(xinit_noise_defuse, n1) = use)) | (~(a_select2(xinit_noise_defuse, n2) = use)) | (~(a_select2(xinit_noise_defuse, n3) = use)) | (~(a_select2(xinit_noise_defuse, n4) = use)) | (~(a_select2(xinit_noise_defuse, n5) = use)) | (~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pv5)) | (~((~(a_select3(u_defuse, E!14, F!13) = use)) | (~(a_select3(z_defuse, E!14, F!13) = use)))))) | (~((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))))) <=> ((~(a_select2(rho_defuse, n0) = use)) | (~(a_select2(rho_defuse, n1) = use)) | (~(a_select2(rho_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(xinit_mean_defuse, n0) = use)) | (~(a_select2(xinit_mean_defuse, n1) = use)) | (~(a_select2(xinit_mean_defuse, n2) = use)) | (~(a_select2(xinit_mean_defuse, n3) = use)) | (~(a_select2(xinit_mean_defuse, n4) = use)) | (~(a_select2(xinit_mean_defuse, n5) = use)) | (~(a_select2(xinit_noise_defuse, n0) = use)) | (~(a_select2(xinit_noise_defuse, n1) = use)) | (~(a_select2(xinit_noise_defuse, n2) = use)) | (~(a_select2(xinit_noise_defuse, n3) = use)) | (~(a_select2(xinit_noise_defuse, n4) = use)) | (~(a_select2(xinit_noise_defuse, n5) = use)) | (~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pv5)) | (~((~(a_select3(u_defuse, E!14, F!13) = use)) | (~(a_select3(z_defuse, E!14, F!13) = use)))))) | (~((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))))))),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(200,plain,
% 145.47/145.65 ((~((~(leq(n0, G!16) & leq(n0, H!15) & leq(G!16, n2) & leq(H!15, minus(pv5, n1)))) | ((a_select3(u_defuse, G!16, H!15) = use) & (a_select3(z_defuse, G!16, H!15) = use)))) <=> (~((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use))))))),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(201,plain,
% 145.47/145.65 ((~((~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))) | ((a_select3(u_defuse, E!14, F!13) = use) & (a_select3(z_defuse, E!14, F!13) = use)))) <=> (~((~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pv5)) | (~((~(a_select3(u_defuse, E!14, F!13) = use)) | (~(a_select3(z_defuse, E!14, F!13) = use))))))),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(202,plain,
% 145.47/145.65 (((~(a_select2(rho_defuse, n0) = use)) | (~(a_select2(rho_defuse, n1) = use)) | (~(a_select2(rho_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(xinit_mean_defuse, n0) = use)) | (~(a_select2(xinit_mean_defuse, n1) = use)) | (~(a_select2(xinit_mean_defuse, n2) = use)) | (~(a_select2(xinit_mean_defuse, n3) = use)) | (~(a_select2(xinit_mean_defuse, n4) = use)) | (~(a_select2(xinit_mean_defuse, n5) = use)) | (~(a_select2(xinit_noise_defuse, n0) = use)) | (~(a_select2(xinit_noise_defuse, n1) = use)) | (~(a_select2(xinit_noise_defuse, n2) = use)) | (~(a_select2(xinit_noise_defuse, n3) = use)) | (~(a_select2(xinit_noise_defuse, n4) = use)) | (~(a_select2(xinit_noise_defuse, n5) = use)) | (~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))) | ((a_select3(u_defuse, E!14, F!13) = use) & (a_select3(z_defuse, E!14, F!13) = use)))) | (~((~(leq(n0, G!16) & leq(n0, H!15) & leq(G!16, n2) & leq(H!15, minus(pv5, n1)))) | ((a_select3(u_defuse, G!16, H!15) = use) & (a_select3(z_defuse, G!16, H!15) = use))))) <=> ((~(a_select2(rho_defuse, n0) = use)) | (~(a_select2(rho_defuse, n1) = use)) | (~(a_select2(rho_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(xinit_mean_defuse, n0) = use)) | (~(a_select2(xinit_mean_defuse, n1) = use)) | (~(a_select2(xinit_mean_defuse, n2) = use)) | (~(a_select2(xinit_mean_defuse, n3) = use)) | (~(a_select2(xinit_mean_defuse, n4) = use)) | (~(a_select2(xinit_mean_defuse, n5) = use)) | (~(a_select2(xinit_noise_defuse, n0) = use)) | (~(a_select2(xinit_noise_defuse, n1) = use)) | (~(a_select2(xinit_noise_defuse, n2) = use)) | (~(a_select2(xinit_noise_defuse, n3) = use)) | (~(a_select2(xinit_noise_defuse, n4) = use)) | (~(a_select2(xinit_noise_defuse, n5) = use)) | (~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pv5)) | (~((~(a_select3(u_defuse, E!14, F!13) = use)) | (~(a_select3(z_defuse, E!14, F!13) = use)))))) | (~((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))))))),
% 145.47/145.65 inference(monotonicity,[status(thm)],[201, 200])).
% 145.47/145.65 tff(203,plain,
% 145.47/145.65 (((~(a_select2(rho_defuse, n0) = use)) | (~(a_select2(rho_defuse, n1) = use)) | (~(a_select2(rho_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(xinit_mean_defuse, n0) = use)) | (~(a_select2(xinit_mean_defuse, n1) = use)) | (~(a_select2(xinit_mean_defuse, n2) = use)) | (~(a_select2(xinit_mean_defuse, n3) = use)) | (~(a_select2(xinit_mean_defuse, n4) = use)) | (~(a_select2(xinit_mean_defuse, n5) = use)) | (~(a_select2(xinit_noise_defuse, n0) = use)) | (~(a_select2(xinit_noise_defuse, n1) = use)) | (~(a_select2(xinit_noise_defuse, n2) = use)) | (~(a_select2(xinit_noise_defuse, n3) = use)) | (~(a_select2(xinit_noise_defuse, n4) = use)) | (~(a_select2(xinit_noise_defuse, n5) = use)) | (~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))) | ((a_select3(u_defuse, E!14, F!13) = use) & (a_select3(z_defuse, E!14, F!13) = use)))) | (~((~(leq(n0, G!16) & leq(n0, H!15) & leq(G!16, n2) & leq(H!15, minus(pv5, n1)))) | ((a_select3(u_defuse, G!16, H!15) = use) & (a_select3(z_defuse, G!16, H!15) = use))))) <=> ((~(a_select2(rho_defuse, n0) = use)) | (~(a_select2(rho_defuse, n1) = use)) | (~(a_select2(rho_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(xinit_mean_defuse, n0) = use)) | (~(a_select2(xinit_mean_defuse, n1) = use)) | (~(a_select2(xinit_mean_defuse, n2) = use)) | (~(a_select2(xinit_mean_defuse, n3) = use)) | (~(a_select2(xinit_mean_defuse, n4) = use)) | (~(a_select2(xinit_mean_defuse, n5) = use)) | (~(a_select2(xinit_noise_defuse, n0) = use)) | (~(a_select2(xinit_noise_defuse, n1) = use)) | (~(a_select2(xinit_noise_defuse, n2) = use)) | (~(a_select2(xinit_noise_defuse, n3) = use)) | (~(a_select2(xinit_noise_defuse, n4) = use)) | (~(a_select2(xinit_noise_defuse, n5) = use)) | (~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~leq(n0, E!14)) | (~leq(n0, F!13)) | (~leq(E!14, n2)) | (~leq(F!13, pv5)) | (~((~(a_select3(u_defuse, E!14, F!13) = use)) | (~(a_select3(z_defuse, E!14, F!13) = use)))))) | (~((~leq(n0, G!16)) | (~leq(n0, H!15)) | (~leq(G!16, n2)) | (~leq(H!15, minus(pv5, n1))) | (~((~(a_select3(u_defuse, G!16, H!15) = use)) | (~(a_select3(z_defuse, G!16, H!15) = use)))))))),
% 145.47/145.65 inference(transitivity,[status(thm)],[202, 199])).
% 145.47/145.65 tff(204,plain,
% 145.47/145.65 (((~(a_select2(rho_defuse, n0) = use)) | (~(a_select2(rho_defuse, n1) = use)) | (~(a_select2(rho_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(xinit_mean_defuse, n0) = use)) | (~(a_select2(xinit_mean_defuse, n1) = use)) | (~(a_select2(xinit_mean_defuse, n2) = use)) | (~(a_select2(xinit_mean_defuse, n3) = use)) | (~(a_select2(xinit_mean_defuse, n4) = use)) | (~(a_select2(xinit_mean_defuse, n5) = use)) | (~(a_select2(xinit_noise_defuse, n0) = use)) | (~(a_select2(xinit_noise_defuse, n1) = use)) | (~(a_select2(xinit_noise_defuse, n2) = use)) | (~(a_select2(xinit_noise_defuse, n3) = use)) | (~(a_select2(xinit_noise_defuse, n4) = use)) | (~(a_select2(xinit_noise_defuse, n5) = use)) | (~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))) | ((a_select3(u_defuse, E!14, F!13) = use) & (a_select3(z_defuse, E!14, F!13) = use)))) | (~((~(leq(n0, G!16) & leq(n0, H!15) & leq(G!16, n2) & leq(H!15, minus(pv5, n1)))) | ((a_select3(u_defuse, G!16, H!15) = use) & (a_select3(z_defuse, G!16, H!15) = use))))) <=> ((~(a_select2(rho_defuse, n0) = use)) | (~(a_select2(rho_defuse, n1) = use)) | (~(a_select2(rho_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(xinit_mean_defuse, n0) = use)) | (~(a_select2(xinit_mean_defuse, n1) = use)) | (~(a_select2(xinit_mean_defuse, n2) = use)) | (~(a_select2(xinit_mean_defuse, n3) = use)) | (~(a_select2(xinit_mean_defuse, n4) = use)) | (~(a_select2(xinit_mean_defuse, n5) = use)) | (~(a_select2(xinit_noise_defuse, n0) = use)) | (~(a_select2(xinit_noise_defuse, n1) = use)) | (~(a_select2(xinit_noise_defuse, n2) = use)) | (~(a_select2(xinit_noise_defuse, n3) = use)) | (~(a_select2(xinit_noise_defuse, n4) = use)) | (~(a_select2(xinit_noise_defuse, n5) = use)) | (~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, E!14) & leq(n0, F!13) & leq(E!14, n2) & leq(F!13, pv5))) | ((a_select3(u_defuse, E!14, F!13) = use) & (a_select3(z_defuse, E!14, F!13) = use)))) | (~((~(leq(n0, G!16) & leq(n0, H!15) & leq(G!16, n2) & leq(H!15, minus(pv5, n1)))) | ((a_select3(u_defuse, G!16, H!15) = use) & (a_select3(z_defuse, G!16, H!15) = use)))))),
% 145.47/145.65 inference(rewrite,[status(thm)],[])).
% 145.47/145.65 tff(205,plain,
% 145.47/145.65 (((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use)))) <=> ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use))))),
% 145.47/145.66 inference(rewrite,[status(thm)],[])).
% 145.47/145.66 tff(206,plain,
% 145.47/145.66 ((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use))))) <=> (~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use)))))),
% 145.47/145.66 inference(monotonicity,[status(thm)],[205])).
% 145.47/145.66 tff(207,plain,
% 145.47/145.66 ((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use))))) <=> (~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use)))))),
% 145.47/145.66 inference(rewrite,[status(thm)],[])).
% 145.47/145.66 tff(208,plain,
% 145.47/145.66 (~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use))))),
% 145.47/145.66 inference(or_elim,[status(thm)],[97])).
% 145.47/145.66 tff(209,plain,
% 145.47/145.66 (~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use))))),
% 145.47/145.66 inference(modus_ponens,[status(thm)],[208, 206])).
% 145.47/145.66 tff(210,plain,
% 145.47/145.66 (~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use))))),
% 145.47/145.67 inference(modus_ponens,[status(thm)],[209, 207])).
% 145.47/145.67 tff(211,plain,
% 145.47/145.67 (~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | ((a_select3(u_defuse, E, F) = use) & (a_select3(z_defuse, E, F) = use))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, n2) & leq(H, minus(pv5, n1)))) | ((a_select3(u_defuse, G, H) = use) & (a_select3(z_defuse, G, H) = use))))),
% 145.47/145.67 inference(modus_ponens,[status(thm)],[210, 206])).
% 145.47/145.67 unexpected number of arguments: (let ((a!1 (~ (not (= (a_select2 rho_defuse n0) use))
% 145.47/145.67 (not (= (a_select2 rho_defuse n0) use))))
% 145.47/145.67 (a!2 (~ (not (= (a_select2 rho_defuse n1) use))
% 145.47/145.67 (not (= (a_select2 rho_defuse n1) use))))
% 145.47/145.67 (a!3 (~ (not (= (a_select2 rho_defuse n2) use))
% 145.47/145.67 (not (= (a_select2 rho_defuse n2) use))))
% 145.47/145.67 (a!4 (~ (not (= (a_select2 sigma_defuse n0) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n0) use))))
% 145.47/145.67 (a!5 (~ (not (= (a_select2 sigma_defuse n1) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n1) use))))
% 145.47/145.67 (a!6 (~ (not (= (a_select2 sigma_defuse n2) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n2) use))))
% 145.47/145.67 (a!7 (~ (not (= (a_select2 sigma_defuse n3) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n3) use))))
% 145.47/145.67 (a!8 (~ (not (= (a_select2 sigma_defuse n4) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n4) use))))
% 145.47/145.67 (a!9 (~ (not (= (a_select2 sigma_defuse n5) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n5) use))))
% 145.47/145.67 (a!10 (~ (not (= (a_select3 u_defuse n0 n0) use))
% 145.47/145.67 (not (= (a_select3 u_defuse n0 n0) use))))
% 145.47/145.67 (a!11 (~ (not (= (a_select3 u_defuse n1 n0) use))
% 145.47/145.67 (not (= (a_select3 u_defuse n1 n0) use))))
% 145.47/145.67 (a!12 (~ (not (= (a_select3 u_defuse n2 n0) use))
% 145.47/145.67 (not (= (a_select3 u_defuse n2 n0) use))))
% 145.47/145.67 (a!13 (~ (not (= (a_select2 xinit_defuse n3) use))
% 145.47/145.67 (not (= (a_select2 xinit_defuse n3) use))))
% 145.47/145.67 (a!14 (~ (not (= (a_select2 xinit_defuse n4) use))
% 145.47/145.67 (not (= (a_select2 xinit_defuse n4) use))))
% 145.47/145.67 (a!15 (~ (not (= (a_select2 xinit_defuse n5) use))
% 145.47/145.67 (not (= (a_select2 xinit_defuse n5) use))))
% 145.47/145.67 (a!16 (~ (not (= (a_select2 xinit_mean_defuse n0) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n0) use))))
% 145.47/145.67 (a!17 (~ (not (= (a_select2 xinit_mean_defuse n1) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n1) use))))
% 145.47/145.67 (a!18 (~ (not (= (a_select2 xinit_mean_defuse n2) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n2) use))))
% 145.47/145.67 (a!19 (~ (not (= (a_select2 xinit_mean_defuse n3) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n3) use))))
% 145.47/145.67 (a!20 (~ (not (= (a_select2 xinit_mean_defuse n4) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n4) use))))
% 145.47/145.67 (a!21 (~ (not (= (a_select2 xinit_mean_defuse n5) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n5) use))))
% 145.47/145.67 (a!22 (~ (not (= (a_select2 xinit_noise_defuse n0) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n0) use))))
% 145.47/145.67 (a!23 (~ (not (= (a_select2 xinit_noise_defuse n1) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n1) use))))
% 145.47/145.67 (a!24 (~ (not (= (a_select2 xinit_noise_defuse n2) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n2) use))))
% 145.47/145.67 (a!25 (~ (not (= (a_select2 xinit_noise_defuse n3) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n3) use))))
% 145.47/145.67 (a!26 (~ (not (= (a_select2 xinit_noise_defuse n4) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n4) use))))
% 145.47/145.67 (a!27 (~ (not (= (a_select2 xinit_noise_defuse n5) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n5) use))))
% 145.47/145.67 (a!28 (refl (~ (not (leq n0 pv5)) (not (leq n0 pv5)))))
% 145.47/145.67 (a!29 (~ (not (leq pv5 (minus n999 n1))) (not (leq pv5 (minus n999 n1)))))
% 145.47/145.67 (a!30 (forall ((E $i) (F $i))
% 145.47/145.67 (let ((a!1 (and (= (a_select3 u_defuse E F) use)
% 145.47/145.67 (= (a_select3 z_defuse E F) use))))
% 145.47/145.67 (or (not (and (leq n0 E) (leq n0 F) (leq E n2) (leq F pv5)))
% 145.47/145.67 a!1))))
% 145.47/145.67 (a!31 (or (not (and (leq n0 E!14)
% 145.47/145.67 (leq n0 F!13)
% 145.47/145.67 (leq E!14 n2)
% 145.47/145.67 (leq F!13 pv5)))
% 145.47/145.67 (and (= (a_select3 u_defuse E!14 F!13) use)
% 145.47/145.67 (= (a_select3 z_defuse E!14 F!13) use))))
% 145.47/145.67 (a!32 (forall ((G $i) (H $i))
% 145.47/145.67 (let ((a!1 (not (and (leq n0 G)
% 145.47/145.67 (leq n0 H)
% 145.47/145.67 (leq G n2)
% 145.47/145.67 (leq H (minus pv5 n1)))))
% 145.47/145.67 (a!2 (and (= (a_select3 u_defuse G H) use)
% 145.47/145.67 (= (a_select3 z_defuse G H) use))))
% 145.47/145.67 (or a!1 a!2))))
% 145.47/145.67 (a!33 (not (and (leq n0 G!16)
% 145.47/145.67 (leq n0 H!15)
% 145.47/145.67 (leq G!16 n2)
% 145.47/145.67 (leq H!15 (minus pv5 n1))))))
% 145.47/145.67 (let ((a!34 (or a!33
% 145.47/145.67 (and (= (a_select3 u_defuse G!16 H!15) use)
% 145.47/145.67 (= (a_select3 z_defuse G!16 H!15) use))))
% 145.47/145.67 (a!35 (not (and (= (a_select2 rho_defuse n0) use)
% 145.47/145.67 (= (a_select2 rho_defuse n1) use)
% 145.47/145.67 (= (a_select2 rho_defuse n2) use)
% 145.47/145.67 (= (a_select2 sigma_defuse n0) use)
% 145.47/145.67 (= (a_select2 sigma_defuse n1) use)
% 145.47/145.67 (= (a_select2 sigma_defuse n2) use)
% 145.47/145.67 (= (a_select2 sigma_defuse n3) use)
% 145.47/145.67 (= (a_select2 sigma_defuse n4) use)
% 145.47/145.67 (= (a_select2 sigma_defuse n5) use)
% 145.47/145.67 (= (a_select3 u_defuse n0 n0) use)
% 145.47/145.67 (= (a_select3 u_defuse n1 n0) use)
% 145.47/145.67 (= (a_select3 u_defuse n2 n0) use)
% 145.47/145.67 (= (a_select2 xinit_defuse n3) use)
% 145.47/145.67 (= (a_select2 xinit_defuse n4) use)
% 145.47/145.67 (= (a_select2 xinit_defuse n5) use)
% 145.47/145.67 (= (a_select2 xinit_mean_defuse n0) use)
% 145.47/145.67 (= (a_select2 xinit_mean_defuse n1) use)
% 145.47/145.67 (= (a_select2 xinit_mean_defuse n2) use)
% 145.47/145.67 (= (a_select2 xinit_mean_defuse n3) use)
% 145.47/145.67 (= (a_select2 xinit_mean_defuse n4) use)
% 145.47/145.67 (= (a_select2 xinit_mean_defuse n5) use)
% 145.47/145.67 (= (a_select2 xinit_noise_defuse n0) use)
% 145.47/145.67 (= (a_select2 xinit_noise_defuse n1) use)
% 145.47/145.67 (= (a_select2 xinit_noise_defuse n2) use)
% 145.47/145.67 (= (a_select2 xinit_noise_defuse n3) use)
% 145.47/145.67 (= (a_select2 xinit_noise_defuse n4) use)
% 145.47/145.67 (= (a_select2 xinit_noise_defuse n5) use)
% 145.47/145.67 (leq n0 pv5)
% 145.47/145.67 (leq pv5 (minus n999 n1))
% 145.47/145.67 a!30
% 145.47/145.67 a!32))))
% 145.47/145.67 (let ((a!36 (or (not (= (a_select2 rho_defuse n0) use))
% 145.47/145.67 (not (= (a_select2 rho_defuse n1) use))
% 145.47/145.67 (not (= (a_select2 rho_defuse n2) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n0) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n1) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n2) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n3) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n4) use))
% 145.47/145.67 (not (= (a_select2 sigma_defuse n5) use))
% 145.47/145.67 (not (= (a_select3 u_defuse n0 n0) use))
% 145.47/145.67 (not (= (a_select3 u_defuse n1 n0) use))
% 145.47/145.67 (not (= (a_select3 u_defuse n2 n0) use))
% 145.47/145.67 (not (= (a_select2 xinit_defuse n3) use))
% 145.47/145.67 (not (= (a_select2 xinit_defuse n4) use))
% 145.47/145.67 (not (= (a_select2 xinit_defuse n5) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n0) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n1) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n2) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n3) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n4) use))
% 145.47/145.67 (not (= (a_select2 xinit_mean_defuse n5) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n0) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n1) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n2) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n3) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n4) use))
% 145.47/145.67 (not (= (a_select2 xinit_noise_defuse n5) use))
% 145.47/145.67 (not (leq n0 pv5))
% 145.47/145.67 (not (leq pv5 (minus n999 n1)))
% 145.47/145.67 (not a!31)
% 145.47/145.67 (not a!34))))
% 145.47/145.67 (nnf-neg (refl a!1)
% 145.47/145.67 (refl a!2)
% 145.47/145.67 (refl a!3)
% 145.47/145.67 (refl a!4)
% 145.47/145.67 (refl a!5)
% 145.47/145.67 (refl a!6)
% 145.47/145.67 (refl a!7)
% 145.47/145.67 (refl a!8)
% 145.47/145.67 (refl a!9)
% 145.47/145.67 (refl a!10)
% 145.47/145.67 (refl a!11)
% 145.47/145.67 (refl a!12)
% 145.47/145.67 (refl a!13)
% 145.47/145.67 (refl a!14)
% 145.47/145.67 (refl a!15)
% 145.47/145.67 (refl a!16)
% 145.47/145.67 (refl a!17)
% 145.47/145.67 (refl a!18)
% 145.47/145.67 (refl a!19)
% 145.47/145.67 (refl a!20)
% 145.47/145.67 (refl a!21)
% 145.47/145.67 (refl a!22)
% 145.47/145.67 (refl a!23)
% 145.47/145.67 (refl a!24)
% 145.47/145.67 (refl a!25)
% 145.47/145.67 (refl a!26)
% 145.47/145.67 (refl a!27)
% 145.47/145.67 a!28
% 145.47/145.67 (refl a!29)
% 145.47/145.67 (sk (~ (not a!30) (not a!31)))
% 145.47/145.67 (sk (~ (not a!32) (not a!34)))
% 145.47/145.67 (~ a!35 a!36)))))
% 145.47/145.67 Proof display could not be completed: unexpected number of arguments
% 145.94/146.16 % E exiting
%------------------------------------------------------------------------------